Scicho

BME Field Overview

Tue, 24 Feb 2026 00:00:00 +0000

Course Information

Course Title: BME Field Overview
Course Type: Practical (Skill & Employability)
Credits: 1
Total Hours: 32
Schedule: Sunday 10:00 - 12:00
Location: Class 43
Instructor: Seyed Sadjad Abedi-Shahri
- Email:
Lecture Materials: Provided via LMS.

Course Overview

This course familiarizes students with career paths in Biomedical Engineering and the technical and soft skills needed for related roles. It offers an overview of major subfields, common professional environments (industry, startups, healthcare, research centers), and includes talks/visits to connect classroom learning with real-world practice.

Learning Objectives

By the end of this course, students will be able to:

Describe major Biomedical Engineering areas (e.g., biomaterials, bioelectric, biomechanics, health technologies).
Identify common job roles and professional opportunities in the health ecosystem.
Explain how core undergraduate courses connect to practical skills and employability.
Gain introductory familiarity with key technical topics and typical tools/software used in the field.
Recognize essential professional and engineering ethics in healthcare-related work.

Syllabus

History of Biomedical Engineering; domains and specializations
Biomedical Engineering careers and job opportunities (including industry guests)
Undergraduate curriculum overview and the need for deep disciplinary understanding
Intro technical topics (signals, biomechanics equipment, orthotics/prosthetics/implants, biomaterials, tissue engineering, data analysis, etc.)
Types of health-related companies and businesses (startups, manufacturers, labs, tech centers)
Incubators, science & technology parks, and health-related research centers
Field visits related to Biomedical Engineering jobs (industry/health services/startups)
General and specialized software overview (e.g., MATLAB, LabVIEW, CATIA, ImageJ, OsiriX)
Professional ethics and engineering ethics in health applications

Evaluation Scheme

Class Activities + Assignments: 50%
- Attendance and participation
- Short reflections or assignments
Written Exam: 50%

Teaching & Learning Methods

A combination of instructor-led sessions, discussion-based learning, guest talks by industry professionals, and field visits.

Session Outline

Session	Date	Outline	Additional Resources
1	3 Esfand	History of Biomedical Engineering	-

Additional Information

Special requirements (if applicable): Scientific visits and seminars (as scheduled).
References: No fixed textbook; materials are provided during the course.

Impact Mechanics in Biomechanics

Wed, 24 Dec 2025 00:00:00 +0000

Course Information

Course Title: Impact Mechanics in Biomechanics
Course Code: 2014353-01
Credits: 3
Schedule: Monday 14:00-16:00 & Tuesday 14:00-16:00
Location: Class 30
Instructor: Seyed Sadjad Abedi-Shahri
- Email:
- Telegram: @Sad4Abd

Lecture Materials: Provided weekly in .

Course Overview

This course introduces advanced concepts in impact mechanics as applied to biomechanics, focusing on theoretical foundations and practical applications. Students will gain an understanding of impact phenomena in engineering and biomechanics, with hands-on experience using ABAQUS for dynamic explicit simulations of human anatomical structures under impact loads.

The course covers impact mechanics theory (including rigid body impacts, wave propagation, and deformation of bodies), and provides an introduction to computational tools, specifically ABAQUS, to model and simulate impact events on biological tissues such as bones and soft tissues.

Learning Objectives

By the end of this course, students will be able to:

Theoretical Foundations
- Understand core principles of impact mechanics.
- Apply impact mechanics to biomechanical problems, including rigid body impacts and material deformation under impact loads.
- Analyze the role of material properties in impact behavior.
Computational Modeling
- Use ABAQUS to develop and simulate impact models for human anatomical structures.
- Set up and analyze dynamic explicit simulations in ABAQUS.
- Implement material models, including failure criteria, for simulating biological tissues under impact.
Biomechanical Applications
- Apply theoretical and computational concepts to real-world biomechanical problems, such as simulating fractures or soft tissue injuries from impact events.
- Interpret simulation results to assess injury risks and mechanical behavior of biological systems.
Problem-Solving Skills
- Design impact scenarios with appropriate material properties, boundary conditions, and loading conditions in ABAQUS.
- Analyze the results from simulations, interpret the impact of different conditions, and generate technical reports.

Syllabus

Introduction to Impact Mechanics
- Overview of impact mechanics and its relevance to biomechanics.
- Basic principles of rigid body impacts and material deformation.
Theoretical Foundations of Impact Mechanics
- Impact of rigid bodies: Impulse-momentum and coefficient of restitution.
- Deformation under impact: One-dimensional and multi-dimensional impact mechanics.
- Wave propagation and stress analysis in deformable bodies.
Computational Impact Mechanics
- Introduction to computational methods for impact analysis.
- Overview of material models for dynamic analysis (elastic, plastic, viscoelastic).
- Introduction to ABAQUS: Setup and basics of dynamic explicit analysis.
ABAQUS Software Tutorial
- Modeling of basic impact problems using ABAQUS.
- Material modeling and dynamic loading conditions in impact simulations.
- Simulating human anatomical structures (bones, soft tissues) under impact.
Advanced Impact Simulation Techniques
- Fracture and failure modeling in ABAQUS.
- Handling large deformations and mesh refinement.
- Simulating impact events like trauma, falls, and accidents.

Software Tools

ABAQUS: Finite element analysis and dynamic explicit simulation.
3D Slicer (if applicable): Medical image processing and segmentation.
MeshMixer and CATIA (if applicable): Geometry modeling and improvement tools.

References

[RAO] Applied Impact Mechanics by C. Lakshmana Rao et. al.
[QIU] Introduction to Impact Dynamics by T.X. Yu and XinMing Qiu
[MEY] Dynamic Behavior of Materials by Marc Andre Meyers

Evaluation Scheme

Homeworks: 30%
Final Exam: 70%
- Theoretical exam on impact mechanics principles and computational methods.

Session Outline

Session	Date	Outline	Additional Resources
1	4 Esfand	Module 1 (U)¹	-
2	5 Esfand	Module 1 (U)¹	-

Additional Information

Prerequisites

Students are expected to have a basic understanding of:

Finite Element Methods in Biomechanics or similar introductory courses in computational biomechanics.

Policies

Regular attendance is recommended to stay on track with the course material.
Collaboration on assignments is encouraged, but all submissions must reflect individual understanding.
Late submissions will incur penalties unless prior arrangements are made.
Academic Integrity: Plagiarism or copying will not be tolerated.

(U): Unfinished ↩︎ ↩︎

Advanced Scaled Boundary Finite Element Framework for Complex and Biological Materials

Sat, 20 Dec 2025 00:00:00 +0000

Description This project focuses on the development of the Scaled Boundary Finite Element Method (SBFEM) for complex material behavior, extending the classical formulation to nonlinear, viscoelastic, and anisotropic hyperelastic responses. The framework preserves the boundary-only discretization of SBFEM while enabling robust treatment of material and geometric nonlinearities.

Key Contributions

Nonlinear SBFEM (NL-SBFEM) formulation for large deformations.
Viscoelastic SBFEM for time-dependent material response.
Modular material interface enabling automatic differentiation.
Extension to anisotropic hyperelastic models for soft tissues.

Biomechanics Focus

The final objective is biomechanical modeling of soft tissues, particularly fiber-reinforced materials relevant to ligaments, tendons, and vascular tissues, avoiding volumetric meshing while retaining high accuracy.

Computational Biomechanics: Necessity, Importance, and Applications

Mon, 15 Dec 2025 00:00:00 +0000

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ICBME 2025 - Oral Presentation 2

Thu, 20 Nov 2025 00:00:00 +0000

ICBME 2025 - Oral Presentation 1

Wed, 19 Nov 2025 00:00:00 +0000

Introduction to Biomedical Engineering - Biomechanics

Mon, 15 Sep 2025 00:00:00 +0000

Course Information

Course Title: Introduction to Biomedical Engineering - Biomechanics
Course Code: 2014170-02
Credits: 3
Schedule: Saturday 12:00–14:00 & Monday 16:00-18:00
Location: Class 32
Instructor: Seyed Sadjad Abedi-Shahri
- Email:

Course Overview

This course introduces the biomechanics of the cardiovascular system and the fundamentals of biomaterials. The first part covers blood flow mechanics, cardiac and vascular function, and simplified modeling of circulation. The second part introduces biomaterials, biocompatibility, and their applications in medical implants. The course provides biomedical engineering students with essential theoretical foundations and applied knowledge at the interface of physiology, mechanics, and materials.

Learning Objectives

Students completing this course will be able to:

Explain the mechanics of blood flow and the cardiovascular system.
Describe cardiac output, vascular resistance, compliance, and related pathologies.
Apply simplified hemodynamic models (resistance, compliance, inertance).
Identify major classes of biomaterials and evaluate their biocompatibility.
Recognize common biomedical implant applications and design considerations.

Syllabus

Cardiovascular Biomechanics:
Fundamentals of hemodynamics, cardiac cycle, vascular mechanics, blood rheology, vascular pathologies, and simplified cardiovascular models.
Biomaterials:
Introduction to biomaterials, biocompatibility and hemocompatibility, types of biomaterials, and their applications in implants.

References

[WAI] Applied Biofluid Mechanics by Lee Waite and Jerry Fine
[END] Introduction to Biomedical Engineering [3rd ed.] by John Enderle and Joseph Bronzino
[BRO] Biomedical Engineering Fundamentals [3rd ed.] by Joseph Bronzino

Evaluation Scheme

Final Exam: 80 points
Continuous Assessment: 20 points
Extracurricular Activities (optional): Up to 20 bonus points

Session Outline

Session	Date	Outline	Additional Resources
1	29 Shahrivar	Part 1	[WAI]: 1.2 and 1.4
2	5 Mehr	Part 2 (U)¹	-
3	7 Mehr	Part 2	[WAI]: 2.1-2.5 and 2.7-2.9
4	12 Mehr	Part 3	[WAI]: 4.1-4.3 and 4.5-4.6
5	14 Mehr	Part 4 (U)	-
6	21 Mehr	Part 4 (U)	-
7	26 Mehr	Part 4	[WAI]: 5.1-5.7
8	28 Mehr	Bonus Lecture (Computational Cardivascular Biomechanics)	-
9	24 Aban	Part 5 (U)	-
10	26 Aban	Part 5	Fundamentals of Biomaterials by Vasif Hasirci & Nesrin Hasirci: [Chapter 1] and Biomaterials Science by Buddy D. Ratner, et al.: [Introduction]

Part 1: Introduction and Fundamentals of Flow
- Fluid Characteristics
- Introduction to Pipe Flow
- Reynolds Number and Flow Types
- Poiseuille’s Law
Part 2: Cardiovascular Structure and Function
- Introduction to Cardiovascular System
- Functional Anatomy of Circulation
- Cardiac Muscle Structure and Function
- Heart Valves and Their Function
- Cardiac Cycle and Pressure-Volume Relationships
- Heart Sounds
- Factors Controlling Blood Pressure and Flow
Part 3: Hematology and Blood Rheology
- Introduction to Blood Rheology
- Elements and Characteristics of Blood
- Types of Fluids and Blood Viscosity
- Erythrocytes (Red Blood Cells)
- Leukocytes (White Blood Cells)
Part 4: Anatomy and Physiology of Blood Vessels
- Introduction
- General Structure of Arteries
- Types of Arteries
- Mechanics of Arterial Walls
- Compliance
- Pulse Wave Velocity and the Moens–Korteweg Equation
- Vascular Pathologies
Part 5: Introduction to Biomaterials
- Biomaterials Definition and Evolution
- Material Categories and Properties
- Biocompatibility
- Hemocompatibility
- Clinical Examples and Case Studies

Additional Information

Prerequisites

Principles of Medical Physics

Policies

Regular attendance is strongly recommended to stay on track with course material and acquire continuous evaluation score
Students are expected to arrive on time. Late arrivals may disrupt the class and could impact participation evaluation.
Collaboration on assignments, exercises, and projects is encouraged. However, all submissions must reflect individual understanding and adhere to academic integrity policies. Plagiarism or copying will not be tolerated.

(U): Unfinished ↩︎

Finite Element Method in Biomechanics

Wed, 10 Sep 2025 00:00:00 +0000

Course Information

Course Title: Special Topics 1 (Finite Element Methods in Biomechanics)
Course Code: 2014352-01
Credits: 3
Schedule: Saturday 12:00–14:00 & Monday 10:00-12:00
Location: Class 25 & Class 2
Instructor: Seyed Sadjad Abedi-Shahri
- Email:
- Telegram: @Sad4Abd

Lecture Materials: Provided weekly in .

Course Overview

This course introduces students to the finite element method (FEM) as applied to biomechanics problems. Students will learn both theoretical foundations and practical implementation of computational biomechanics using professional software tools. The course emphasizes hands-on experience with medical imaging data, geometric modeling, and finite element analysis of biological structures.

Learning Objectives

By the end of this course, students will be able to:

Theoretical Foundations
- Understand fundamental concepts of computational biomechanics
- Apply finite element method principles to biomechanical problems
- Comprehend the mathematical framework underlying FEM
Medical Imaging and Geometry
- Extract geometry from medical images using 3D Slicer software
- Perform segmentation of anatomical structures from medical imaging data
- Create and improve geometric models using CATIA and MeshMixer
Computational Modeling
- Develop finite element models in ABAQUS software
- Perform biomechanical simulations of various anatomical structures
- Analyze and interpret computational results
Problem-Solving Skills
- Apply FEM to real biomechanical problems
- Design simulation scenarios for different loading conditions
- Generate comprehensive technical reports

Syllabus

Introduction to Computational Biomechanics
- Necessity, importance, and future of computational biomechanics
- Overview of biomechanical modeling applications
Medical Imaging and Geometry Extraction
- Types of medical images and their applications
- Segmentation techniques using 3D Slicer software
- Geometry extraction from medical imaging data
Geometric Model Development and Improvement
- Creating geometric models using CATIA and MeshMixer
- Quality improvement techniques for geometric models
- Model preparation for finite element analysis
Introduction to Finite Element Method
- Theoretical foundations of FEM
- Basic equations and mathematical framework
- Fundamentals of discretization and numerical methods
Modeling with ABAQUS Software
- Introduction to ABAQUS environment
- Model setup and boundary conditions
- Material properties and loading scenarios
- Mesh generation and quality assessment
- Solution procedures and convergence

Software Tools

3D Slicer: Medical image processing and segmentation
MeshMixer: Mesh processing and improvement
CATIA: Geometric modeling and design
ABAQUS: Finite element analysis and simulation

References

Provided in Lecture Materials

Evaluation Scheme

Group Project: 60 points
- Project Phase 1 (10%): Due: 3rd week of Mehr
  - Topic selection
  - Anatomical and biomechanical review of chosen topic
  - Medical image acquisition
- Project Phase 2 (15%): Due: 4th week of Aban
  - Geometry extraction from medical images
  - Geometric model improvement
- Project Phase 3 (20%): Due: 2nd week of Azar
  - Model import into ABAQUS
  - Initial simulation setup
- Project Phase 4 (35%): Due: 2nd week of Dey
  - Main simulations based on different scenarios
  - Analysis of various loading conditions
- Final Project Report (20%): Due: 17th of Dey
  - Analysis results
  - Comprehensive report preparation
Exercises: 10 points
Final Exam: 30 points
Extracurricular Activities (optional): Up to 10 bonus points

Session Outline

Session	Date	Outline
1	31 Shahrivar	Course Introduction
2	5 Mehr	An Introduction to Computational Biomechanics
3	7 Mehr	An Introduction to Finite Element Method
4	14 Mehr	Medical Images in Computational Biomechanics
5	19 Mehr	3D-Slicer and MeshMixer
6	21 Mehr	CATIA
7	28 Mehr	FEM - Spring
8	26 Aban	FEM - Bar
9	27 Aban	FEM - Truss
10	1 Azar	FEM - ABAQUS 1
11	11 Azar	FEM - ABAQUS 2
12	15 Azar	FEM - ABAQUS 3
13	17 Azar	FEM - ABAQUS 4
14	18 Azar	FEM - ABAQUS 5
15	24 Azar	FEM - ABAQUS 6
16	25 Azar	FEM - ABAQUS 7
17	29 Azar	FEM - ABAQUS 8
18	1 Dey	FEM - ABAQUS 9
19	8 Dey	Review and Exercises

Additional Information

Prerequisites

Students are expected to have a basic understanding of:

Mechanics of Materials (Optional)

Policies

Regular attendance is strongly recommended to stay on track with course material.
Students are expected to arrive on time. Late arrivals may disrupt the class and could impact participation evaluation.
Collaboration on assignments, exercises, and projects is encouraged. However, all submissions must reflect individual understanding and adhere to academic integrity policies. Plagiarism or copying will not be tolerated.
Project phases have strict deadlines due to sequential dependencies. Late submissions may significantly impact final grades.

Fluid Mechanics

Wed, 10 Sep 2025 00:00:00 +0000

Course Information

Course Title: Fluid Mechanics
Course Code: 2014091-01
Credits: 3
Schedule: Saturday 16:00–18:00 & Sunday 16:00-18:00
Location: Class 32
Instructor: Seyed Sadjad Abedi-Shahri
- Email:

Lecture Materials: Provided weekly in LMS

Course Overview

This fluid mechanics course provides a comprehensive foundation in the principles of fluid mechanics. The course covers fundamental concepts from basic fluid properties to advanced flow analysis, including static fluid systems, flow kinematics and dynamics, viscous flow, and dimensional analysis. Students will develop both theoretical understanding and practical problem-solving skills essential for engineering applications in various fields including mechanical, civil, chemical, and biomedical engineering.

Learning Objectives

By the end of this course, students will be able to:

Fundamental Understanding
- Understand basic fluid properties and behavior in both static and dynamic systems
- Apply conservation principles (mass, momentum, energy) to fluid flow problems
- Analyze pressure distribution and forces in static fluid systems
Mathematical Analysis
- Apply differential and integral analysis methods to fluid flow problems
- Use dimensional analysis for scaling, similitude studies, and parameter reduction
- Solve viscous flow problems in pipes, channels, and external flow systems
Problem-Solving Skills
- Design and analyze fluid systems for engineering applications
- Select appropriate analysis methods for different flow regimes
- Apply engineering analysis to biomechanical problems

Syllabus

Introduction & Fundamental Concepts
Fluid Statics
Control Volume Analysis
Differential Analysis of Fluid Motion
Incompressible Inviscid Flow
Dimensional Analysis & Similitude
Internal Viscous Flow

Primary Textbook

[FOX] Introduction to Fluid Mechanics by Fox, McDonald, and Mitchell

Evaluation Scheme

Midterm Exam 1: 15 points
- Fundamental concepts, fluid statics, and control volume analysis
Midterm Exam 2: 15 points
- Differential analysis, inviscid flow, and dimensional analysis
Final Examination: 55 points
- Comprehensive exam covering all topics
Continuous Assessment: 15 points
Bonus Activities (optional): Up to 10 bonus points

Session Outline

Session	Date	Outline	Additional Resources
1	29 Shahrivar	Chapter 1	[FOX]: 1.1-1.6
2	30 Shahrivar	Chapter 2 (U)¹	-
3	5 Mehr	Chapter 2 (U)	-
4	6 Mehr	Chapter 2	[FOX]: 2.1-2.7
5	12 Mehr	Chapter 3 (U)	-
6	13 Mehr	Chapter 3 (U)	-
7	19 Mehr	Chapter 3	[FOX]: 3.1-3.5
8	20 Mehr	Chapter 4 (U)	-
9	26 Mehr	Chapter 4 (U)	-
10	27 Mehr	Chapter 4	[FOX]: 4.1-4.5
11	24 Aban	Exc. 2	-
12	25 Aban	Exc. 3	-
13	27 Aban	Exc. 3	-
14	1 Azar	Chapter 5 (U)	-
15	2 Azar	Chapter 5 (U)	-
16	8 Azar	Chapter 5	[FOX]: 5.1-5.4
17	9 Azar	Chapter 6 (U)	-
18	11 Azar	Exc. 4	-
19	15 Azar	Chapter 6	[FOX]: 6.1-6.3, 6.5, 6.7
20	16 Azar	Chapter 7 (U)	-
21	18 Azar	Chapter 7	[FOX]: 7.1-7.6
22	22 Azar	Midterm 1	-
23	23 Azar	Review	-
24	25 Azar	Exc. 5	-
25	30 Azar	Exc. 6	-
26	2 Dey	Exc. 7	-
27	6 Dey	Midterm 2	-
28	7 Dey	Chapter 8 (U)	-
29	9 Dey	Chapter 8	[FOX]: 8.1-8.3

Chapter 1: Introduction
- Scope of Fluid Mechanics
- Definition of Fluid
- Basic Equations
- Methods of Analysis
- Dimensions and Units
Chapter 2: Fundamental Concepts
- Fluid as a Continuum
- Velocity Fields
- Stress Fields
- Viscosity
- Surface Tension
- Description and Classification of Fluid Motion
Chapter 3: Fluid Statics
- The Basic Equation of Fluid Statics
- The Standard Atmosphere
- Pressure Variation in a Static Fluid
- Hydrostatic Force on Submerged Sufaces
Chapter 4: Basic Equations in Integral Form for a Control Volume
- Basic Laws for a System
- Relation of System Derivatives to the Control Volume Formulation
- Conservation of Mass
- Momentum Equation for Inertial Control Volume
- Momentum Equation for Control Volume with Rectilinear Acceleration
Chapter 5: Introduction to Differential Analysis of Fluid Motion
- Conservation of Mass
- Stream Function for Two-Dimensional Incompressible Flow
- Motion of a Fluid Particle (Kinematics)
- Momentum Equation
Chapter 6: Incompressible Inviscid Flow
- Momentum Equation for Frictionless Flow: Euler’s Equation
- Euler’s Equation in Streamline Coordinates
- Bernoulli Equation: Integration of Euler’s Equation Along a Streamline for Steady Flow
- Energy Grade Line and Hydraulic Grade Line
- Irrotational Flow
Chapter 7: Dimensional Analysis and Similitude
- Nondimensionalizing the Basic Differential Equations
- Nature of Dimensional Analysis
- Buckingham Pi Theorem
- Determining the $\Pi$ Groups
- Significant Dimensionless Groups in Fluid Mechanics
- Flow Similarity and Model Studies
Chapter 8: Internal Incompressible Viscous Flow
- Introduction
- Fully Developed Laminar Flow Between Infinite Parallel Plates
- Fully Developed Laminar Flow in a Pipe

Projects:

Additional Information

Prerequisites

Students are expected to have a basic understanding of:

Statics
Dynamics (Optional but strongly recommended)
Thermodynamics (Optional but strongly recommended)

Policies

Regular attendance is strongly recommended to stay on track with course material and acquire continuous evaluation score.
Students are expected to arrive on time. Late arrivals may disrupt the class and could impact participation evaluation.
Collaboration on assignments, exercises, and projects is encouraged. However, all submissions must reflect individual understanding and adhere to academic integrity policies. Plagiarism or copying will not be tolerated.

(U): Unfinished ↩︎

Project Card 01

Sat, 01 Mar 2025 00:00:00 +0000

Low-Cost Head Injury Dummy - Proof-of-Concept Design

Project Pathway

🟩 Experimental / Test System Design (Proof-of-Concept)

1. Background & Motivation

Head injuries are among the most common and severe outcomes of traumatic events in automotive crashes, sports impacts, falls, and occupational accidents. Experimental testing using instrumented headforms or anthropomorphic test devices (ATDs) plays a critical role in understanding injury mechanisms, validating injury criteria, and evaluating protective equipment such as helmets.

However, commercial head injury dummies and headforms (e.g., Hybrid III head, EuroSID headforms) are expensive and often inaccessible in developing countries. This limits experimental research, education, and safety evaluation.

This project aims to develop a low-cost, mechanically meaningful, proof-of-concept head injury dummy, suitable for basic impact testing, education, and preliminary safety assessment under local resource constraints.

2. Core Biomechanical Question

How can the essential biomechanical mechanisms of head injury be captured using a simplified, low-cost head injury dummy suitable for experimental testing?

3. Injury Mechanisms & Relevant Injury Criteria

The project should address the following biomechanical aspects:

Primary head injury mechanisms:
- Translational acceleration
- Rotational acceleration
Conceptual skull-brain interaction
Impact loading scenarios (e.g., drop test, guided impact, oblique impact)

Relevant injury metrics may include (but are not limited to):

Resultant head acceleration
Head Injury Criterion (HIC)
Peak rotational acceleration (conceptual discussion)
Limitations of acceleration-based criteria

Students must justify why selected injury criteria are relevant for the proposed dummy design.

4. Modeling / Design Approach

This is a proof-of-concept experimental design project, not a manufacturing task.

The student is expected to:

Conceptually model the head as a mechanical system
Translate injury mechanisms into design requirements
Propose a simplified headform/dummy architecture that captures key dynamic behavior

Numerical simulations (e.g., FEM) may be used optionally to support design decisions but are not required.

5. Technical Specification (Core Section)

The project must include a detailed technical proposal covering:

a) Mechanical Structure

Headform geometry (size, shape, mass)
Internal structure (solid, layered, modular, etc.)
Material selection and mechanical justification

b) Instrumentation

Type and number of sensors (e.g., accelerometers)
Sensor placement and orientation
Expected signal outputs and sampling considerations

c) Mounting & Boundary Conditions

Neck interface concept (rigid, compliant, simplified neck)
Degrees of freedom and constraints

d) Impact Scenarios

Proposed impact test types (drop, pendulum, guided impact)
Impact velocities or heights
Repeatability and safety considerations

Clear schematics, block diagrams, or CAD drafts are expected (hand-drawn or digital).

6. Validation Strategy & Limitations

The project must explicitly discuss:

How the dummy’s response could be validated:
- comparison with literature data,
- comparison with simplified analytical models,
- qualitative trend validation
What injury claims cannot be made using this dummy
Limitations due to:
- reduced biofidelity,
- material simplifications,
- absence of internal brain deformation measurements

This section is mandatory.

7. Feasibility & Resource Awareness

The project must include a realistic feasibility analysis addressing:

Estimated cost of components (order-of-magnitude)
Availability of materials and sensors in Iran
Required equipment (e.g., basic workshop tools, DAQ)
Safety considerations during testing

Overly idealized or impractical designs will be penalized.

8. Expected Outcomes

By the end of the project, the student should deliver:

A detailed design manual for the head injury dummy
Technical drawings and system schematics
Proposed test protocols
Clearly defined use cases (education, preliminary testing, research)

The outcome should be suitable as a foundation for future laboratory development.

9. Deliverables

Final Report (20-25 pages, excluding appendices)
Figures, schematics, and design drafts
Cost estimation table
Oral presentation (15-20 minutes)

Optional appendices:

CAD files
Sensor datasheets
Supporting calculations

10. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of injury problem and societal relevance	10%
Injury mechanism understanding	Correct identification and explanation of head injury mechanisms	15%
Injury criteria justification	Appropriate selection and critical discussion of injury metrics	10%
Design concept quality	Coherence, logic, and biomechanical grounding of dummy design	20%
Technical specification & clarity	Precision of schematics, descriptions, and system layout	15%
Validation & limitations	Realistic validation strategy and honest limitation analysis	15%
Feasibility & professionalism	Cost awareness, local feasibility, safety considerations	15%
Total		100%

11. Project Scope Agreement

By choosing this project, the student agrees to:

Focus on conceptual and technical rigor, not manufacturing
Respect local resource constraints
Clearly state assumptions and limitations

Note:
A well-designed proof-of-concept dummy can be more scientifically valuable than a poorly validated simulation.

Project Card 02

Sat, 01 Mar 2025 00:00:00 +0000

Helmet Testing Rig - Conceptual Design and Experimental Evaluation Protocol

Project Pathway

🟩 Experimental Test System (Proof-of-Concept)

1. Background & Motivation

Helmets are among the most effective personal protective equipment (PPE) for preventing or mitigating head injuries in sports, transportation, and occupational environments. Their protective performance depends not only on material properties, but also on test conditions, injury metrics, and evaluation protocols.

Commercial helmet testing laboratories rely on expensive standardized rigs and equipment, often inaccessible in developing countries. As a result, locally produced or widely used helmets may not undergo biomechanically meaningful evaluation.

This project aims to develop a conceptual and technical design of a helmet testing rig, suitable for evaluating helmet performance using biomechanically relevant injury metrics under realistic resource constraints.

2. Core Biomechanical Question

How can helmet protective performance be evaluated using a simplified but biomechanically meaningful testing rig and injury assessment protocol?

3. Injury Mechanisms & Relevant Injury Criteria

The project should consider:

Head injury mechanisms relevant to helmeted impacts:
- Linear acceleration
- Rotational acceleration
- Impact energy dissipation
Helmet-head interaction
Effect of impact direction and surface compliance

Relevant injury metrics may include:

Resultant head acceleration
Head Injury Criterion (HIC)
Peak rotational acceleration (conceptual discussion)
Energy absorption and impact attenuation indicators

Students must justify the selection of injury metrics with respect to helmet performance evaluation.

4. Modeling / Design Approach

This is a proof-of-concept system design project.

The student is expected to:

Translate injury mechanisms into test objectives
Design a helmet testing rig concept (drop, pendulum, guided impact, or hybrid)
Propose a testing protocol, not just a device

Numerical modeling or FEM may be used optionally to support design decisions, but is not required.

5. Technical Specification (Core Section)

The project must include a detailed system design covering:

a) Test Rig Architecture

Overall configuration (drop tower, pendulum, guided rail, etc.)
Impact surface characteristics
Adjustability (impact velocity, angle)

b) Headform / Dummy Interface

Type of headform assumed (rigid, simplified dummy, conceptual ATD)
Helmet mounting considerations
Repeatability of positioning

c) Instrumentation

Sensors required (e.g., accelerometers)
Sensor placement and coordinate systems
Data acquisition requirements

d) Test Protocol

Impact scenarios (locations, directions)
Number of tests per helmet
Pass/fail or comparative evaluation logic

Clear schematics, block diagrams, or system layouts are expected.

6. Validation Strategy & Limitations

The project must explicitly address:

How the testing results could be validated:
- comparison with existing standards,
- comparison with literature data,
- qualitative trend validation
What injury claims cannot be made using the proposed rig
Limitations related to:
- simplified headform,
- lack of full biofidelity,
- reduced instrumentation

This section is mandatory.

7. Feasibility & Resource Awareness

The project must include a realistic feasibility assessment:

Estimated cost (order-of-magnitude)
Locally available materials and components
Required infrastructure (space, safety, power)
Operational and safety considerations

Designs assuming access to advanced laboratories or proprietary equipment will be penalized.

8. Expected Outcomes

By the end of the project, the student should deliver:

A conceptual design of a helmet testing rig
A rig-specific experimental evaluation protocol for helmet testing
Proposed injury metrics and interpretation strategy
Recommendations for local helmet safety assessment

The outcome should be suitable as a foundation for future laboratory setup or policy guidance.

9. Deliverables

Final Report (20-25 pages, excluding appendices)
System schematics and design drawings
Testing protocol documentation
Cost estimation table
Oral presentation (15-20 minutes)

Optional appendices:

CAD models
Sensor datasheets
Example test scenarios

10. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear safety problem definition and context	10%
Injury mechanism understanding	Correct biomechanical reasoning for helmeted impacts	15%
Injury metric selection & justification	Appropriateness and critical discussion of metrics	10%
System design quality	Coherence and logic of test rig and protocol	20%
Technical specification & clarity	Quality of schematics, protocols, and descriptions	15%
Validation & limitations	Realistic validation strategy and limitations analysis	15%
Feasibility & professionalism	Cost realism, local feasibility, safety awareness	15%
Total		100%

11. Project Scope Agreement

By choosing this project, the student agrees to:

Focus on evaluation methodology, not certification
Respect local resource constraints
Clearly state assumptions and limitations

Note:
A meaningful helmet evaluation framework does not require expensive equipment - it requires correct biomechanical thinking.

Project Card 03

Sat, 01 Mar 2025 00:00:00 +0000

Simplified Finite Element Model of Head Impact for Injury Assessment

Project Pathway

🟦 Numerical / Computational Modeling (FEM)

1. Background & Motivation

Finite element (FE) modeling has become a central tool in trauma biomechanics for investigating head injury mechanisms that cannot be directly measured experimentally, such as internal stress and strain distributions in the skull and brain. Simplified FE head models are widely used for educational purposes, sensitivity studies, and early-stage injury analysis.

This project focuses on developing and using a simplified FE model of head impact to investigate head injury mechanisms and extract commonly used injury metrics. Emphasis is placed on modeling assumptions, injury metric interpretation, and sensitivity to impact conditions, rather than on geometric or material complexity.

2. Core Biomechanical Question

How do impact conditions and modeling assumptions influence biomechanical injury metrics predicted by a simplified finite element head model?

3. Injury Mechanisms & Relevant Injury Criteria

The project should consider:

Head injury mechanisms associated with impact:
- Translational acceleration
- Rotational motion
- Stress/strain development in cranial structures (conceptual level)
Role of impact direction and velocity

Relevant injury metrics may include:

Resultant head acceleration
Head Injury Criterion (HIC)
Peak rotational acceleration
Simplified strain-based indicators

Students must justify the choice of injury metrics and discuss their physical meaning and limitations.

4. Modeling / Analysis Approach

This is a numerical modeling project using a simplified FE framework.

The student is expected to:

Develop or adapt a simplified FE head model (e.g., skull-brain system)
Define appropriate material models (linear elastic, viscoelastic, or simplified alternatives)
Apply impact loading scenarios representative of head trauma
Extract and interpret injury-related outputs

High anatomical fidelity is not required. Model clarity and biomechanical reasoning are prioritized.

5. Technical Specification (Core Section)

The project must include a clear and detailed description of:

a) Geometry and Mesh

Head model geometry (simplified representation)
Mesh type and resolution
Justification of simplifications

b) Material Models

Material assumptions for skull and brain
Rate-dependence (if considered)
Rationale for chosen parameters

c) Boundary Conditions and Loading

Impact configuration (e.g., rigid surface, helmeted/unhelmeted)
Impact velocity or acceleration
Constraints and contacts

d) Output Quantities

Extracted kinematic signals
Injury metrics computation
Post-processing workflow

6. Parametric / Sensitivity Study

A limited parametric study is required, such as:

Variation of impact velocity
Variation of material stiffness or damping
Variation of boundary conditions

The goal is to assess trends, not precise injury thresholds.

7. Validation Strategy & Limitations

The project must explicitly discuss:

Qualitative or quantitative comparison with literature data
Sensitivity to modeling assumptions
Limitations due to:
- simplified geometry,
- material modeling,
- lack of experimental validation

Students must clearly state what conclusions are justified and what are not.

8. Feasibility & Computational Considerations

The project must address:

Software used (e.g., Abaqus/Explicit, LS-DYNA)
Computational cost and runtime
Mesh and timestep considerations
Reproducibility of simulations

Models requiring excessive computational resources are discouraged.

9. Expected Outcomes

By the end of the project, the student should deliver:

A working simplified FE head impact model
Injury metric results for selected scenarios
Sensitivity analysis results
A critical interpretation of injury predictions

The outcome should demonstrate numerical competence and biomechanical insight.

10. Deliverables

Final Report (20-25 pages, excluding appendices)
Model description and key figures
Injury metric plots and tables
Oral presentation (15-20 minutes)

Optional appendices:

Input files
Post-processing scripts
Additional simulation cases

11. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of injury scenario and objectives	10%
Injury mechanism understanding	Correct biomechanical interpretation of head impact	15%
Injury metric selection & justification	Appropriate and critical use of injury criteria	10%
FEM model formulation	Quality of geometry, materials, BCs, and assumptions	20%
Parametric / sensitivity analysis	Meaningful exploration and interpretation of trends	15%
Validation & limitations	Honest discussion of model credibility and limits	15%
Technical clarity & professionalism	Quality of documentation, figures, and explanations	15%
Total		100%

12. Project Scope Agreement

By choosing this project, the student agrees to:

Prioritize interpretation over complexity
Clearly document assumptions and limitations
Avoid unjustified injury claims based on simplified models

Note:
A simplified FE model, when correctly interpreted, can provide deeper insight than a complex but poorly validated one.

Project Card 04

Sat, 01 Mar 2025 00:00:00 +0000

Finite Element Simulation of Whiplash Injury and Neck Injury Criteria

Project Pathway

🟦 Numerical / Computational Modeling (FEM)

1. Background & Motivation

Whiplash-associated disorders (WAD) are among the most frequent injuries in low-speed rear-end vehicle collisions and remain a major challenge in trauma biomechanics. Despite extensive experimental and clinical research, whiplash injury mechanisms are still not fully understood, partly due to the complex anatomy and dynamic response of the cervical spine.

Finite element (FE) modeling provides a powerful framework for investigating cervical spine kinematics, load transmission, and neck injury criteria under whiplash loading conditions. Simplified FE models are widely used to study injury trends, compare injury criteria, and evaluate sensitivity to loading conditions.

This project focuses on developing and using a simplified FE model of the head-neck system to study whiplash injury mechanisms and compare commonly used neck injury criteria.

2. Core Biomechanical Question

How do whiplash loading conditions and modeling assumptions influence predicted neck injury metrics in a simplified finite element model of the cervical spine?

3. Injury Mechanisms & Relevant Injury Criteria

The project should address the following biomechanical aspects:

Whiplash injury mechanisms:
- Relative motion between head and torso
- Flexion-extension dynamics
- Shear forces and bending moments in the cervical spine
Early- and late-phase whiplash kinematics

Relevant neck injury criteria may include:

Neck Injury Criterion (NIC)
Nij criterion
Neck protection criterion (Nkm)
Upper/lower neck force-moment measures (conceptual discussion)

Students must justify the selection of injury criteria and explain their biomechanical meaning and limitations.

4. Modeling / Analysis Approach

This is a numerical FEM-based project using a simplified head-neck or cervical spine model.

The student is expected to:

Develop or adapt a simplified FE model of the head-neck system
Represent cervical vertebrae, intervertebral discs, and major ligaments at a conceptual level
Apply whiplash-relevant loading or kinematic boundary conditions
Compute and interpret neck injury metrics

High anatomical fidelity is not required. Emphasis is placed on mechanisms, trends, and interpretation.

5. Technical Specification (Core Section)

The project must include a clear description of:

a) Geometry and Model Structure

Level of anatomical detail (e.g., lumped segments, simplified vertebrae)
Modeling of head mass and inertia
Justification of simplifications

b) Material and Joint Modeling

Representation of discs and ligaments
Assumed stiffness, damping, or nonlinear behavior
Rationale for material parameter selection

c) Boundary Conditions and Loading

Whiplash loading scenario (e.g., imposed acceleration, velocity, or displacement)
Representation of torso support or seat interaction
Contact or coupling assumptions

d) Output Quantities

Head and neck kinematics
Forces and moments at relevant cervical levels
Computation of injury criteria (NIC, Nij, Nkm, etc.)

6. Parametric / Sensitivity Study

A limited parametric study is required, for example:

Variation of loading severity or pulse shape
Variation of neck stiffness or damping parameters
Comparison of different injury criteria responses

The focus should be on relative trends, not absolute injury thresholds.

7. Validation Strategy & Limitations

The project must explicitly discuss:

Comparison with published whiplash experiments or ATD data
Sensitivity of injury metrics to modeling assumptions
Limitations related to:
- simplified anatomy,
- lack of muscle activation modeling,
- absence of experimental validation

Students must clearly state which conclusions are justified by the model.

8. Feasibility & Computational Considerations

The project must address:

Software used (e.g., Abaqus/Explicit, LS-DYNA)
Computational cost and runtime
Time-step stability and numerical considerations
Reproducibility of simulations

Overly complex or computationally expensive models are discouraged.

9. Expected Outcomes

By the end of the project, the student should deliver:

A simplified FE model of whiplash loading
Computed neck injury metrics for selected scenarios
Sensitivity analysis results
A critical interpretation of whiplash injury predictions

The outcome should demonstrate numerical competence and biomechanical judgment.

10. Deliverables

Final Report (20-25 pages, excluding appendices)
Model description and representative figures
Injury metric plots and tables
Oral presentation (15-20 minutes)

Optional appendices:

Input files
Post-processing scripts
Additional simulation cases

11. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of whiplash scenario and objectives	10%
Injury mechanism understanding	Correct interpretation of whiplash biomechanics	15%
Injury metric selection & justification	Appropriate and critical use of neck injury criteria	10%
FEM model formulation	Quality of geometry, joints, BCs, and assumptions	20%
Parametric / sensitivity analysis	Insightful exploration of trends and comparisons	15%
Validation & limitations	Realistic assessment of model credibility	15%
Technical clarity & professionalism	Quality of documentation and figures	15%
Total		100%

12. Project Scope Agreement

By choosing this project, the student agrees to:

Focus on mechanistic interpretation, not model complexity
Clearly document assumptions and limitations
Avoid overclaiming injury prediction accuracy

Note:
In whiplash biomechanics, understanding trends and mechanisms is often more valuable than predicting exact injury thresholds.

Project Card 05

Sat, 01 Mar 2025 00:00:00 +0000

Finite Element Simulation of Thoracic Compression and Injury Criteria

Project Pathway

🟦 Numerical / Computational Modeling (FEM)

1. Background & Motivation

Thoracic injuries are a leading cause of morbidity and mortality in automotive crashes, falls, and blunt impact accidents. The thorax exhibits a complex biomechanical response due to its composite structure, including ribs, sternum, spine, and internal organs. Injury mechanisms range from rib fractures to lung contusions and cardiovascular injuries.

In trauma biomechanics, thoracic injury risk is commonly assessed using global kinematic and deformation-based injury criteria, such as chest acceleration, chest compression, and the Viscous Criterion (VC). Finite element (FE) modeling provides a valuable tool for studying thoracic response under controlled loading conditions and for comparing the behavior of different injury criteria.

This project focuses on developing and using a simplified FE model of the thorax to investigate thoracic compression mechanisms and evaluate commonly used thoracic injury criteria.

2. Core Biomechanical Question

How do thoracic compression characteristics and loading conditions influence thoracic injury criteria predicted by a simplified finite element model?

3. Injury Mechanisms & Relevant Injury Criteria

The project should address the following biomechanical aspects:

Thoracic injury mechanisms:
- Chest wall compression
- Rib cage deformation
- Rate-dependent thoracic response
Frontal blunt loading scenarios

Relevant thoracic injury metrics may include:

Chest compression (deflection-based criteria)
Chest acceleration
Viscous Criterion (VC)
Combined thoracic indices (conceptual discussion)

Students must justify the selection of injury criteria and explain their biomechanical significance and limitations.

4. Modeling / Analysis Approach

This is a numerical FEM-based project using a simplified thoracic model.

The student is expected to:

Develop or adapt a simplified FE representation of the thorax
Model key structural components (rib cage, sternum, spine) at a conceptual level
Apply frontal compression or impact loading representative of thoracic trauma
Compute and interpret thoracic injury metrics

High anatomical fidelity is not required. The emphasis is on mechanisms, trends, and injury metric interpretation.

5. Technical Specification (Core Section)

The project must include a clear and structured description of:

a) Geometry and Model Structure

Simplified thoracic geometry
Representation of ribs and sternum
Justification of geometric simplifications

b) Material Modeling

Material assumptions for bony and soft tissues
Rate-dependence or damping (if considered)
Rationale for parameter selection

c) Boundary Conditions and Loading

Loading configuration (e.g., rigid impactor, distributed compression)
Loading rate or velocity
Constraints and contacts

d) Output Quantities

Chest deflection and compression
Chest acceleration
Computation of VC and other injury metrics
Post-processing workflow

6. Parametric / Sensitivity Study

A limited parametric study is required, such as:

Variation of loading rate or impact velocity
Variation of thoracic stiffness parameters
Comparison between different injury criteria responses

The goal is to identify relative trends and sensitivities, not absolute injury thresholds.

7. Validation Strategy & Limitations

The project must explicitly discuss:

Qualitative or quantitative comparison with published thoracic impact experiments
Sensitivity of injury metrics to modeling assumptions
Limitations related to:
- simplified thoracic anatomy,
- absence of internal organ modeling,
- lack of experimental validation

Students must clearly state which conclusions are supported by the model.

8. Feasibility & Computational Considerations

The project must address:

Software used (e.g., Abaqus/Explicit, LS-DYNA)
Computational cost and runtime
Mesh density and timestep considerations
Numerical stability and contact handling

Models requiring excessive computational resources are discouraged.

9. Expected Outcomes

By the end of the project, the student should deliver:

A simplified FE thoracic compression model
Computed thoracic injury metrics for selected loading scenarios
Sensitivity analysis results
A critical interpretation of thoracic injury predictions

The outcome should demonstrate numerical competence and biomechanical insight.

10. Deliverables

Final Report (20-25 pages, excluding appendices)
Model description and representative figures
Injury metric plots and tables
Oral presentation (15-20 minutes)

Optional appendices:

Input files
Post-processing scripts
Additional simulation cases

11. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of thoracic injury scenario	10%
Injury mechanism understanding	Correct interpretation of thoracic biomechanics	15%
Injury metric selection & justification	Appropriate and critical use of thoracic criteria	10%
FEM model formulation	Quality of geometry, materials, BCs, and assumptions	20%
Parametric / sensitivity analysis	Insightful exploration of trends and criteria comparison	15%
Validation & limitations	Realistic discussion of model credibility	15%
Technical clarity & professionalism	Quality of documentation and figures	15%
Total		100%

12. Project Scope Agreement

By choosing this project, the student agrees to:

Emphasize injury mechanism interpretation over model complexity
Clearly document assumptions and limitations
Avoid overinterpretation of simplified injury predictions

Note:
Thoracic injury criteria are context-dependent; understanding their assumptions is as important as computing their values.

Project Card 06

Sat, 01 Mar 2025 00:00:00 +0000

Finite Element Simulation of Femur or Pelvic Impact Injury Using Force-Based Criteria

Project Pathway

🟦 Numerical / Computational Modeling (FEM)

1. Background & Motivation

Injuries to the pelvis and lower extremities, particularly the femur, are common in automotive crashes, pedestrian impacts, falls, and industrial accidents. These injuries can lead to severe long-term disability and are therefore a major focus of trauma biomechanics and safety system design.

Unlike head or thoracic injuries, femur and pelvic injury assessment often relies on force-based injury criteria, reflecting the load-bearing role of these structures. Finite element (FE) modeling enables detailed investigation of load transfer, stress distribution, and sensitivity of injury metrics to impact conditions and modeling assumptions.

This project focuses on developing and using a simplified FE model of the femur or pelvis to study impact injury mechanisms and evaluate commonly used force-based injury criteria.

2. Core Biomechanical Question

How do impact conditions and modeling assumptions influence force-based injury criteria predicted by a simplified finite element model of the femur or pelvis?

3. Injury Mechanisms & Relevant Injury Criteria

The project should address the following biomechanical aspects:

Lower extremity injury mechanisms:
- Axial compression
- Bending and shear
- Load transmission through the pelvis or femur
Impact scenarios relevant to automotive or pedestrian trauma

Relevant injury metrics may include:

Femur axial force
Femur Force Criterion (FFC)
Pelvic compression force (conceptual discussion)
Stress- or strain-based indicators (optional, with justification)

Students must justify the selection of injury criteria and explain their biomechanical relevance and limitations.

4. Modeling / Analysis Approach

This is a numerical FEM-based project using a simplified lower-extremity model.

The student is expected to:

Develop or adapt a simplified FE model of the femur or pelvic structure
Represent cortical and cancellous bone at a conceptual level
Apply impact or compressive loading representative of traumatic events
Extract and interpret force-based injury metrics

High anatomical detail is not required. Emphasis is placed on load paths, injury metrics, and interpretation.

5. Technical Specification (Core Section)

The project must include a clear and structured description of:

a) Geometry and Model Structure

Choice of femur or pelvis geometry (simplified)
Mesh type and resolution
Justification of geometric simplifications

b) Material Modeling

Material assumptions for bone (linear elastic or simplified nonlinear)
Treatment of heterogeneity (if any)
Rationale for parameter selection

c) Boundary Conditions and Loading

Loading configuration (axial impact, bending, or combined loading)
Impact velocity or applied force
Constraints and contact definitions

d) Output Quantities

Internal forces and reaction forces
Force-based injury metrics (e.g., FFC)
Stress or strain distributions (if used)

6. Parametric / Sensitivity Study

A limited parametric study is required, such as:

Variation of impact velocity or loading magnitude
Variation of bone stiffness or boundary conditions
Comparison between different loading configurations

The goal is to assess relative trends and sensitivities, not precise fracture thresholds.

7. Validation Strategy & Limitations

The project must explicitly discuss:

Comparison with published femur or pelvis impact tolerance data
Sensitivity of injury predictions to modeling assumptions
Limitations related to:
- simplified geometry,
- absence of fracture modeling,
- lack of experimental validation

Students must clearly state what conclusions are justified by the model.

8. Feasibility & Computational Considerations

The project must address:

Software used (e.g., Abaqus/Explicit, LS-DYNA)
Computational cost and runtime
Mesh density and timestep considerations
Numerical stability under high loads

Overly complex fracture or damage models are discouraged.

9. Expected Outcomes

By the end of the project, the student should deliver:

A simplified FE femur or pelvis impact model
Computed force-based injury metrics for selected scenarios
Sensitivity analysis results
A critical interpretation of lower-extremity injury predictions

The outcome should demonstrate numerical competence and biomechanical reasoning.

10. Deliverables

Final Report (20-25 pages, excluding appendices)
Model description and representative figures
Injury metric plots and tables
Oral presentation (15-20 minutes)

Optional appendices:

Input files
Post-processing scripts
Additional simulation cases

11. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of lower-extremity injury scenario	10%
Injury mechanism understanding	Correct interpretation of femur/pelvic biomechanics	15%
Injury metric selection & justification	Appropriate and critical use of force-based criteria	10%
FEM model formulation	Quality of geometry, materials, BCs, and assumptions	20%
Parametric / sensitivity analysis	Insightful exploration of trends and load paths	15%
Validation & limitations	Realistic discussion of model credibility	15%
Technical clarity & professionalism	Quality of documentation and figures	15%
Total		100%

12. Project Scope Agreement

By choosing this project, the student agrees to:

Focus on load-path interpretation, not fracture prediction
Clearly document assumptions and limitations
Avoid unjustified claims about injury thresholds

Note:
In lower-extremity trauma biomechanics, understanding force transmission is often more informative than predicting exact fracture locations.

Project Card 07

Sat, 01 Mar 2025 00:00:00 +0000

Thoracic Impact Test Setup - Proof-of-Concept Design for Injury Assessment

Project Pathway

🟩 Experimental / Test System Design (Proof-of-Concept)

1. Background & Motivation

Thoracic injuries are a major contributor to serious trauma and fatality in automotive crashes, falls, and blunt impact accidents. The thorax exhibits complex biomechanical behavior due to its composite structure, including the rib cage, sternum, spine, and internal organs. Experimental testing has played a key role in establishing thoracic injury criteria and validating safety systems such as seatbelts and airbags.

However, standardized thoracic impact test systems are expensive and rarely accessible in developing countries. This limits experimental investigation of thoracic injury mechanisms and evaluation of protective concepts.

This project aims to develop a proof-of-concept thoracic impact test setup, capable of reproducing key thoracic loading conditions and measuring biomechanically relevant injury metrics under realistic local resource constraints.

2. Core Biomechanical Question

How can thoracic injury mechanisms and injury criteria be experimentally investigated using a simplified, low-cost thoracic impact test setup?

3. Injury Mechanisms & Relevant Injury Criteria

The project should consider the following biomechanical aspects:

Thoracic injury mechanisms:
- Chest wall compression
- Rate-dependent thoracic response
- Load transfer through ribs and sternum
Frontal or localized blunt impact scenarios

Relevant injury metrics may include:

Chest deflection or compression
Chest acceleration
Viscous Criterion (VC)
Force-based or combined thoracic indices (conceptual discussion)

Students must justify the selection of injury metrics with respect to the proposed test setup.

4. Modeling / Design Approach

This is a proof-of-concept experimental system design project.

The student is expected to:

Translate thoracic injury mechanisms into test objectives
Propose a simplified thoracic impact test configuration
Design a system that enables controlled loading and repeatable measurement

Numerical modeling may be used optionally to support design decisions but is not required.

5. Technical Specification (Core Section)

The project must include a detailed technical proposal covering:

a) Test Setup Architecture

Overall configuration (impactor-based, drop test, guided mass, etc.)
Impact surface geometry and compliance
Adjustability of loading severity (velocity, mass, displacement)

b) Thoracic Surrogate / Interface

Type of thoracic surrogate assumed (simplified chest block, dummy torso, conceptual ATD)
Mounting and support conditions
Repeatability and alignment considerations

c) Instrumentation

Sensors required (e.g., displacement sensors, accelerometers, force sensors)
Sensor placement and orientation
Expected signal outputs

d) Test Protocol

Impact configurations and locations
Loading rates and repetitions
Safety and operational considerations

Clear schematics, block diagrams, or system layouts are expected.

6. Validation Strategy & Limitations

The project must explicitly address:

How test results could be validated:
- comparison with published thoracic impact experiments,
- comparison with simplified analytical models,
- qualitative trend validation
What injury claims cannot be made using the proposed setup
Limitations related to:
- simplified thoracic surrogate,
- reduced biofidelity,
- limited instrumentation

This section is mandatory.

7. Feasibility & Resource Awareness

The project must include a realistic feasibility analysis:

Estimated cost (order-of-magnitude)
Availability of materials, sensors, and equipment in Iran
Required infrastructure (space, safety shielding, power)
Risk and safety management during testing

Designs assuming access to advanced laboratories or proprietary equipment will be penalized.

8. Expected Outcomes

By the end of the project, the student should deliver:

A conceptual and technical design of a thoracic impact test setup
Defined injury metrics and interpretation framework
Proposed test protocols
Recommendations for educational or preliminary research use

The outcome should be suitable as a foundation for future experimental capability development.

9. Deliverables

Final Report (20-25 pages, excluding appendices)
System schematics and design drawings
Testing protocol documentation
Cost estimation table
Oral presentation (15-20 minutes)

Optional appendices:

CAD drawings
Sensor datasheets
Example test configurations

10. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of thoracic injury problem	10%
Injury mechanism understanding	Correct biomechanical reasoning for thoracic trauma	15%
Injury metric selection & justification	Appropriate and critical use of thoracic criteria	10%
Test system design quality	Coherence and logic of test setup and protocol	20%
Technical specification & clarity	Quality of schematics and system descriptions	15%
Validation & limitations	Realistic validation strategy and limitations analysis	15%
Feasibility & professionalism	Cost realism, local feasibility, safety awareness	15%
Total		100%

11. Project Scope Agreement

By choosing this project, the student agrees to:

Focus on mechanism-oriented testing, not certification
Respect local resource and safety constraints
Clearly state assumptions and limitations

Note:
A well-designed thoracic impact setup can provide meaningful biomechanical insight even without full biofidelity.

Project Card 08

Sat, 01 Mar 2025 00:00:00 +0000

Whiplash Sled Test System - Proof-of-Concept Design and Evaluation Framework

Project Pathway

🟩 Experimental / Test System Design (Proof-of-Concept)

1. Background & Motivation

Whiplash-associated disorders (WAD) are among the most common injuries in low-speed rear-end vehicle collisions. Experimental sled testing has been central to the development of whiplash injury criteria, seat and head restraint design, and regulatory standards. These tests aim to reproduce characteristic rear-impact acceleration pulses and study the dynamic response of the head-neck system.

Standard whiplash sled facilities are complex, expensive, and rarely accessible in developing countries. This limits experimental research, education, and local evaluation of seat and head restraint concepts.

This project aims to develop a simplified, low-cost, proof-of-concept whiplash sled test system, capable of reproducing essential whiplash loading characteristics and enabling biomechanically meaningful measurement and interpretation.

2. Core Biomechanical Question

How can the essential biomechanical features of whiplash injury be experimentally reproduced and studied using a simplified sled-based test system?

3. Injury Mechanisms & Relevant Injury Criteria

The project should address the following biomechanical aspects:

Whiplash injury mechanisms:
- Relative motion between head and torso
- Flexion-extension dynamics of the cervical spine
- Shear forces and bending moments in the neck
Early- and late-phase whiplash response

Relevant injury metrics may include:

Neck Injury Criterion (NIC)
Nij criterion
Neck protection criterion (Nkm)
Head and torso kinematic measures (conceptual discussion)

Students must justify the selection of injury criteria and explain their biomechanical relevance and limitations.

4. Modeling / Design Approach

This is a proof-of-concept experimental system design project.

The student is expected to:

Translate whiplash injury mechanisms into sled motion requirements
Design a simplified sled system capable of generating rear-impact-like acceleration pulses
Propose a test protocol for whiplash evaluation

Numerical simulations may be used optionally to support design decisions but are not required.

5. Technical Specification (Core Section)

The project must include a detailed technical proposal covering:

a) Sled System Architecture

Overall configuration (rail-based sled, wheeled cart, guided platform)
Method of sled acceleration or deceleration (spring, gravity, pneumatic, motorized)
Control of pulse shape and severity

b) Seat and Occupant Interface

Simplified seat structure
Head restraint concept
Assumed occupant surrogate (simplified dummy or torso-head mass system)

c) Instrumentation

Sensors required (e.g., accelerometers, displacement sensors)
Sensor placement on sled, torso, and head surrogate
Data acquisition requirements

d) Test Protocol

Acceleration pulse characteristics (magnitude, duration)
Test repeatability
Safety considerations for equipment and operators

Clear schematics, block diagrams, or system layouts are expected.

6. Validation Strategy & Limitations

The project must explicitly address:

How sled-generated pulses could be validated:
- comparison with published whiplash sled pulses,
- comparison with simplified analytical models,
- qualitative kinematic comparison
What injury claims cannot be made using the proposed system
Limitations related to:
- simplified occupant surrogate,
- lack of active muscle response,
- reduced biofidelity

This section is mandatory.

7. Feasibility & Resource Awareness

The project must include a realistic feasibility analysis:

Estimated cost (order-of-magnitude)
Availability of materials and sensors in Iran
Required infrastructure (space, rails, safety barriers)
Operational and safety considerations

Designs assuming access to full-scale crash facilities will be penalized.

8. Expected Outcomes

By the end of the project, the student should deliver:

A conceptual and technical design of a whiplash sled system
Defined whiplash injury metrics and interpretation framework
Proposed test protocols
Recommendations for educational or preliminary research use

The outcome should be suitable as a foundation for future experimental whiplash research.

9. Deliverables

Final Report (20-25 pages, excluding appendices)
System schematics and design drawings
Test protocol documentation
Cost estimation table
Oral presentation (15-20 minutes)

Optional appendices:

CAD drawings
Sensor datasheets
Example acceleration pulse definitions

10. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of whiplash testing objectives	10%
Injury mechanism understanding	Correct biomechanical interpretation of whiplash	15%
Injury metric selection & justification	Appropriate and critical use of neck injury criteria	10%
Sled system design quality	Coherence and logic of sled architecture and protocol	20%
Technical specification & clarity	Quality of schematics and system descriptions	15%
Validation & limitations	Realistic validation strategy and limitations analysis	15%
Feasibility & professionalism	Cost realism, local feasibility, safety awareness	15%
Total		100%

11. Project Scope Agreement

By choosing this project, the student agrees to:

Focus on pulse reproduction and kinematic interpretation, not certification
Respect local resource and safety constraints
Clearly state assumptions and limitations

Note:
In whiplash biomechanics, reproducing realistic acceleration pulses is often more important than achieving full anatomical detail.

Project Card 09

Sat, 01 Mar 2025 00:00:00 +0000

Comparative Evaluation of Head Injury Criteria in Traumatic Impacts

Project Pathway

🟨 Data-Driven / Analytical Modeling

1. Background & Motivation

Head injury assessment in trauma biomechanics relies heavily on injury criteria derived from head kinematics, such as acceleration- and rotation-based metrics. Over the past decades, numerous head injury criteria have been proposed and adopted in different contexts, including automotive safety, sports concussion, and helmet evaluation.

Despite their widespread use, these injury criteria are based on different biomechanical assumptions and often lead to inconsistent injury predictions for the same impact scenario. Understanding when different criteria agree, when they diverge, and why is essential for responsible interpretation and application of injury metrics.

This project focuses on a comparative, data-driven analysis of head injury criteria, emphasizing biomechanical meaning, assumptions, and limitations rather than numerical simulation or experimentation.

2. Core Biomechanical Question

Under what impact conditions do commonly used head injury criteria provide consistent or conflicting injury assessments, and what biomechanical assumptions explain these differences?

3. Injury Mechanisms & Injury Criteria

The project should consider the following head injury mechanisms:

Translational head motion
Rotational head motion
Duration and shape of acceleration pulses

Injury criteria to be considered may include (at least three):

Head Injury Criterion (HIC)
3 ms criterion (a₃ms)
Peak resultant acceleration
Peak rotational acceleration
Generalized Acceleration Model (GAM) or similar concepts

Students must explain:

The biomechanical basis of each criterion
The injury mechanisms each criterion emphasizes or neglects

4. Modeling / Analysis Approach

This is a data-driven and analytical project.

The student is expected to:

Select representative head impact datasets from literature or open sources
Analyze acceleration and/or rotational kinematic signals
Compute multiple head injury criteria from the same data
Compare injury predictions across criteria

No FEM or laboratory experiments are required.

5. Data Sources and Signal Processing

The project must include:

Description of selected datasets (experimental, dummy, or simulation-based)
Signal processing steps:
- filtering,
- integration (if applicable),
- window selection
Clear documentation of assumptions and processing choices

Students must discuss how signal processing choices influence injury metric outcomes.

6. Comparative Analysis

The project should include a structured comparison, such as:

Agreement and disagreement between criteria
Sensitivity to pulse duration and magnitude
Sensitivity to rotational vs translational motion
Scenarios where criteria may fail or overpredict injury

Visual comparison (plots, tables) is strongly encouraged.

7. Interpretation, Validation & Limitations

The project must explicitly discuss:

Biomechanical interpretation of observed differences
Comparison with reported injury risk thresholds in literature
Limitations related to:
- dataset selection,
- absence of biological validation,
- criterion-specific assumptions

Students must clearly state what conclusions are justified and what are not.

8. Feasibility & Reproducibility

The project must address:

Software used (e.g., MATLAB, Python, spreadsheet tools)
Computational simplicity and reproducibility
Transparency of analysis steps

The project should be fully reproducible using commonly available tools.

9. Expected Outcomes

By the end of the project, the student should deliver:

A comparative evaluation of multiple head injury criteria
Identification of conditions under which criteria agree or diverge
A biomechanically grounded interpretation of differences
Recommendations for responsible use of head injury metrics

The outcome should demonstrate analytical maturity and critical thinking.

10. Deliverables

Final Report (20-25 pages, excluding appendices)
Processed data plots and comparison figures
Injury metric tables
Oral presentation (15-20 minutes)

Optional appendices:

Data processing scripts
Raw datasets
Supplementary analyses

11. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear framing of comparative injury question	10%
Injury mechanism understanding	Correct biomechanical interpretation of head injury	15%
Injury criterion understanding	Depth of understanding of criteria assumptions	15%
Data analysis & processing rigor	Quality and transparency of signal processing	15%
Comparative insight	Quality of comparison and identification of trends	15%
Interpretation & limitations	Honest, critical discussion of validity	15%
Technical clarity & professionalism	Quality of figures, tables, and explanations	15%
Total		100%

12. Project Scope Agreement

By choosing this project, the student agrees to:

Focus on interpretation and comparison, not proposing new criteria
Clearly document all assumptions and processing steps
Avoid overstating injury prediction accuracy

Note:
Understanding why injury criteria disagree is often more important than computing their values.

Project Card 10

Sat, 01 Mar 2025 00:00:00 +0000

Development of a Simplified Mechanical (Lumped-Parameter) Model for Traumatic Injury Analysis

Project Pathway

🟨 Data-Driven / Analytical Modeling

1. Background & Motivation

Many traumatic injury mechanisms can be understood using simplified mechanical representations that capture the dominant dynamic behavior of tissues and body segments. Before the widespread use of finite element models, lumped-parameter models (e.g., mass-spring-damper systems) played a central role in trauma biomechanics, injury tolerance studies, and the development of injury criteria.

Even today, simplified mechanical models are invaluable for:

understanding injury mechanisms,
interpreting experimental and numerical results,
identifying dominant parameters and sensitivities.

This project focuses on developing a simplified lumped-parameter mechanical model to represent a selected traumatic injury scenario and to analyze how mechanical parameters influence injury-related response metrics.

2. Core Biomechanical Question

How can a simplified mechanical model capture the dominant dynamics of a traumatic injury scenario, and what insights does it provide into injury mechanisms and injury criteria?

3. Injury Scenario and Mechanisms

The student must select one injury scenario, such as:

Head impact (translational or rotational)
Thoracic compression
Whiplash neck response
Lower-extremity axial loading

The project should describe:

Dominant load paths
Key tissues or structures involved
Relevant injury mechanisms (e.g., acceleration, deformation, force transmission)

4. Modeling / Analysis Approach

This is an analytical and computational modeling project based on lumped-parameter systems.

The student is expected to:

Develop a mechanical model (e.g., mass-spring-damper, multi-degree-of-freedom)
Define governing equations of motion
Select representative mechanical parameters
Simulate the dynamic response under traumatic loading

The focus is on mechanical insight, not mathematical complexity.

5. Model Formulation (Core Section)

The project must include a clear and structured description of:

a) Model Structure

Number of degrees of freedom
Physical interpretation of each element
Model schematic and free-body diagrams

b) Governing Equations

Equations of motion
Assumptions (linearity, damping type, coupling)
Initial and boundary conditions

c) Input Loading

Representation of traumatic loading (force, acceleration, displacement input)
Justification of loading shape and magnitude

6. Injury Metrics and Response Quantities

The project should define and compute response quantities such as:

Acceleration
Displacement or deformation
Force or internal load measures
Simplified injury metrics derived from the model

Students must explain how these quantities relate to real injury criteria used in trauma biomechanics.

7. Parametric / Sensitivity Analysis

A limited parametric study is required, for example:

Variation of stiffness or damping
Variation of mass or inertia
Influence of loading rate or pulse duration

The goal is to identify dominant parameters and trends, not exact injury thresholds.

8. Validation Strategy & Limitations

The project must explicitly discuss:

Comparison of model behavior with published experimental or numerical results
Physical plausibility of predicted trends
Limitations related to:
- oversimplification,
- linear assumptions,
- lack of anatomical detail

Students must clearly state what insights the model can and cannot provide.

9. Feasibility & Reproducibility

The project must address:

Software or tools used (e.g., MATLAB, Python, spreadsheet tools)
Computational simplicity
Reproducibility of simulations
Transparency of assumptions and parameters

The model should be easily reproducible with minimal resources.

10. Expected Outcomes

By the end of the project, the student should deliver:

A clear lumped-parameter mechanical model
Simulated dynamic responses for selected scenarios
Sensitivity analysis results
Biomechanically meaningful interpretation of injury mechanisms

The outcome should demonstrate mechanical intuition and analytical maturity.

11. Deliverables

Final Report (20-25 pages, excluding appendices)
Model schematics and equations
Simulation results and plots
Oral presentation (15-20 minutes)

Optional appendices:

Code or spreadsheets
Additional parametric cases
Supporting derivations

12. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of injury scenario	10%
Injury mechanism understanding	Correct biomechanical interpretation	15%
Model formulation quality	Clarity and physical meaning of the model	20%
Governing equations & assumptions	Correctness and transparency	15%
Parametric / sensitivity analysis	Insight into dominant parameters	15%
Validation & limitations	Realistic assessment of model credibility	15%
Technical clarity & professionalism	Quality of figures, equations, and explanations	10%
Total		100%

13. Project Scope Agreement

By choosing this project, the student agrees to:

Emphasize physical interpretation over mathematical complexity
Clearly document all assumptions and simplifications
Avoid overclaiming predictive accuracy

Note:
A well-constructed lumped-parameter model can reveal injury mechanisms that remain hidden in complex simulations.

Project Card 11

Sat, 01 Mar 2025 00:00:00 +0000

Meta-Analysis of Sports Injury Mechanisms from a Biomechanical Perspective

Project Pathway

🟨 Data-Driven / Analytical Modeling

1. Background & Motivation

Sports-related injuries represent a major source of traumatic injury worldwide, particularly among young and active populations. Unlike automotive trauma, sports injuries often involve complex, repetitive, or non-standard loading conditions, making injury mechanisms more difficult to identify and quantify.

A large body of experimental, observational, and computational research exists on sports injuries; however, findings are often fragmented across disciplines such as biomechanics, sports science, medicine, and ergonomics. A biomechanically grounded meta-analysis can provide valuable insight into dominant injury mechanisms, loading conditions, and limitations of existing injury metrics.

This project focuses on conducting a systematic, biomechanics-oriented meta-analysis of sports injury mechanisms, emphasizing mechanical loading, tissue response, and injury criteria rather than clinical outcomes alone.

2. Core Biomechanical Question

What are the dominant biomechanical mechanisms underlying selected sports-related injuries, and how consistently are these mechanisms supported by existing literature?

3. Injury Focus and Scope

The student must select one injury type or anatomical region commonly associated with sports trauma, such as:

Sports-related concussion
Cervical spine injury in contact sports
Thoracic injuries in high-impact sports
Lower-extremity injuries (e.g., knee, ankle, femur)
Overuse or repetitive loading injuries (conceptual discussion)

The scope must be clearly defined and justified.

4. Analysis Approach

This is a systematic literature-based analytical project.

The student is expected to:

Identify and select relevant peer-reviewed studies
Categorize injury mechanisms based on biomechanical loading
Extract key mechanical variables (e.g., acceleration, force, deformation)
Synthesize findings across studies from a biomechanical perspective

This project does not involve FEM or experimental work.

5. Literature Selection and Methodology

The project must include:

Clear inclusion and exclusion criteria
Description of search strategy (databases, keywords)
Categorization of studies by:
- injury mechanism,
- loading type,
- measurement approach,
- modeling method (experimental, numerical, observational)

Transparency and reproducibility are essential.

6. Biomechanical Synthesis

The core of the project should involve:

Identification of dominant injury mechanisms
Comparison of mechanical variables reported across studies
Discussion of consistency or disagreement between findings
Assessment of how injury criteria are used or misused in sports contexts

Figures, tables, and conceptual diagrams are strongly encouraged.

7. Interpretation, Validation & Limitations

The project must explicitly discuss:

Strength of biomechanical evidence supporting proposed mechanisms
Gaps or contradictions in existing research
Limitations related to:
- measurement techniques,
- population differences,
- lack of controlled loading conditions

Students must clearly state what conclusions are well supported and what remain speculative.

8. Implications for Injury Prevention

The project should include a biomechanical discussion of:

Implications for equipment design (e.g., helmets, padding)
Training or rule changes from a mechanical perspective
Limitations of current prevention strategies

This section should remain biomechanically focused, not policy-driven.

9. Feasibility & Resource Awareness

The project must address:

Accessibility of literature and data
Reproducibility of the review process
Transparency of assumptions and interpretations

The project should be feasible using standard academic resources.

10. Expected Outcomes

By the end of the project, the student should deliver:

A structured biomechanical synthesis of sports injury mechanisms
Identification of dominant and secondary injury mechanisms
Clear articulation of gaps in current biomechanical understanding
Recommendations for future biomechanics-focused research

The outcome should demonstrate critical thinking and synthesis ability.

11. Deliverables

Final Report (20-25 pages, excluding appendices)
Summary tables of reviewed studies
Conceptual figures illustrating injury mechanisms
Oral presentation (15-20 minutes)

Optional appendices:

Detailed literature tables
Search strategy documentation
Supplementary figures

12. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of sports injury focus	10%
Biomechanical understanding	Depth of biomechanical interpretation	20%
Literature methodology	Rigor and transparency of review process	15%
Synthesis quality	Ability to integrate findings across studies	20%
Interpretation & limitations	Critical assessment of evidence strength	15%
Implications for prevention	Biomechanically grounded recommendations	10%
Technical clarity & professionalism	Quality of writing, figures, and tables	10%
Total		100%

13. Project Scope Agreement

By choosing this project, the student agrees to:

Maintain a biomechanics-centered perspective
Avoid purely clinical or epidemiological summaries
Clearly distinguish evidence-based conclusions from speculation

Note:
A strong biomechanical meta-analysis can be as impactful as a new experiment when it clarifies mechanisms and exposes knowledge gaps.

Project Card 12

Sat, 01 Mar 2025 00:00:00 +0000

Uncertainty, Sensitivity, and Robustness in Traumatic Injury Assessment

Project Pathway

🟨 Data-Driven / Analytical Modeling

1. Background & Motivation

Traumatic injury assessment is inherently uncertain. Injury predictions depend on measurements, models, assumptions, and biological variability, all of which introduce uncertainty. Despite this, injury criteria and risk metrics are often treated as deterministic thresholds in design, regulation, and research.

A mature trauma biomechanist must understand where uncertainty enters the injury assessment process, how it propagates through models and criteria, and how robust conclusions can (or cannot) be drawn.

This project focuses on a systematic analysis of uncertainty, sensitivity, and robustness in traumatic injury assessment, emphasizing interpretation, responsibility, and decision-making rather than prediction accuracy.

2. Core Biomechanical Question

How do different sources of uncertainty influence injury assessment outcomes, and how can robustness be improved in biomechanical injury evaluation?

3. Injury Context and Scope

The student must select one injury context, such as:

Head injury (e.g., HIC, rotational criteria)
Whiplash and neck injury criteria
Thoracic injury criteria (compression, VC)
Lower-extremity force-based criteria

The scope must be clearly defined and justified.

4. Analysis Approach

This is a conceptual, analytical, and data-informed project.

The student is expected to:

Identify key sources of uncertainty in injury assessment
Analyze how uncertainty affects injury metrics and conclusions
Discuss robustness strategies used (or ignored) in trauma biomechanics

No FEM or experimental work is required.

5. Sources of Uncertainty (Core Section)

The project must include a structured discussion of uncertainty sources, such as:

a) Measurement Uncertainty

Sensor noise
Filtering and signal processing
Coordinate system definition

b) Modeling Uncertainty

Simplified geometry
Material assumptions
Boundary conditions

c) Biological Variability

Age, sex, anthropometry
Inter-subject variability
Tissue tolerance variability

d) Criterion Uncertainty

Threshold selection
Risk curve construction
Context dependence of criteria

6. Sensitivity Analysis (Conceptual or Quantitative)

The project should include:

Sensitivity analysis concepts (local vs global)
Examples of parameter sensitivity from literature
Demonstration (conceptual or simple numerical) of how small changes affect injury metrics

The goal is insight, not exhaustive computation.

7. Robustness and Decision-Making

The project must discuss:

What makes an injury assessment robust
Trade-offs between sensitivity and robustness
Conservative vs optimistic injury interpretation
Implications for:
- design,
- regulation,
- research,
- ethical responsibility

This section is central to the project.

8. Validation, Interpretation & Limitations

The project must explicitly address:

Limits of validation in trauma biomechanics
Difference between model validation and decision validation
Risk of overconfidence in injury prediction

Students must clearly articulate what conclusions are justified under uncertainty.

9. Feasibility & Reproducibility

The project must address:

Transparency of assumptions
Reproducibility of reasoning
Use of simple tools (conceptual diagrams, tables, illustrative calculations)

The project should be feasible using standard academic resources.

10. Expected Outcomes

By the end of the project, the student should deliver:

A structured framework for understanding uncertainty in injury assessment
Identification of dominant uncertainty sources
Strategies to improve robustness of injury evaluation
Biomechanically and ethically grounded recommendations

The outcome should demonstrate intellectual maturity and professional judgment.

11. Deliverables

Final Report (20-25 pages, excluding appendices)
Conceptual diagrams and uncertainty maps
Summary tables of uncertainty sources and impacts
Oral presentation (15-20 minutes)

Optional appendices:

Simple sensitivity calculations
Literature-based examples
Supporting figures

12. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of injury context and uncertainty scope	10%
Understanding of injury biomechanics	Correct biomechanical framing of the problem	15%
Identification of uncertainty sources	Completeness and clarity of uncertainty analysis	20%
Sensitivity & robustness reasoning	Insightful discussion of sensitivity and robustness	20%
Interpretation & ethical awareness	Maturity in interpreting uncertain injury predictions	15%
Technical clarity & professionalism	Quality of structure, figures, and explanations	10%
Original insight & synthesis	Depth of critical thinking and synthesis	10%
Total		100%

13. Project Scope Agreement

By choosing this project, the student agrees to:

Focus on understanding and managing uncertainty, not eliminating it
Avoid deterministic injury claims
Clearly distinguish evidence, assumptions, and judgment

Note:
In trauma biomechanics, responsible interpretation under uncertainty is often more important than precise numerical prediction.

Project Card 13

Sat, 01 Mar 2025 00:00:00 +0000

Conceptual Design of a Trauma Biomechanics Laboratory

Project Pathway

🟥 Prevention, Design & Systems Thinking

1. Background & Motivation

Trauma biomechanics research and education rely heavily on experimental facilities capable of reproducing injury-relevant loading conditions and measuring biomechanical response. Well-designed trauma biomechanics laboratories support injury mechanism research, validation of numerical models, safety equipment testing, and education.

In developing countries, including Iran, the establishment of such laboratories is often constrained by limited funding, infrastructure, and access to commercial equipment. However, strategic, phased, and purpose-driven laboratory design can enable meaningful trauma biomechanics research even under these constraints.

This project aims to develop a conceptual and strategic design of a trauma biomechanics laboratory, tailored to local needs, priorities, and resources, while maintaining biomechanical relevance and scientific credibility.

2. Core Biomechanical Question

How can a trauma biomechanics laboratory be strategically designed to investigate injury mechanisms and support education and research under realistic resource constraints?

3. Laboratory Focus and Scope

The student must define a clear laboratory focus, such as one (or a combination) of:

Automotive trauma biomechanics
Sports injury biomechanics
Personal protective equipment (PPE) testing
Occupational or fall-related trauma
Educational and teaching-focused laboratory

The chosen focus must be justified based on societal relevance, research impact, and feasibility.

4. Design Approach

This is a systems-level design and planning project.

The student is expected to:

Translate injury biomechanics objectives into laboratory functions
Define required experimental capabilities
Propose a modular and scalable laboratory architecture
Balance ambition with feasibility

This project does not require actual construction or procurement.

5. Laboratory Architecture (Core Section)

The project must include a structured laboratory design covering:

a) Experimental Capabilities

Injury types and loading scenarios to be studied
Types of tests (impact, compression, sled, drop, etc.)
Measurement needs (kinematics, forces, deformation)

b) Equipment and Instrumentation

Essential equipment (core)
Optional equipment (future expansion)
Sensors and data acquisition systems

c) Space and Infrastructure

Required space and layout
Safety zones and shielding
Power, data, and environmental considerations

Conceptual layouts or block diagrams are expected.

6. Phased Development Strategy

The project must propose a phased implementation plan, for example:

Phase I: minimal viable laboratory
Phase II: expanded testing capability
Phase III: advanced research capacity

Each phase should include:

goals,
added capabilities,
approximate cost range.

7. Validation, Standards & Credibility

The project must address:

How experimental results would be validated or benchmarked
Relationship to international standards (e.g., ISO, FMVSS, ECE)
Strategies to ensure scientific credibility despite simplified setups

Students must discuss what claims the lab can and cannot support.

8. Feasibility & Resource Awareness

The project must include a realistic feasibility assessment:

Cost estimation (order-of-magnitude)
Local availability of equipment and expertise
Staffing and training considerations
Safety, ethics, and operational risks

Overly idealized laboratory designs will be penalized.

9. Expected Outcomes and Impact

The project should articulate:

Research questions the lab could realistically address
Educational impact (MSc, PhD, industry training)
Potential for collaboration, funding, or policy influence

This section should reflect strategic thinking, not just technical design.

10. Deliverables

Final Report (20-25 pages, excluding appendices)
Conceptual laboratory layout and system diagrams
Equipment lists and phased cost estimates
Oral presentation (15-20 minutes)

Optional appendices:

Example test protocols
Risk assessment tables
Expansion roadmaps

11. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of lab mission and context	10%
Biomechanical grounding	Strength of biomechanical rationale for lab focus	15%
System design quality	Coherence and logic of lab architecture	20%
Phased development strategy	Realism and strategic planning quality	15%
Validation & credibility	Understanding of standards and limitations	15%
Feasibility & resource awareness	Cost realism, local feasibility, safety	15%
Technical clarity & professionalism	Quality of figures, structure, and writing	10%
Total		100%

12. Project Scope Agreement

By choosing this project, the student agrees to:

Focus on strategic and biomechanically grounded planning
Respect local constraints and ethical responsibilities
Clearly distinguish between current capability and future vision

Note:
A well-designed laboratory concept can shape years of trauma biomechanics research, even before the first experiment is performed.

Project Card 14

Sat, 01 Mar 2025 00:00:00 +0000

Design Study of Seatbelt or Padding Systems for Injury Mitigation

Project Pathway

🟥 Prevention, Design & Systems Thinking

1. Background & Motivation

Seatbelts, padding systems, and energy-absorbing components are among the most effective injury mitigation technologies in transportation, occupational safety, and consumer products. Their protective performance depends not only on material properties, but also on system-level design choices such as load paths, geometry, timing, and interaction with the human body.

In many developing countries, safety systems are often adapted from international designs without sufficient consideration of local vehicle fleets, usage patterns, manufacturing constraints, or injury epidemiology. A biomechanically grounded design study can help bridge this gap by linking injury mechanisms to system-level design decisions.

This project focuses on a conceptual and biomechanical design study of a seatbelt or padding system aimed at mitigating traumatic injury under realistic constraints.

2. Core Biomechanical Question

How can a seatbelt or padding system be designed to mitigate specific injury mechanisms through biomechanically informed system-level design choices?

3. Injury Context and Design Focus

The student must select one design focus, such as:

Automotive seatbelt system (frontal or rear impact)
Padding systems for vehicle interiors
Padding for occupational or industrial environments
Energy-absorbing systems for sports or public safety

The selected context must be justified based on:

injury prevalence,
biomechanical relevance,
local applicability.

4. Design Approach

This is a systems-level design and analysis project.

The student is expected to:

Identify dominant injury mechanisms associated with the chosen context
Translate biomechanical injury mechanisms into design objectives
Propose and analyze a safety system concept at the system level
Discuss trade-offs between protection, usability, cost, and manufacturability

This project does not require FEM or experimental testing.

5. Biomechanical Injury Mechanisms (Core Section)

The project must include a biomechanically grounded discussion of:

Target injury mechanisms (e.g., thoracic compression, abdominal loading, head excursion)
Load paths between the body and the safety system
Time-dependent aspects of injury mitigation (e.g., force limiting, energy absorption)

Relevant injury criteria (e.g., chest compression, VC, abdominal force) should be discussed conceptually.

6. System Design Concept

The project should propose a clear system design, including:

a) System Architecture

Overall layout and components
Interaction with the human body
Integration into existing environments (e.g., vehicle interior)

b) Functional Mechanisms

Energy absorption strategies
Load distribution or redirection
Timing and rate effects

c) Design Variables

Geometry
Stiffness or compliance
Adjustability or adaptability

Conceptual sketches or block diagrams are strongly encouraged.

7. Design Trade-offs and Constraints

The project must explicitly discuss:

Protection vs comfort
Performance vs cost
Manufacturability vs idealized biomechanics
Applicability to local vehicle fleets or environments

This section distinguishes engineering judgment from idealized design.

8. Evaluation and Validation Strategy

The project must address:

How the proposed design would be evaluated biomechanically
Relevant standards or test procedures (conceptual level)
What injury claims could and could not be made without experimental validation

Students must avoid overstating performance.

9. Feasibility & Resource Awareness

The project must include a realistic feasibility analysis:

Estimated cost range
Local manufacturing or implementation considerations
Maintenance and durability considerations
Ethical and safety implications

Designs ignoring real-world constraints will be penalized.

10. Expected Outcomes

By the end of the project, the student should deliver:

A biomechanically justified seatbelt or padding system concept
Clear explanation of injury mitigation mechanisms
Design trade-off analysis
Recommendations for future refinement or testing

The outcome should reflect systems-level biomechanical thinking.

11. Deliverables

Final Report (20-25 pages, excluding appendices)
Conceptual design sketches or diagrams
Injury mechanism and load-path illustrations
Oral presentation (15-20 minutes)

Optional appendices:

Comparative design tables
Conceptual performance metrics
References to standards or guidelines

12. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of injury and design context	10%
Biomechanical grounding	Quality of injury mechanism analysis	20%
System design quality	Coherence and logic of design concept	20%
Design trade-off analysis	Depth of engineering judgment	15%
Evaluation & limitations	Realistic assessment of performance claims	15%
Feasibility & resource awareness	Cost realism and local applicability	10%
Technical clarity & professionalism	Quality of writing and figures	10%
Total		100%

13. Project Scope Agreement

By choosing this project, the student agrees to:

Focus on system-level injury mitigation, not component optimization
Respect real-world constraints and ethical responsibilities
Clearly distinguish between conceptual design and validated performance

Note:
Effective injury prevention often depends more on intelligent system design than on advanced materials or complex models.

Project Card 15

Sat, 01 Mar 2025 00:00:00 +0000

Standards-Based Critique and Redesign Proposal for Injury Assessment

(FMVSS / ECE in Relation to Local Needs)

Project Pathway

🟥 Prevention, Design & Systems Thinking

1. Background & Motivation

International injury assessment and safety standards-such as the U.S. Federal Motor Vehicle Safety Standards (FMVSS) and United Nations Economic Commission for Europe (ECE) regulations-play a central role in defining how traumatic injury risk is evaluated, regulated, and mitigated. These standards strongly influence vehicle design, testing procedures, and safety requirements worldwide.

However, these standards are developed based on specific assumptions regarding:

vehicle fleets,
road infrastructure,
user behavior,
anthropometry,
injury epidemiology.

When applied directly in developing countries, such as Iran, these assumptions may not fully reflect local conditions. A biomechanically informed critique and redesign proposal can help identify mismatches between international standards and local injury realities, while maintaining scientific credibility and regulatory rigor.

2. Core Biomechanical Question

To what extent do existing injury assessment standards reflect local injury mechanisms and conditions, and how can they be biomechanically adapted or supplemented to better address local needs?

3. Standard Selection and Scope

The student must select one standard or regulatory framework, such as:

FMVSS (e.g., FMVSS 208, 214)
ECE regulations (e.g., R94, R95, R129)
Helmet safety standards (e.g., ECE R22)
Related injury assessment protocols

The scope must be clearly defined and justified.

4. Analysis Approach

This is a standards-focused, analytical, and design-oriented project.

The student is expected to:

Analyze the biomechanical assumptions embedded in the selected standard
Identify the injury mechanisms prioritized by the standard
Compare these assumptions with local conditions (vehicles, usage, population)
Propose biomechanically grounded adaptations or supplements

This project does not involve experimental testing or numerical simulation.

5. Biomechanical Assumptions in Standards (Core Section)

The project must include a structured analysis of:

Target injury mechanisms and metrics
Dummy types and anthropometric assumptions
Test configurations and loading conditions
Injury criteria and thresholds

Students must clearly explain what the standard assumes biomechanically.

6. Local Context Analysis

The project must analyze relevant local factors, such as:

Vehicle fleet characteristics
Road and traffic conditions
Typical crash scenarios
Anthropometric differences
Injury epidemiology trends (if available)

The analysis should remain biomechanical, not purely sociological.

7. Gap Identification

The project should identify and justify specific gaps, for example:

Injury mechanisms underrepresented or ignored
Test conditions not representative of local crashes
Injury criteria with questionable relevance locally
Over- or under-conservatism of thresholds

Each identified gap must be biomechanically justified.

8. Redesign or Supplement Proposal

The project must propose one or more biomechanically grounded improvements, such as:

Modified test conditions or impact scenarios
Additional injury metrics or criteria
Supplemental local test procedures
Context-specific interpretation guidelines

Proposals must be realistic and defensible.

9. Evaluation and Credibility

The project must address:

How proposed changes could be validated
Alignment with international regulatory philosophy
Risks of divergence from global standards
Ethical and legal considerations

Students must clearly state what claims can and cannot be made.

10. Feasibility & Implementation Considerations

The project must include:

Practical feasibility of proposed adaptations
Cost and infrastructure implications
Pathways for gradual adoption or pilot implementation
Compatibility with existing regulatory frameworks

Unrealistic proposals will be penalized.

11. Expected Outcomes

By the end of the project, the student should deliver:

A biomechanically grounded critique of an existing standard
Clear identification of local mismatches
A defensible redesign or supplementation proposal
Recommendations for research, policy, or testing practice

The outcome should demonstrate systems-level thinking and professional responsibility.

12. Deliverables

Final Report (20-25 pages, excluding appendices)
Comparative tables of standard assumptions vs local conditions
Conceptual diagrams illustrating proposed changes
Oral presentation (15-20 minutes)

Optional appendices:

Excerpts of relevant standards
Supporting epidemiological data
Regulatory comparison tables

13. Project-Specific Grading Rubric

Criterion	Description	Weight
Problem formulation & relevance	Clear definition of standard and context	10%
Understanding of injury biomechanics	Depth of biomechanical analysis	20%
Standards analysis quality	Accuracy and insight in interpreting standards	15%
Gap identification	Clarity and biomechanical justification of gaps	15%
Redesign / supplement proposal	Quality and realism of proposed improvements	20%
Feasibility & ethical awareness	Implementation realism and responsibility	10%
Technical clarity & professionalism	Quality of writing, figures, and structure	10%
Total		100%

14. Project Scope Agreement

By choosing this project, the student agrees to:

Maintain a biomechanics-centered perspective
Avoid purely political or legal argumentation
Clearly distinguish evidence, assumptions, and judgment

Note:
Standards shape injury prevention not only through rules, but through the biomechanical assumptions they encode.

Project Card 16

Sat, 01 Mar 2025 00:00:00 +0000

Helmet Safety Evaluation Framework: Injury Metrics, Protocols, and Design Trade-offs

Project Pathway

🟥 Prevention, Design & Systems Thinking

1. Background & Motivation

Helmets are widely used in transportation, sports, and occupational environments as a primary means of head injury prevention. While helmet performance is often evaluated through standardized tests, these evaluations rely on specific injury metrics, test configurations, and pass/fail criteria that implicitly encode biomechanical assumptions.

In many contexts-particularly in developing countries-helmet usage patterns, impact scenarios, and injury epidemiology may differ from those assumed in international standards. A system-level evaluation framework is therefore essential to interpret helmet performance responsibly and to guide design and policy decisions.

This project focuses on developing a biomechanically grounded helmet safety evaluation framework, independent of any specific testing hardware.

2. Core Biomechanical Question

How should helmet protective performance be evaluated biomechanically, and what trade-offs exist between different injury metrics, test protocols, and design priorities?

3. Injury Mechanisms and Metrics

The project should analyze:

Head injury mechanisms relevant to helmet use:
- linear acceleration
- rotational motion
- impact energy dissipation
Common helmet injury metrics:
- Head Injury Criterion (HIC)
- peak linear acceleration
- rotational acceleration metrics
- energy absorption indicators

Students must critically assess what each metric captures and what it neglects.

4. Evaluation Framework Design

This is a systems-level analytical project.

The student is expected to:

Propose a structured framework for helmet safety evaluation
Define which injury metrics should be prioritized for different use cases
Discuss appropriate test scenarios (conceptual, not hardware-specific)
Define performance interpretation strategies

No experimental setup or FEM is required.

5. Test Protocol Logic (Conceptual)

The project must include a conceptual discussion of:

Impact locations and directions
Severity levels
Single vs multiple impacts
Repeatability and robustness

The focus is on why certain protocols are chosen, not how to build them.

6. Design Trade-offs

The project must explicitly discuss trade-offs such as:

Linear vs rotational injury mitigation
Protection vs comfort
Performance vs cost
Certification thresholds vs real-world injury reduction

This section is central to Pathway D.

7. Standards and Contextual Adaptation

The project should examine:

Existing helmet standards (e.g. ECE R22, EN standards, sports standards)
Biomechanical assumptions behind these standards
Potential mismatches with local usage or injury patterns

Students must propose interpretation or supplementation strategies, not new standards.

8. Validation, Limitations, and Ethics

The project must address:

Limits of helmet evaluation metrics
Risk of over-reliance on pass/fail criteria
Ethical implications of safety certification

9. Expected Outcomes

By the end of the project, the student should deliver:

A coherent helmet safety evaluation framework
Justified selection of injury metrics and protocols
Clear articulation of design and policy trade-offs
Recommendations for responsible helmet assessment

10. Deliverables

Final Report (20-25 pages)
Conceptual framework diagrams
Comparative tables of metrics and protocols
Oral presentation (15-20 minutes)

11. Project-Specific Grading Rubric

Criterion	Weight
Biomechanical understanding	20%
Evaluation framework quality	20%
Metric and protocol justification	15%
Design trade-off analysis	15%
Standards interpretation	15%
Technical clarity & professionalism	15%
Total	100%

Note:
A helmet is only as safe as the biomechanical assumptions used to evaluate it.

Trauma Biomechanics

Sat, 01 Mar 2025 00:00:00 +0000

Course Information

Course Title: Trauma Biomechanics
Course Code: 2014471-01
Credits: 3
Level: MSc
Class Schedule: Sunday 8:00-10:00 & Monday 14:00-16:00
Class Location: Class 30
Instructor: Seyed Sadjad Abedi-Shahri
- Email:
- Telegram: @Sad4Abd
Lecture Materials: Provided weekly via LMS

Course Overview

This course introduces the biomechanical principles underlying traumatic injuries of the human body under high-rate and impact loading. Emphasis is placed on injury mechanisms, injury criteria, and models used in trauma biomechanics, including numerical, experimental, analytical, and systems-level approaches.

The course adopts a model-driven and interpretation-focused philosophy, enabling students to analyze trauma problems. Students will engage with realistic injury scenarios drawn from automotive safety, sports, occupational accidents, and protective equipment design.

Learning Objectives

By the end of the course, students will be able to:

Explain major traumatic injury mechanisms across different anatomical regions
Interpret and apply commonly used injury criteria and injury metrics
Compare experimental, numerical, analytical, and systems-level models in trauma biomechanics
Critically evaluate trauma biomechanics studies and standards
Design and justify injury assessment or prevention strategies under real-world constraints
Communicate biomechanical reasoning clearly, including assumptions and limitations

Syllabus (Topics)

Module 1 - Foundations of Trauma Biomechanics
Module 2 - Methods in Trauma Biomechanics
Module 3 - Head and Brain Trauma
Module 4 - Spine and Thoracic Trauma
Module 5 - Abdomen and Extremities
Module 6 - Special Topics and Synthesis

References

Schmitt, K.U., Niederer, P.F., Cronin, D.S., Muser, M.H., Walz, F. Trauma Biomechanics: An Introduction to Injury Biomechanics, 5th ed.

Evaluation Scheme

Final Project: 50%
- Individual project, chosen from structured project cards
- Includes report and oral presentation
Final Exam: 50%
- Conceptual and interpretive questions

This course uses continuous assessment through a major project rather than frequent quizzes.

Project Structure

Each student selects one project from a curated set of project cards, organized into four equally valued pathways:

🟦 Numerical / Computational Modeling (FEM)
🟩 Experimental / Proof-of-Concept Design
🟨 Data-Driven / Analytical Modeling
🟥 Prevention, Design & Systems Thinking

All pathways:

Have comparable difficulty
Use pathway-specific grading rubrics
Are equally weighted in assessment

See the Project Cards document and the guide for details.

Project Timeline & Milestones

The course project is a semester-long individual project designed to support deep, mature engagement with trauma biomechanics.
Project assessment combines process-based milestones with final quality-based evaluation, and applies equally to all project pathways.

Overall Grading Context

Final Exam: 50% of course grade
Project (total): 50% of course grade

Important:
The detailed grading rubric provided in each Project Card is applied only to the final written report and oral presentation.
Early milestones are assessed using simplified criteria focused on progress, clarity, and appropriate scope.

Week 1-2 | Project Orientation

Introduction to project pathways and expectations
Release of:
- Project Cards (all projects)
- “How to Choose Your Project Pathway” guide
Discussion of grading philosophy and examples

📌 No graded deliverables

Week 3 | Project Selection

Students review all project cards
Each student submits:
- Ranked list of three preferred projects
- Brief justification (2-3 sentences per choice)

📌 Instructor confirms project assignments
📌 Not graded

Week 4 | Project Proposal (Milestone 1)

Deliverable: Short written proposal (2-3 pages)

Must include:

Selected project card and pathway
Problem statement and objectives
Planned approach and scope
Key assumptions and anticipated challenges

Assessment focus:

Clarity of problem definition
Appropriate project scope
Feasibility of the proposed approach

📊 Weight: 5% of course grade

Week 6-7 | Mid-Project Review (Milestone 2)

Deliverable: Progress review (written summary or oral meeting)

Should cover:

Work completed to date
Preliminary analysis, design, or concepts
Identified difficulties or limitations
Revised plan if needed

Assessment focus:

Evidence of meaningful progress
Quality of reasoning and engagement
Awareness of limitations and challenges

📊 Weight: 10% of course grade

Week 11-12 | Draft Check (Optional, Not Graded)

Informal submission of:
- report outline,
- preliminary figures or concepts,
- early results or designs
Feedback provided by the instructor

📌 Strongly recommended but not graded

Final Week | Final Submission & Presentation (Milestone 3)

Final Written Report

Length: 20-25 pages (excluding appendices)
Evaluated using the Project Card grading rubric

📊 Weight: 25% of course grade

Oral Presentation & Discussion

Duration: 15-20 minutes + discussion
Evaluated using presentation-related criteria from the Project Card rubric

📊 Weight: 10% of course grade

Summary of Project Assessment

Component	Course Weight	Evaluation Method
Project Proposal	5%	Milestone criteria (scope, clarity, feasibility)
Mid-Project Review	10%	Progress and reasoning
Final Written Report	25%	Project Card rubric
Oral Presentation	10%	Project Card rubric
Total Project Weight	50%

General Notes

All milestones apply equally to all project pathways
Projects are individual by default
Final project quality is evaluated using pathway-specific rubrics
Early milestones are designed to support learning, not penalize exploration

A successful project is one that is well-scoped, well-argued, and intellectually honest.

Session Outline

Session	Date	Outline	Additional Resources
1	3 Esfand	Module 1 (U)¹	-

Policies

Attendance is recommended but not mandatory.
Active participation in discussions is encouraged.
Collaboration in discussion is allowed; all submitted work must be individual.
Academic integrity is strictly enforced. Plagiarism or misrepresentation will not be tolerated.

(U): Unfinished ↩︎

Trauma Biomechanics - How to Choose Your Project Pathway

Sat, 01 Mar 2025 00:00:00 +0000

This course offers four project pathways, each representing a different way of doing trauma biomechanics.
All pathways are equally valued, equally graded, and equally rigorous - they simply emphasize different skills and interests.

There is no “best” pathway.
The best pathway is the one that matches how you think and how you want to work.

🟦 Pathway A - Numerical / Computational Modeling (FEM)

Choose this pathway if you:

Enjoy simulations and computational modeling
Are comfortable with FEM software
Like exploring “what happens if…” questions
Want hands-on experience with injury modeling

What you will do:

Build or adapt simplified FE models
Apply impact or injury-relevant loading
Compute and interpret injury metrics
Perform sensitivity or parametric studies

You do NOT need:

Very complex geometry
Advanced material models
High computational resources

Typical outputs:

FE models
Injury metric plots
Interpretation of trends and limitations

Good fit for students interested in:

Computational biomechanics
Automotive safety
Further numerical or PhD research

🟩 Pathway B - Experimental / Proof-of-Concept Design

Choose this pathway if you:

Like thinking about how things are tested in the real world
Enjoy system design, instrumentation, and feasibility
Are interested in building research capability, not just using tools
Prefer practical, engineering-oriented thinking

What you will do:

Design experimental test setups (rigs, dummies, sleds)
Define sensors, protocols, and safety considerations
Think about repeatability, validation, and cost
Work at the level of how testing could realistically be done

You do NOT need:

Access to a real laboratory
To build or manufacture anything

Typical outputs:

Test system designs
Experimental protocols
Schematics and feasibility analyses

Good fit for students interested in:

Experimental biomechanics
Lab development
Applied engineering and industry work

🟨 Pathway C - Data-Driven / Analytical Modeling

Choose this pathway if you:

Enjoy deep thinking and analysis more than tools
Like asking “why does this work?” or “when does this fail?”
Prefer literature-based or conceptual work
Are interested in research, theory, or PhD studies

What you will do:

Analyze injury criteria, models, or mechanisms
Develop simplified mechanical or conceptual models
Study uncertainty, robustness, or injury evidence
Synthesize and critique existing biomechanical knowledge

You do NOT need:

FEM software
Experimental equipment
Advanced programming

Typical outputs:

Analytical models
Conceptual diagrams
Critical synthesis and interpretation

Good fit for students interested in:

Research
Theory development
Critical evaluation of biomechanics

🟥 Pathway D - Prevention, Design & Systems Thinking

Choose this pathway if you:

Think at the system or policy level
Are interested in safety design, standards, or regulation
Like connecting biomechanics to real-world decisions
Want to address local or national needs

What you will do:

Design safety systems conceptually
Analyze standards and injury assessment frameworks
Study design trade-offs and feasibility
Propose improvements grounded in biomechanics

You do NOT need:

FEM
Experiments
Hardware design

Typical outputs:

Evaluation frameworks
System-level designs
Standards critiques and redesign proposals

Good fit for students interested in:

Safety engineering
Industry, policy, or regulation
Capacity building in developing contexts

⚖️ Important Notes

All pathways are graded using rigorous, pathway-specific rubrics
No pathway gives an advantage in grading
Difficulty is comparable across all pathways
You will be graded on:
- biomechanical reasoning,
- clarity of thinking,
- justification of assumptions,
- awareness of limitations

This course values thinking like a trauma biomechanist, not using a particular tool.

✅ How to Decide

Ask yourself:

Do I prefer models, systems, data, or design?
Do I want to work with software, concepts, experiments, or frameworks?
Which project would I be excited to work on for several weeks?

If unsure, talk to the instructor - guidance is part of the course.

Final Thought

Trauma biomechanics needs modelers, experimentalists, analysts, and system thinkers.

This course allows you to grow in the direction that fits you best.

Weekly Schedule

Sun, 02 Feb 2025 00:00:00 +0000

Last Update: 2025/Sep/19

	8:00-10:00	10:00-12:00	12:00-14:00	14:00-16:00	16:00-18:00
Saturday	MeetingUpon Appointment	Engineering Mathematics Class 39	Research	MeetingUpon Appointment	Research
Sunday	Trauma Biomechanics Class 30	Field OverviewClass 43	Research	MeetingUpon Appointment	Research
Monday	MSc ConsultationUpon Appointment	BSc ConsultationUpon Appointment	Research	Impact Mechanics in BiomechanicsClass 30 Trauma BiomechanicsClass 30	Research
Tuesday	MeetingUpon Appointment	Engineering Mathematics Class 39	CommitteeDepartment	Impact Mechanics in Biomechanics Class 39	Research
Wednesday	Research	Research	Research	Research	Research

My Research and Passion

Wed, 15 Jan 2025 00:00:00 +0000

My Research and Passion

Seyed Sadjad Abedi-Shahri

Faculty of Engineering, University of Isfahan

About Me

🎓 Background:
- BSc in Mechanical Eng.
- MSc and PhD in Biomedical Eng.
💼 Current Position:
- Assistant Professor of Biomedical Engineering

Research Interests

Numerical Methods ( , )

(go down to see details)

Numerical Methods (FEM)

Linear and Nonlinear Problems
Viscoelastic and Hyperelastic Materials
Impact Simulation
Buckling and Post-Buckling Analysis
Homogenization Techniques
Tools: ABAQUS, LS-DYNA, and Open-Source Solutions

Numerical Methods (SBFEM)

Developing formulation for specific problems
Linear and Nonlinear Problems
Viscoelastic and Hyperelastic Materials
Tools: In-house program for 2D Viscoelastic and Nonlinear Problems

Scientific Computing

Developing Research Software
Best Practices in Research Software Engineering (RSE)
Contribution to Open-Source Programs
Implementation in Fields of PDEs, Matrix Computations, etc.
Scientific Visualization
Tools: Python, Fortran, Octave/MATLAB

Computational (Bio)Mechanics

Nonlinear Solid Mechanics
Soft & Hard Tissue Biomechanics
Trauma Biomechanics
Image-Based Simulations
Impact Mechanics (Low & High velocity)
Fracture Mechanics
Topology Optimization
Inverse Problems

Computational Geometry

Mesh Generation and Optimization
Computational Topology in Meshing
Image-Based Mesh Generation
Delaunay and Voronoi-Based Methods

Machine Learning for Biomedical Applications

Data-driven Surrogate Models
Artificial Neural Networks for PDEs
Selected applications in Biomedical Image Processing

Some Examples of Projects

(go down to see details)

Scaled Boundary Finite Element Method (SBFEM)

Head Trauma

pyPolyMesher

is a python package for generating unstructured polygonal meshes in arbitrarily defined 2D domains. It allows users to mathematically specify domains using signed distance functions (SDFs).

QTREEMESH

is a python package that can create a Quadtree structure from an image. The Quadtree algorithm in this package is based on pixels’ intensity.

Bone Microcracks

Generation of bone RVE with random osteons and microcracks (using ABAQUS & python script) for homogenization problem

Composite Design Assistant(ComDA)

Composite Design Assistant(ComDA) is a scientific toolbox that provides a straightforward framework for industrial and academic analysis and design of composite structures.

Machine Learning for Biomedical Applications

Ongoing Projects

Finite Strain Viscoelasticty in SBFEM
Neural Network-Based Inverse Model for Cornea
DL in Pulmonary Vascular Histological Images

Collaboration & Contact

🤝 Open to research collaborations

📧

🌐

🔗

👨‍💻

Thank You! 🎤

Neural Network-Based Inverse Model for Non-Invasive Estimation of Corneal Mechanical Properties

Wed, 01 Jan 2025 00:00:00 +0000

ReSIST 2024 - Oral Presentation

Wed, 01 Jan 2025 00:00:00 +0000

Slides and Presentation made by

NL-SBFEM: A pure SBFEM formulation for geometrically and materially nonlinear problems

Mon, 30 Dec 2024 00:00:00 +0000

Heat and Mass Transfer Project 5: 2D Transient Heat Transfer Analysis using Implicit Methods

Wed, 18 Dec 2024 00:00:00 +0000

Project Overview

This project explores numerical solutions to time-dependent (transient) heat conduction problems in two-dimensional rectangular domains using implicit finite difference methods. Students will develop a computational tool that simulates the dynamic temperature evolution within materials with the advantage of unconditional stability, allowing for larger time steps than explicit methods. This project connects theoretical heat transfer principles with advanced numerical methods used in engineering simulations where efficiency and stability are critical considerations.

Learning Objectives

Understand the mathematical formulation of implicit schemes for transient heat conduction
Implement and analyze fully implicit and Crank-Nicolson methods for 2D problems
Compare the advantages and limitations of implicit methods versus explicit approaches
Develop computational skills to efficiently solve large systems of equations at each time step
Analyze the trade-offs between accuracy, stability, and computational efficiency
Apply implicit methods to practical engineering thermal problems

Project Description

Background

The transient heat conduction in a 2D domain is governed by the following partial differential equation:

$$ \rho c_p \frac{\partial T}{\partial t} = \frac{\partial}{\partial x}\left(k \frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(k \frac{\partial T}{\partial y}\right) + \dot{q} $$

Where:

$T(x,y,t)$ is the temperature distribution as a function of space and time
$\rho$ is the material density
$c_p$ is the specific heat capacity
$k$ is the thermal conductivity of the material
$\dot{q}$ is the volumetric heat generation rate
$t$ is time

For homogeneous materials with constant thermal properties, this can be rewritten using thermal diffusivity $\alpha = k/(\rho c_p)$:

$$ \frac{\partial T}{\partial t} = \alpha \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} \right) + \frac{\dot{q}}{\rho c_p} $$

This project focuses on developing implicit finite difference solutions to this equation, which evaluate spatial derivatives at the future time step.

Project Stages

1. Theoretical Foundation (25%)

Review the derivation of the 2D transient heat conduction equation
Study implicit finite difference approximations for both time and space derivatives
Analyze the unconditional stability advantage of fully implicit methods
Develop the discretized forms of the governing equation for implicit methods
Analyze the implementation of different boundary conditions in implicit formulations:
- Dirichlet boundary condition (constant temperature)
- Neumann boundary condition (constant heat flux)
- Convection boundary condition (convective heat transfer)
Discuss the structure of the resulting linear system of equations

2. Computational Implementation (40%)

Develop a program to implement implicit finite difference methods for 2D transient heat conduction. Tasks include:

Program Input Requirements:
- Material properties (thermal conductivity, density, specific heat)
- Internal heat generation rates (constant or time-dependent)
- Grid size (number of nodes in x and y directions)
- Time step and total simulation time
- Initial temperature distribution
- Boundary condition specifications for each edge (type and values)
- Solution method parameters (direct or iterative solver options)
Spatial and Temporal Discretization:
- Create a mesh for the rectangular domain with specified dimensions $W \times H$
- Implement time stepping using implicit formulations
- Handle boundary nodes appropriately in the coefficient matrix
Matrix Assembly and Solution:
- Generate the coefficient matrix for the system of equations at each time step
- Implement boundary conditions into the matrix structure:
  - Constant temperature (Dirichlet)
  - Constant heat flux (Neumann)
  - Convection (Robin): $-k\frac{\partial T}{\partial n} = h(T - T_{\infty})$
- Create the right-hand side vector incorporating the previous time step solution
- Implement efficient solution methods
Program Output Requirements:
- Temperature distribution at specified time intervals
- Temperature history at user-defined monitoring points
- Heat fluxes across the domain at selected times
- Visualization of temperature evolution through animations or time sequence plots
- Energy balance verification at each time step
- Performance metrics (computation time, memory usage)

3. Validation and Verification (20%)

Compare numerical solutions with available analytical solutions for simple transient cases
Verify the implementation by comparing with benchmark problems
Conduct time step sensitivity studies to evaluate accuracy versus computational cost
Analyze truncation error and convergence behavior
Verify conservation of energy across the domain for each time step
Compare results with the explicit method for identical problems (if available)
Validate the implementation of different boundary conditions

4. Case Studies and Analysis (15%)

Select and apply the developed code to solve a practical transient heat conduction problem of your choice
The case study should demonstrate the advantages of implicit methods and have relevance to engineering applications
Examples of potential applications include (but are not limited to):
- Long-time thermal simulations where stability is crucial
- Systems with widely varying time scales
- Problems with complex boundary conditions
- Applications requiring large time steps for efficiency
Analyze the chosen problem thoroughly, including:
- Time step selection and its impact on accuracy
- Computational efficiency compared to theoretical explicit method requirements
- Effect of solver choice on overall performance
Interpret results in terms of practical engineering implications
Discuss the advantages and limitations of implicit methods for your specific application

Technical Requirements

Implement in a programming language of choice (MATLAB, Python, or FORTRAN recommended)
Create modular code with clear structure and documentation
Ensure proper input/output interfaces for parameters and results
Implement efficient matrix operations and system solvers
Develop algorithms that balance computational efficiency and accuracy
Include error handling and convergence monitoring capabilities

Deliverables

Comprehensive report including:
- Theoretical background on implicit finite difference methods
- Detailed mathematical formulation and stability analysis
- Description of numerical implementation with focus on coefficient matrix assembly
- Explanation of system solution approaches
- Validation results and verification approach
- Case study description, results, and engineering interpretation
- Computational performance analysis
- Limitations and potential improvements
Well-documented source code:
- Core program for solving 2D transient heat conduction
- Matrix assembly and solution routines
- Supporting functions for time stepping, visualization, etc.
- User manual explaining how to use the program
- Example input files for validation cases
Presentation:
- Clear explanation of implicit finite difference method advantages
- Demonstration of program capabilities
- Presentation of key results and computational performance
- Discussion of challenges and solutions

Evaluation Criteria

Report Quality (20%): Clarity, depth, and presentation of theoretical and computational details
Code Efficiency and Quality (30%): Correctness, modularity, and optimization
Presentation (50%): Delivery, visual appeal, and depth of understanding

Bonus Challenges (Optional)

For students interested in extending their understanding and skills beyond the core requirements:

Advanced Implicit Schemes
- Implement the Alternating Direction Implicit (ADI) method
- Compare computational efficiency between different implicit approaches
Adaptive Time Stepping
- Implement variable time step control based on error estimates
- Develop strategies for automatic time step adjustment
- Analyze the efficiency gains from adaptive versus fixed time stepping
Non-Linear Thermal Problems
- Extend the code to handle temperature-dependent material properties
- Implement radiation boundary conditions: $-k\frac{\partial T}{\partial n} = \epsilon\sigma(T^4 - T_{\infty}^4)$
- Develop linearization techniques and iterative approaches for non-linear terms
Multi-Domain Problems
- Implement capabilities for handling multiple materials with different properties
- Develop interface conditions between different materials
- Analyze the impact of thermal contact resistance at material interfaces

Submission Guidelines

Submission deadline: TBA
Format: PDF report, source code (with comments), and presentation slides
Groups of up to three members are allowed, provided each member’s contribution is documented clearly
For every project, only one group with the best performance will be selected to present

Heat and Mass Transfer Project 4: 2D Transient Heat Transfer Analysis using Explicit Methods

Sun, 15 Dec 2024 00:00:00 +0000

Project Overview

This project explores numerical solutions to time-dependent (transient) heat conduction problems in two-dimensional rectangular domains using explicit finite difference methods. Students will develop a computational tool that simulates the dynamic temperature evolution within materials in response to changing boundary conditions and internal heat generation. This project bridges theoretical heat transfer principles with practical numerical methods essential for analyzing thermal systems under non-steady conditions.

Learning Objectives

Understand the mathematical formulation of transient heat conduction problems
Implement and analyze explicit finite difference schemes for time-dependent problems
Assess stability criteria and accuracy limitations of explicit methods
Develop computational skills to simulate and visualize time-evolving thermal solutions
Analyze the effects of boundary conditions and material properties on transient thermal responses

Project Description

Background

The transient heat conduction in a 2D domain is governed by the following partial differential equation:

Where:

$T(x,y,t)$ is the temperature distribution as a function of space and time
$\rho$ is the material density
$c_p$ is the specific heat capacity
$k$ is the thermal conductivity of the material
$\dot{q}$ is the volumetric heat generation rate
$t$ is time

For homogeneous materials with constant thermal properties, this can be rewritten using thermal diffusivity $\alpha = k/(\rho c_p)$:

$$ \frac{\partial T}{\partial t} = \alpha \left( \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} \right) + \frac{\dot{q}}{\rho c_p} $$

This project focuses on developing an explicit finite difference solution to this equation.

Project Stages

1. Theoretical Foundation (25%)

Review the derivation of the 2D transient heat conduction equation
Study explicit finite difference approximations for both time and space derivatives
Analyze the stability criteria for explicit methods (Fourier number constraint)
Develop the discretized form of the governing equation
Analyze the implementation of different boundary conditions:
- Dirichlet boundary condition (constant temperature)
- Neumann boundary condition (constant heat flux)
- Convection boundary condition (convective heat transfer)
Discuss initialization techniques for initial temperature distributions

2. Computational Implementation (40%)

Develop a program to implement the explicit finite difference method for 2D transient heat conduction. Tasks include:

Program Input Requirements:
- Material properties (thermal conductivity, density, specific heat)
- Internal heat generation rates (constant or time-dependent)
- Grid size (number of nodes in x and y directions)
- Time step and total simulation time
- Initial temperature distribution
- Boundary condition specifications for each edge (type and values)
- Stability parameters and output control options
Spatial and Temporal Discretization:
- Create a mesh for the rectangular domain with specified dimensions $W \times H$
- Implement time stepping using the explicit scheme
- Calculate and enforce the stability criterion
- Handle boundary nodes appropriately for different boundary conditions
Algorithm Implementation:
- Develop the explicit time-marching algorithm
- Implement heat generation terms in the domain
- Apply boundary conditions at each time step:
  - Constant temperature (Dirichlet)
  - Constant heat flux (Neumann)
  - Convection (Robin): $-k\frac{\partial T}{\partial n} = h(T - T_{\infty})$
- Track temperature evolution throughout the domain
Program Output Requirements:
- Temperature distribution at specified time intervals
- Temperature history at user-defined monitoring points
- Heat fluxes across the domain at selected times
- Visualization of temperature evolution through animations or time sequence plots
- Energy balance verification at each time step

3. Validation and Verification (20%)

Compare numerical solutions with available analytical solutions for simple transient cases
Verify the implementation of stability criteria
Conduct time step and grid size convergence studies
Validate temperature evolution against known thermal responses
Verify conservation of energy across the domain for each time step
Validate the implementation of different boundary conditions

4. Case Studies and Analysis (15%)

Select and apply the developed code to solve a practical transient heat conduction problem of your choice
The case study should demonstrate the temporal evolution of the thermal field and have relevance to engineering applications
Examples of potential applications include (but are not limited to):
- Thermal response of materials to sudden heating or cooling
- Heat treatment processes in manufacturing
- Thermal cycling and fatigue analysis
- Building thermal performance under variable conditions
Analyze the chosen problem thoroughly, including:
- Characteristic thermal response times
- Effect of material properties on transient behavior
- Sensitivity to boundary conditions
Interpret results in terms of practical engineering implications
Discuss limitations of the explicit method for your specific application

Technical Requirements

Implement in a programming language of choice (MATLAB, Python, or FORTRAN recommended)
Create modular code with clear structure and documentation
Ensure proper input/output interfaces for parameters and results
Include stability checking and adaptive time stepping if appropriate
Develop efficient algorithms that minimize computational time
Include error handling and solution monitoring capabilities

Deliverables

Comprehensive report including:
- Theoretical background on explicit finite difference methods
- Detailed mathematical formulation and stability analysis
- Description of numerical implementation and algorithm flowchart
- Validation results and verification approach
- Case study description, results, and engineering interpretation
- Limitations and potential improvements
Well-documented source code:
- Core program for solving 2D transient heat conduction
- Supporting functions for time stepping, visualization, etc.
- User manual explaining how to use the program
- Example input files for validation cases
Presentation:
- Clear explanation of the numerical approach
- Demonstration of program capabilities
- Presentation of key results and temporal evolution
- Discussion of challenges and solutions

Evaluation Criteria

Report Quality (20%): Clarity, depth, and presentation of theoretical and computational details
Code Efficiency and Quality (30%): Correctness, modularity, and optimization
Presentation (50%): Delivery, visual appeal, and depth of understanding

Bonus Challenges (Optional)

For students interested in extending their understanding and skills beyond the core requirements:

Variable Thermal Properties
- Implement temperature-dependent thermal properties (k, ρ, cp)
- Analyze how variable properties affect stability criteria
- Compare solutions with constant and variable properties
Advanced Boundary Conditions
- Implement time-dependent boundary conditions
- Add radiation boundary conditions: $-k\frac{\partial T}{\partial n} = \epsilon\sigma(T^4 - T_{\infty}^4)$
- Develop mixed boundary conditions (combinations of different types)
Phase Change Implementation
- Extend the code to handle phase change problems (melting/solidification)
- Implement the effective heat capacity or enthalpy method
- Track the movement of phase boundaries over time
User Interface and Visualization
- Create an interactive GUI for problem setup and simulation control
- Develop advanced visualization tools for time-evolving thermal fields
- Implement animation capabilities for temperature evolution
- Create tools for parametric studies of transient responses

Submission Guidelines

Submission deadline: TBA
Format: PDF report, source code (with comments), and presentation slides
Groups of up to three members are allowed, provided each member’s contribution is documented clearly
For every project, only one group with the best performance will be selected to present

Engineering Mathematics Project 1: Mandelbrot Set Exploration

Thu, 12 Dec 2024 00:00:00 +0000

Project Overview

This project aims to explore the fascinating world of complex numbers through the lens of the Mandelbrot set—a quintessential mathematical object that beautifully demonstrates the complexity arising from simple iterative processes in the complex plane. By combining mathematical theory, computational methods, and visualizations, this project offers a hands-on journey into the intersection of mathematics and computational science.

Learning Objectives

Develop a deep understanding of complex number operations and their behavior
Apply mathematical concepts to solve computational problems creatively
Explore the intersection of mathematics, computational methods, and visual art
Gain practical experience in scientific programming and visualization techniques

Project Description

Background

The Mandelbrot set is defined by a simple yet powerful iterative function in the complex plane: $$z_{n+1} = z_n^2 + c$$ Where:

$z_0 = 0$
$c$ is a complex number from the complex plane
The set consists of all complex numbers $c$ for which the function does not diverge when iterated from $z_0$

This simple formula generates one of the most intricate and aesthetically fascinating structures in mathematics, offering a deep connection between numerical computation and visual patterns.

Project Stages

1. Theoretical Foundation (20%)

Provide a comprehensive mathematical explanation of:
- Complex number representation
- Complex plane coordinates
- Iteration process of the Mandelbrot set
- Criteria for divergence and its implications
Derive and explain the mathematical properties and boundaries of the Mandelbrot set
Discuss the significance of complex numbers in this context

2. Computational Implementation (40%)

Develop a program to generate the Mandelbrot set with the following requirements:

Implement in a programming language of choice (Python, MATLAB, or FORTRAN recommended)
Create functions for:
- Complex number operations
- Mandelbrot set iteration
- Divergence testing and escape-time calculation
Generate a visual representation of the Mandelbrot set
Implement color mapping based on iteration count
Provide annotations in the code for clarity and reproducibility

3. Advanced Exploration (20%)

Choose and implement at least two of the following:

Zoom functionality to explore fractal details
Optimization techniques to reduce computational runtime
Explore and implement creative color-mapping strategies
Comparative analysis with Julia sets, discussing similarities and differences
Leverage parallel computing for faster generation

4. Mathematical Analysis (20%)

Investigate the mathematical properties of the Mandelbrot set:

Analyze the mathematical properties of the Mandelbrot set
Investigate:
- Boundary conditions
- Iteration convergence
- Symmetry properties
- Relationship to complex number behavior

Technical Requirements

Use double-precision complex number representations
Implement a grid-based visualization of the complex plane
Handle computational challenges:
- Numerical precision
- Iteration limits
- Computational complexity

Deliverables

Comprehensive report including:
- Theoretical background
- Detailed explanation of implementation
- Source code with annotations
- Visualizations and advanced explorations
- Mathematical analysis and insights
Executable program: Capable of generating and visualizing the Mandelbrot set
Presentation: A clear and engaging explanation of the project, its significance, and findings

Evaluation Criteria

Report Quality (20%): Clarity, depth, and presentation of theoretical and computational details
Code Efficiency and Quality (30%): Correctness, modularity, and optimization
Presentation (50%): Delivery, visual appeal, and depth of understanding

Bonus Challenges

Implement adaptive resolution to refine details dynamically during zooming
Develop an interactive Mandelbrot set explorer with GUI
Explore connections to chaos theory and other mathematical fields
Investigate real-world applications or connections to physics and computer science

Submission Guidelines

Submission deadline: TBA
Format: PDF report, source code, and presentation slides
Groups of up to three members are allowed, provided each member’s contribution is documented clearly.
For every project, only one group with the best performance will be selected to present.

Engineering Mathematics Project 2: Joukowski Transformation

Thu, 12 Dec 2024 00:00:00 +0000

Project Overview

This project explores the elegant mathematical concept of the Joukowski Transformation—a conformal mapping used to transform simple geometric shapes into airfoil-like structures in the complex plane. By leveraging your understanding of complex numbers, this project bridges theoretical mathematics with visually intriguing outcomes.

Learning Objectives

Understand the concept of conformal mapping in the complex plane.
Apply complex number transformations to practical geometries.
Develop computational skills to visualize and analyze mapped structures.
Gain a stronger foundation in complex analysis and its applications.

Project Description

Background

The Joukowski Transformation is defined as:

$$ w = z + \frac{1}{z} $$

Where:

$z = x + iy$ is a point in the complex plane.
$w$ is the transformed point in a new plane.

This transformation maps circles in the $z$-plane into airfoil-like shapes or flattened ovals in the $w$-plane. It serves as a fundamental concept in aerodynamics and complex analysis.

Project Stages

1. Theoretical Foundation (30%)

Study the concept of conformal mappings and transformations.
Derive and explain the effect of the Joukowski transformation on:
- A unit circle $|z| = 1$.
- A shifted circle $|z - z_0| = r$ with parameters $z_0$ and $r$.
Discuss the geometric meaning of singularities and mapping behavior.

2. Computational Implementation (40%)

Develop a program to implement and visualize the Joukowski transformation. Tasks include:

Input Parameters:
- Define a circle in the complex plane (radius $r$ and center $z_0$).
Transformation:
- Apply the Joukowski formula to map points on the circle into the $w$-plane.
Visualization
- Plot the original circle and the transformed shape.
- Allow adjustments to the circle parameters and observe how the resulting shape changes.

3. Geometric Exploration (20%)

Explore how changing the circle’s radius or center influences the transformed shape.
Investigate special cases where the Joukowski transformation produces:
- Symmetric shapes.
- Sharp edges resembling airfoil trailing edges.

4. Mathematical Analysis (10%)

Analyze and describe why the transformation generates flattened or stretched shapes
Discuss the geometric properties preserved by the transformation.
Identify limitations, such as singularities in the transformation.

Technical Requirements

Implement in a programming language of choice (Python, MATLAB, or FORTRAN recommended)
Ensure proper parameter control for circle position and radius.
Present clear and well-annotated plots showing transformations.

Deliverables

Comprehensive report including:
- Theoretical background
- Detailed explanation of implementation
- Source code with annotations
- Visualizations and advanced explorations
- Mathematical analysis and insights
Executable program: Clean and annotated code for the transformation and visualization.
Presentation: A clear and engaging explanation of the project, visual results, and key findings.

Evaluation Criteria

Report Quality (20%): Clarity, depth, and presentation of theoretical and computational details
Code Efficiency and Quality (30%): Correctness, modularity, and readability
Presentation (50%): Delivery, visual appeal, and depth of understanding

Here’s the enriched version of the Bonus Challenges section, incorporating studies of potential flow and related topics:

Bonus Challenges (Optional)

Explore the mapping of ellipses or other shapes instead of circles.
Add an interactive feature to dynamically adjust parameters and observe the transformation.
Investigate and explain how singularities appear during the transformation.

For students seeking deeper insights and a broader understanding, explore the following extensions that provide opportunities to connect complex analysis with fluid dynamics concepts:

Potential Flow Around the Joukowski Airfoil
- Study the potential flow (ideal, inviscid, and irrotational flow) around the Joukowski airfoil.
- Analyze how the Joukowski transformation simplifies solving the Laplace equation for potential flow.
- Visualize streamlines and equipotential lines around the airfoil shape.
Lift Calculation Using the Kutta-Joukowski Theorem
- Introduce the Kutta-Joukowski theorem for lift generation: $$ L = \rho V \Gamma $$ where $L$ is lift, $\rho$ is fluid density, $V$ is freestream velocity, and $\Gamma$ is the circulation.
- Apply the theorem to estimate lift for the Joukowski airfoil, assuming ideal flow conditions.
- Relate lift generation to the geometry of the transformed shape.
Effect of Circle Parameters on Airfoil Geometry
- Systematically study how varying the parameters $z_0$ (circle center) and $r$ (circle radius) influences the resulting airfoil geometry.
- Document relationships between input parameters and airfoil features, such as thickness, camber, and chord length.
Comparison with Real Airfoil Shapes
- Compare the Joukowski airfoil with real-world airfoils used in aerodynamics (e.g., NACA airfoils).
- Discuss the limitations of the Joukowski transformation in modeling practical airfoil shapes.
Numerical Simulation of Flow
- Use numerical tools (e.g., CFD software like OpenFOAM or COMSOL) to simulate flow over the Joukowski airfoil.
- Compare idealized potential flow predictions with numerical results to identify discrepancies caused by viscosity and other real-world factors.
Explore Related Transformations
- Study alternative conformal mappings (e.g., Kármán-Trefftz transformation) and compare their ability to generate airfoil shapes.
- Discuss how modifications to the Joukowski transformation can produce different aerodynamic features.

Submission Guidelines

Submission deadline: TBA
Format: PDF report, source code, and presentation slides
Groups of up to three members are allowed, provided each member’s contribution is documented clearly.
For every project, only one group with the best performance will be selected to present.

Heat and Mass Transfer Project 1: Human Body Heat Balance

Thu, 12 Dec 2024 00:00:00 +0000

Project Overview

This project focuses on understanding and analyzing heat balance in the human body through theoretical study and computational modeling. Students will explore the fundamental principles of heat transfer mechanisms in the human body and their relationship to heat stress indices, developing a comprehensive understanding of thermoregulation principles.

Learning Objectives

Understand the fundamental mechanisms of heat transfer in the human body
Learn to analyze and evaluate each term in the human body heat balance equation
Develop basic computational skills to model heat transfer processes
Understand the relationship between environmental conditions and heat stress
Apply engineering principles to biological systems

Project Description

Background

The human body maintains its core temperature through various heat transfer mechanisms. This thermal regulation is described by the heat balance equation: $$M - W = E + R + C + K + S$$ where M is metabolic heat production, W is mechanical work, E is evaporative heat loss, R is radiative heat exchange, C is convective heat exchange, K is conductive heat exchange, and S is heat storage. Understanding these components is crucial for evaluating human thermal comfort and heat stress.

Project Stages

1. Literature Review

Research and summarize each component of the heat balance equation
Study how each term is evaluated and calculated
Investigate factors affecting each heat transfer mechanism
Review common heat stress indices

2. Component Analysis

Detailed study of each heat balance term:
Metabolic heat production in different activities
Evaporative heat loss mechanisms
Radiative heat transfer with environment
Convective heat transfer effects
Conductive heat transfer significance
Develop simple calculations for each component

3. Heat Stress Analysis

Study various heat stress indices
Understand environmental factors affecting heat stress
Learn to calculate common indices like WBGT and Heat Stress Index
Analyze the relationship between heat balance and heat stress

4. Case Study Development

Select and analyze real-world scenarios
Apply heat balance principles to specific situations
Calculate heat stress indices for different conditions
Propose recommendations for thermal comfort

Technical Requirements

Basic understanding of heat transfer principles
Basic calculation and analytical skills
Ability to research and synthesize information

Deliverables

Comprehensive report including:

Theoretical background of each heat transfer mechanism
Detailed analysis of heat balance components
Heat stress indices calculations and analysis
Case study findings and recommendations

Presentation slides

Evaluation Criteria

Report Quality (50%): Understanding of theoretical concepts, Quality of analysis and calculations
Presentation (50%): Delivery, visual appeal, and depth of understanding

Bonus Challenges (Optional)

Create a simple program for heat balance calculations
Analyze heat stress in different climatic conditions
Compare different heat stress indices
Investigate the effect of clothing on heat balance
Study special cases (athletes, industrial workers)

Submission Guidelines

Submission deadline: TBA
Format: PDF report and presentation slides
Groups of up to three members are allowed, provided each member’s contribution is documented clearly.
For every project, only one group with the best performance will be selected to present.

Heat and Mass Transfer Project 2: Microvascular Heat Transfer

Thu, 12 Dec 2024 00:00:00 +0000

Project Overview

This project explores microvascular heat transfer mechanisms through a detailed theoretical study. Students will analyze existing models, understand fundamental principles, and explore applications in biomedical engineering.

Learning Objectives

Understand the principles of heat transfer in biological tissues
Analyze models of perfused tissues and their implications for heat transport
Study theoretical models of microvascular heat transport
Explore applications in biomedical engineering, such as hyperthermia treatment

Project Description

Background

Blood flow plays a critical role in tissue heat transfer, affecting temperature regulation and medical treatments. Understanding microvascular heat transfer requires analyzing conduction, convection, and perfusion effects. The bioheat equation models these interactions, accounting for tissue properties, metabolic heat generation, and perfusion rates.

Project Stages

1. Literature Review

Study heat transfer mechanisms in vascular tissues
Review the Pennes’ bioheat equation and alternative models
Investigate models of perfused tissues and their role in heat transport

2. Theoretical Analysis

Compare different vascular heat transfer models (Pennes, effective conductivity, etc.)
Examine key parameters like thermal conductivity, perfusion rate, and equilibration length
Discuss the assumptions and limitations of existing models

3. Case Study Development

Apply microvascular heat transfer models to a clinical or physiological scenario
Evaluate temperature profiles in tissues with different perfusion rates
Propose improvements for biomedical applications (e.g., thermal therapies)

Technical Requirements

Basic knowledge of heat transfer principles
Ability to research and synthesize information from literature

Deliverables

Comprehensive report including:

Theoretical background of microvascular heat transfer
Analysis of bioheat models
Case study findings and biomedical implications

Presentation slides summarizing key results

Evaluation Criteria

Report Quality (50%): Depth of analysis, clarity of explanation, and accuracy of information
Presentation (50%): Clarity, visual quality, and understanding of concepts

Bonus Challenges (Optional)

Develop a simplified computational model for microvascular heat transfer
Analyze heat transfer differences in various tissue types
Investigate the impact of vascular architecture on heat transport
Study pulsatile blood flow effects on thermal regulation

Submission Guidelines

Submission deadline: TBA
Format: PDF report and presentation slides
Groups of up to three members are allowed, with clearly documented contributions
The best-performing group will present their findings in class

Heat and Mass Transfer Project 3: 2D Steady-State Heat Transfer Analysis

Thu, 12 Dec 2024 00:00:00 +0000

Project Overview

This project explores numerical solutions to steady-state heat conduction problems in two-dimensional rectangular domains using the finite difference method. Students will develop a computational tool that can analyze heat distribution across materials with different thermal properties under various boundary conditions. This project connects theoretical heat transfer principles with practical numerical methods used extensively in engineering applications.

Learning Objectives

Understand the mathematical foundation of finite difference methods for heat transfer problems
Apply numerical techniques to solve the 2D steady-state heat equation
Develop computational skills to implement and visualize thermal solutions
Analyze the effects of different boundary conditions on temperature distributions
Gain proficiency in validating numerical solutions against analytical benchmarks

Project Description

Background

The steady-state heat conduction in a 2D domain is governed by the following partial differential equation:

$$ \frac{\partial}{\partial x}\left(k_x \frac{\partial T}{\partial x}\right) + \frac{\partial}{\partial y}\left(k_y \frac{\partial T}{\partial y}\right) + \dot{q} = 0 $$

Where:

$T(x,y)$ is the temperature distribution
$k$ is the thermal conductivity of the material
$\dot{q}$ is the volumetric heat generation rate

For homogeneous materials with constant thermal conductivity and no internal heat generation, this simplifies to:

$$ \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0 $$

This is the Laplace equation for temperature.

For cases with internal heat generation, the governing equation becomes:

$$ \frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} + \frac{\dot{q}}{k} = 0 $$

This is the Poisson equation, which must be addressed in this project.

Project Stages

1. Theoretical Foundation (25%)

Review the derivation of the 2D heat conduction equation
Study the finite difference approximations for second derivatives
Develop the discretized form of the governing equation
Analyze the implementation of different boundary conditions:
- Dirichlet boundary condition (constant temperature)
- Neumann boundary condition (constant heat flux)
- Convection boundary condition (convective heat transfer)
Discuss solution methods for the resulting system of algebraic equations

2. Computational Implementation (40%)

Develop a program to implement the finite difference method for 2D steady-state heat conduction. Tasks include:

Program Input Requirements:
- Material properties (thermal conductivity, which may be directional)
- Internal heat generation rates
- Grid size (number of nodes in x and y directions)
- Boundary condition specifications for each edge (type and values)
- Solution method parameters (e.g., convergence criteria)
Domain Discretization:
- Create a mesh for the rectangular domain with specified dimensions $W \times H$
- Handle boundary nodes appropriately for different boundary conditions
- Implement heat generation terms in the domain
Matrix Assembly:
- Generate the coefficient matrix for the system of algebraic equations
- Implement different boundary conditions into the matrix structure:
  - Constant temperature (Dirichlet)
  - Constant heat flux (Neumann)
  - Convection (Robin): $-k\frac{\partial T}{\partial n} = h(T - T_{\infty})$
- Create the right-hand side vector for the system
Solution Methods:
- Implement direct solver methods (e.g., Gaussian elimination)
- Implement iterative solver methods (e.g., Gauss-Seidel)
- Compare performance
Program Output Requirements:
- Nodal temperatures throughout the domain
- Heat fluxes at all nodes (magnitude and direction)
- Overall heat transfer rates at boundaries
- Visualization of temperature distribution and heat flow

3. Validation and Verification (20%)

Compare numerical solutions with available analytical solutions for simple cases
Conduct grid independence studies to determine optimal mesh sizes
Analyze convergence rates and solution accuracy
Verify conservation of energy across the domain
Validate the implementation of different boundary conditions

4. Case Studies and Analysis (15%)

Select and apply the developed code to solve a practical heat conduction problem of your choice
The case study should demonstrate the capabilities of your code and have relevance to engineering applications
Analyze the chosen problem thoroughly, including:
- Effect of grid resolution on results
- Impact of boundary conditions on temperature distribution
- Sensitivity to material properties or heat generation
Interpret results in terms of practical engineering implications
Discuss limitations of the numerical approach for your specific application

Technical Requirements

Implement in a programming language of choice (MATLAB, Python, or FORTRAN recommended)
Create modular code with clear structure and documentation
Ensure proper input/output interfaces for parameters and results
Develop efficient algorithms that minimize computational time
Include error handling and solution convergence criteria

Deliverables

Comprehensive report including:
- Theoretical background on finite difference methods
- Detailed mathematical formulation
- Description of numerical implementation
- Validation results and analysis
- Case studies and their engineering interpretations
- Limitations and potential improvements
Well-documented source code:
- Core program for solving 2D heat conduction
- Supporting functions for mesh generation, visualization, etc.
- User manual explaining how to use the program
Presentation:
- Clear explanation of the numerical approach
- Demonstration of program capabilities
- Presentation of key results and insights
- Discussion of challenges and solutions

Evaluation Criteria

Report Quality (20%): Clarity, depth, and presentation of theoretical and computational details
Code Efficiency and Quality (30%): Correctness, modularity, and optimization
Presentation (50%): Delivery, visual appeal, and depth of understanding

Bonus Challenges (Optional)

For students interested in extending their understanding and skills beyond the core requirements:

Variable Grid Size Implementation
- Develop capabilities for non-uniform grid spacing in both x and y directions
- Implement local mesh refinement in regions of interest
- Compare solution accuracy between uniform and non-uniform grids
- Analyze computational efficiency gains from strategic grid refinement
Radiation Boundary Condition
- Implement radiation boundary conditions: $-k\frac{\partial T}{\partial n} = \epsilon\sigma(T^4 - T_{\infty}^4)$
- Handle the non-linearity introduced by the fourth-power temperature dependence
- Develop a linearization technique or iterative approach for solution
- Compare combined radiation and convection effects on boundaries
Spatially Variable Material Properties
- Implement capabilities for handling different materials within the domain
- Allow specification of thermal conductivity as a function of position
- Handle interfaces between different materials appropriately
- Analyze the impact of material property variations on temperature distribution
User Interface Development
- Create a graphical user interface (GUI) for easier problem setup
- Implement interactive visualization of results
- Develop tools for parametric studies and sensitivity analysis
- Design a user-friendly method for specifying complex boundary conditions

Submission Guidelines

Submission deadline: TBA
Format: PDF report, source code (with comments), and presentation slides
Groups of up to three members are allowed, provided each member’s contribution is documented clearly
For every project, only one group with the best performance will be selected to present

Dynamics

Tue, 12 Nov 2024 00:00:00 +0000

Course Information

Course Title: Dynamics
Course Code: 2014054
Credits: 3
Class Schedule:
- Days: Sunday, Thuesday
- Time: 14:00-16:00
Class Location: Class 9, Class 32
Instructor: Seyed Sadjad Abedi-Shahri
- Email:
- Office Hours:

Lecture Materials: Provided weekly in .

Course Overview

This course introduces the fundamental principles of dynamics, focusing on the theoretical aspects of particle and rigid body motion, force analysis, and energy methods, and their relevance to human movement and biomechanical systems. While the course primarily addresses traditional dynamics concepts, occasional examples related to human body mechanics will also be provided.

Learning Objectives

By the end of the course, students will be able to:

Understand and apply the principles of kinematics and kinetics for particles and rigid bodies.
Use work-energy and impulse-momentum methods for solving dynamic problems.
Analyze three-dimensional motion and dynamics of rigid bodies.
Relate classical mechanics principles to biomechanics applications such as human motion analysis.

Syllabus

Kinematics of a Particle
Kinetics of a Particle: Force and Acceleration
Kinetics of a Particle: Work and Energy
Kinetics of a Particle: Impulse and Momentum
Planar Kinematics of a Rigid Body
Planar Kinetics of a Rigid Body: Force and Acceleration
Planar Kinetics of a Rigid Body: Work and Energy
Planar Kinetics of a Rigid Body: Impulse and Momentum
Three-Dimensional Kinematics and Kinetics of a Rigid Body
Related Topics in Biomechanics

References

[HIB] Engineering Mechanics: Dynamics [14th ed.] by Russell C. Hibbeler
[MER] Engineering Mechanics: Dynamics [6th ed.] by J.L. Meriam and L. Kraige
[PYT] Engineering Mechanics: Dynamics [3rd ed.] by Andrew Pytel and Jaan Kiusalaas
[OZK] Fundamentals of Biomechanics [4th ed.] by Nihat Özkaya, David Goldsheyder, and Margareta Nordin
[TOZ] Human Body Dynamics: Classical Mechanics and Human Movement by Aydin Tozeren

Evaluation Scheme

Midterm Evaluation: 35 points
- Covers Chapters 1-4.
Final Evaluation: 50 points
- Covers all remaining chapters.
Continuous Evaluation: 15 points
- Based on exercises, quizzes, and participation during lectures and discussions.
Extracurricular Activities (optional): Up to 10 bonus points
- Awarded for participation in activities such as group projects, presentations, or relevant research outside the classroom.

Session Outline

Session	Date	Outline	Additional Resources
1	21 Bahman	Lecture 1 (U)¹	-
2	23 Bahman	Lecture 1 + Lecture 2 (U)	[HIB]:12.1-12.3 & [MER]: 2.1-2.2
3	28 Bahman	Lecture 2	[HIB]:12.4-12.7 & [MER]: 2.3-2.5
4	30 Bahman	Lecture 3	[HIB]:12.8-12.10 & [MER]: 2.6-2.9
5	5 Esfand	Lecture 4 (U)	-
6	12 Esfand	Lecture 4 + Lecture 5 (U)	[HIB]:13.1-13.6 & [MER]: 3.1-3.5, 4.1-4.2
7	14 Esfand	Lecture 5 (U)	-
8	19 Esfand	Lecture 5 + Exc. 1	[HIB]:14.1-14.6 & [MER]: 3.6-3.7, 4.3
9	21 Esfand	Exc. 2 + Exc. 3	-
10	17 Farvardin	Lecture 6 (U)	-
11	19 Farvardin	Lecture 6 + Lecture 7 (U)	[HIB]:15.1-15.4 & [MER]: 3.9, 3.12
12	24 Farvardin	Lecture 7 + Review	[HIB]:15.5-15.8 & [MER]: 3.10, 4.4-4.6
13	26 Fravardin	Exc. 4 + Exc. 5	-
14	31 Farvardin	Lecture 8 (U)	-
15	2 Ordibehesht	Lecture 8 + Lecture 9 (U)	[HIB]:16.1-16.4 & [MER]: 5.1-5.3
16	7 Ordibehesht	Lecture 9 + Lecture 10 (U)	[HIB]:16.5-16.6 & [MER]: 5.4-5.5
17	9 Ordibehesht	Lecture 10	[HIB]:16.7-16.8 & [MER]: 5.6-5.7
18	14 Ordibehesht	Exc. 6	-
19	16 Ordibehesht	Exc. 6 + Exc. 7	-
20	21 Ordibehesht	Lecture 11 (U)	-
21	23 Ordibehesht	Midterm Exam	-
22	28 Ordibehesht	Lecture 11	[HIB]:17.1-17.3 & [MER]: 6.1-6.3
23	30 Ordibehesht	Lecture 12	[HIB]:17.4-17.5 & [MER]: 6.4-6.5
24	4 Khordad	Lecture 13	[HIB]:18.1-18.5 & [MER]: 6.6-6.7
25	6 Khordad	Lecture 14	[HIB]:19.1-19.3 & [MER]: 6.8
26	11 Khordad	Exc. 8 + Exc. 9	-

Lecture 1: Kinematics of a Particle - Part 1
- Introduction
- Rectilinear Kinematics: Continuous Motion
- Rectilinear Kinematics: Erratic Motion
Lecture 2: Kinematics of a Particle - Part 2
- General Curvilinear Motion
- Curvilinear Motion: Rectangular Components
- Motion of a Projectile
- Curvilinear Motion: Normal and Tangential Components
Lecture 3: Kinematics of a Particle - Part 3
- Curvilinear Motion: Cylindrical Components
- Absolute Dependent Motion Analysis of Two Particles
- Relative-Motion of Two Particles Using Translating Axes
Lecture 4: Kinetics of a Particle: Force and Acceleration
- Newton’s Second Law of Motion
- The Equation of Motion
- Equation of Motion for a System of Particles
- Equations of Motion: Rectangular Coordinates
- Equations of Motion: Normal and Tangential Coordinates
- Equations of Motion: Cylindrical Coordinates
Lecture 5: Kinetics of a Particle: Work and Energy
- The Work of a Force
- Principle of Work and Energy
- Principle of Work and Energy for a System of Particles
- Power and Efficiency
- Conservative Forces and Potential Energy
- Conservation of Energy
Lecture 6: Kinetics of a Particle: Linear Impulse and Momentum
- Principle of Linear Impulse and Momentum
- Principle of Linear Impulse and Momentum for a System of Particles
- Conservation of Linear Momentum for a System of Particles
- Impact
Lecture 7: Kinetics of a Particle: Angular Impulse and Momentum
- Angular Momentum
- Relation Between Moment of a Force and Angular Momentum
- Principle of Angular Impulse and Momentum
- Steady Flow of a Fluid Stream
Lecture 8: Planar Kinematics of a Rigid Body - Part 1
- Planar Rigid-Body Motion
- Translation
- Rotation about a Fixed Axis
- Absolute Motion Analysis
Lecture 9: Planar Kinematics of a Rigid Body - Part 2
- Relative-Motion Analysis: Velocity
- Instantaneous Center of Zero Velocity
Lecture 10: Planar Kinematics of a Rigid Body - Part 3
- Relative-Motion Analysis: Acceleration
- Relative-Motion Analysis Using Rotating Axes
Lecture 11: Planar Kinetics of a Rigid Body: Force and Acceleration - Part 1
- Mass Moment of Inertia
- Planar Kinetic Equations of Motion
- Equations of Motion: Translation
Lecture 12: Planar Kinetics of a Rigid Body: Force and Acceleration - Part 2
- Equations of Motion: Rotation about a Fixed Axis
- Equations of Motion: General Plane Motion
Lecture 13: Planar Kinetics of a Rigid Body: Work and Energy
- Kinetic Energy
- The Work of a Force
- The Work of a Couple Moment
- Principle of Work and Energy
- Conservation of Energy
Lecture 14: Planar Kinetics of a Rigid Body: Impulse and Momentum
- Linear and Angular Momentum
- Principle of Impulse and Momentum
- Conservation of Momentum

Additional Information

Prerequisites

Students are expected to have a basic understanding of:

Calculus II
Statics

Policies

Attendance is not mandatory but may influence your continuous evaluation score. Regular attendance is strongly recommended to stay on track with course material.
Students are expected to arrive on time. Late arrivals may disrupt the class and could impact participation evaluation.
Collaboration on assignments, exercises, and projects is encouraged. However, all submissions must reflect individual understanding and adhere to academic integrity policies. Plagiarism or copying will not be tolerated.

Announcements

The midterm will be held on 13 May 2025 (23 Ordibehesht 1404) from 14:00 to 16:00. Don’t forget to bring a formula sheet and engineering calculator.

(U): Unfinished ↩︎

Engineering Mathematics

Tue, 12 Nov 2024 00:00:00 +0000

Course Information

Course Title: Engineering Mathematics
Course Code: 2014197-01
Credits: 3
Schedule: Saturday 10:00-12:00 & Tuesday 10:00-12:00
Location: Class 39 & Class 2
Instructor: Seyed Sadjad Abedi-Shahri
- Email:

Lecture Materials: Provided weekly in .

Course Overview

This advanced engineering mathematics course is designed to provide students with a comprehensive understanding of key mathematical techniques essential for engineering and applied science disciplines. The course focuses on three critical areas: Complex Analysis, Fourier Analysis, and Partial Differential Equations, equipping students with powerful mathematical tools for modeling and solving complex engineering problems.

Learning Objectives

By the end of this course, students will be able to:

Complex Analysis
- Manipulate complex functions and understand their properties
- Apply complex integration techniques
- Use conformal mapping and residue theorem to solve engineering problems
Fourier Analysis
- Understand and apply Fourier series and transforms
- Solve engineering problems using Fourier techniques
Partial Differential Equations (PDEs)
- Classify and solve different types of PDEs (Wave/Heat/Laplace)
- Apply separation of variables and transform methods
- Model physical phenomena using PDEs in engineering contexts

Syllabus

Complex Analysis
Fourier Analysis
Partial Differential Equations

References

[ZIL] Advanced Engineering Mathematics [6th ed.] by Dennis G. Zill
[KRE] Advanced Engineering Mathematics [9th ed.] by Erwin Kreyszig
[ONE] Advanced Engineering Mathematics [7th ed.] by Peter V. O’Neil
[DUF] Advanced Engineering Mathematics with MATLAB [4th ed.] by Dean G. Duffy
[YAN] Engineering Mathematics with MATLAB by Won Y. Yan et al.

Evaluation Scheme

Midterm Evaluation: 30 points
- Complex Analysis
Final Evaluation: 55 points
- Fourier Analysis + Partial Differential Equations
Continuous Evaluation: 15 points
- Based on exercises, quizzes, and participation during lectures and discussions.
Extracurricular Activities (optional): Up to 10 bonus points
- Awarded for participation in activities such as group , presentations, or relevant research outside the classroom.

Session Outline

Session	Date	Outline	Additional Resources
1	5 Esfand	Lecture 1 (U)¹	-

Projects:

Additional Information

Prerequisites

Students are expected to have a basic understanding of:

Calculus II
Differential Equations
Introductory programming (optional)

Policies

Regular attendance is strongly recommended to stay on track with course material and acquire continuous evaluation score
Students are expected to arrive on time. Late arrivals may disrupt the class and could impact participation evaluation.
Collaboration on assignments, exercises, and projects is encouraged. However, all submissions must reflect individual understanding and adhere to academic integrity policies. Plagiarism or copying will not be tolerat

(U): Unfinished ↩︎

Engineering Mathematics

Tue, 12 Nov 2024 00:00:00 +0000

Course Information

Course Title: Engineering Mathematics
Course Code: 2014197
Credits: 3
Class Schedule:
- Days: Sunday, Tuesday
- Time: 8:00-10:00
Class Location: Class 2
Instructor: Seyed Sadjad Abedi-Shahri
- Email:
- Office Hours:

Lecture Materials: Provided weekly in .

Course Overview

Learning Objectives

By the end of this course, students will be able to:

Complex Analysis
- Manipulate complex functions and understand their properties
- Apply complex integration techniques
- Use conformal mapping and residue theorem to solve engineering problems
Fourier Analysis
- Understand and apply Fourier series and transforms
- Solve engineering problems using Fourier techniques
Partial Differential Equations (PDEs)
- Classify and solve different types of PDEs (Wave/Heat/Laplace)
- Apply separation of variables and transform methods
- Model physical phenomena using PDEs in engineering contexts

Syllabus

Complex Analysis
Fourier Analysis
Partial Differential Equations

References

[ZIL] Advanced Engineering Mathematics [6th ed.] by Dennis G. Zill
[KRE] Advanced Engineering Mathematics [9th ed.] by Erwin Kreyszig
[ONE] Advanced Engineering Mathematics [7th ed.] by Peter V. O’Neil
[DUF] Advanced Engineering Mathematics with MATLAB [4th ed.] by Dean G. Duffy
[YAN] Engineering Mathematics with MATLAB by Won Y. Yan et al.

Evaluation Scheme

Midterm Evaluation: 25 points
- Complex Analysis
Final Evaluation: 60 points
- Fourier Analysis + Partial Differential Equations
Continuous Evaluation: 15 points
- Based on exercises, quizzes, and participation during lectures and discussions.
Extracurricular Activities (optional): Up to 10 bonus points
- Awarded for participation in activities such as group , presentations, or relevant research outside the classroom.

Session Outline

Session	Date	Outline	Additional Resources
1	21 Bahman	Lecture 1 (U)¹	-
2	23 Bahman	Lecture 1	[ZIL]:17.1-17.8 & [KRE]: 13.1-13.7 & [ONE]: 19.1-19.5
3	28 Bahman	Lecture 2 (U)	-
4	30 Bahman	Lecture 2 + Lecture 3 (U)	[ZIL]:18.1-18.4 & [KRE]: 14.1-14.4 & [ONE]: 20.1-20.3
5	5 Esfand	Lecture 3	[ZIL]:19.1-19.3 & [KRE]: 15.1-15.5, 16.1 & [ONE]: 21.1-21.2
6	12 Esfand	Lecture 4	[ZIL]:19.4-19.6 & [KRE]: 16.2-16.4 & [ONE]: 22.1-22.3
7	14 Esfand	Lecture 5 (U)	-
8	19 Esfand	Lecture 5	[ZIL]:20.1-20.3 & [KRE]: 17.1-17.4 & [ONE]: 23.1-23.2
9	21 Esfand	Exc. 1 + Exc. 2	-
10	17 Farvardin	Lecture 6 (U)	-
11	19 Farvardin	Lecture 6	[ZIL]:12.1-12.4 & [KRE]: 11.1-11.5 & [ONE]: 13.1-13.6
12	24 Farvardin	Exc. 3	-
13	26 Farvardin	Exc. 4 + Exc. 5	-
14	31 Farvardin	Lecture 7 (U)	-
15	2 Ordibehesht	Midterm Exam	-
16	7 Ordibehesht	Lecture 7	[ZIL]:13.1-13.2 & [KRE]: 12.1-12.2
17	9 Ordibehesht	Lecture 8 (U)	-
18	14 Ordibehesht	Lecture 8 + Exc. 6	[ZIL]:13.3-13.5 & [KRE]: 12.3-12.5
19	16 Ordibehesht	Exc. 6 + Lecture 9 (U)	-
20	21 Ordibehesht	Lecture 9 (U)	-
21	23 Ordibehesht	Lecture 9	[ZIL]:13.6-13.8 & [KRE]: 12.7-12.8
22	28 Ordibehesht	Lecture 10 (U)	-
23	30 Ordibehesht	Lecture 10	[ZIL]:15.1-15.4 & [KRE]: 11.7-11.9 , 12.6, 12.11
24	4 Khordad	Exc. 7	-
25	6 Khordad	Exc. 7 + Exc. 8	-
26	11 Khordad	Exc. 8	-
27	13 Khordad	Exc. 9	-

Module 1: Complex Analysis
- Lecture 1: Complex Numbers and Functions
  - Complex Numbers
  - Powers and Roots
  - Sets in the Complex Plane
  - Functions of a Complex Variable
  - Cauchy–Riemann Equations
  - Exponential and Logarithmic Functions
  - Trigonometric and Hyperbolic Functions
  - Inverse Trigonometric and Hyperbolic Functions
- Lecture 2: Complex Integration
  - Contour Integrals
  - Cauchy–Goursat Theorem
  - Independence of the Path
  - Cauchy’s Integral Formulas
- Lecture 3: Series
  - Sequences and Series
  - Taylor Series
  - Laurent Series
- Lecture 4: Residues
  - Zeros and Poles
  - Residues and Residue Theorem
  - Evaluation of Real Integrals
- Lecture 5: Conformal Mappings
  - Complex Functions as Mappings
  - Conformal Mappings
  - Linear Fractional Transformations
Module 2: Partial Differential Equations
- Lecture 6: Orthogonal Functions and Fourier Series
  - Orthogonal Functions
  - Fourier Series
  - Fourier Cosine and Sine Series
  - Complex Fourier Series
- Lecture 7: Boundary-Value Problems in Rectangular Coordinates - Part 1
  - Separable Partial Differential Equations
  - Classical PDEs and Boundary-Value Problems
- Lecture 8: Boundary-Value Problems in Rectangular Coordinates - Part 2
  - Heat Equation
  - Wave Equation
  - Laplace Equation
- Lecture 9: Boundary-Value Problems in Rectangular Coordinates - Part 3
  - Nonhomogeneous Boundary-Value Problems
  - Orthogonal Series Expansions
  - Fourier Series in Two Variables
- Lecture 10: Integral Transform Method
  - Error Function
  - Applications of the Laplace Transform
  - Fourier Integral
  - Fourier Transforms

Projects:

Additional Information

Prerequisites

Students are expected to have a basic understanding of:

Calculus II
Differential Equations
Introductory programming (optional)

Policies

Attendance is not mandatory but may influence your continuous evaluation score. Regular attendance is strongly recommended to stay on track with course material.
Students are expected to arrive on time. Late arrivals may disrupt the class and could impact participation evaluation.
Collaboration on assignments, exercises, and projects is encouraged. However, all submissions must reflect individual understanding and adhere to academic integrity policies. Plagiarism or copying will not be tolerated.

Announcements

The midterm will be held on 22 Apr 2025 (2 Ordibehesht 1404) from 08:00 to 10:00. Don’t forget to bring an engineering calculator.

(U): Unfinished ↩︎

Engineering Mathematics

Tue, 12 Nov 2024 00:00:00 +0000

Course Information

Course Title: Engineering Mathematics
Course Code: 2014197-01
Credits: 3
Schedule: Sunday 10:00–12:00 & Monday 14:00-16:00
Location: Class 1 & Class 9
Instructor: Seyed Sadjad Abedi-Shahri
- Email:

Lecture Materials: Provided weekly in .

Course Overview

Learning Objectives

By the end of this course, students will be able to:

Complex Analysis
- Manipulate complex functions and understand their properties
- Apply complex integration techniques
- Use conformal mapping and residue theorem to solve engineering problems
Fourier Analysis
- Understand and apply Fourier series and transforms
- Solve engineering problems using Fourier techniques
Partial Differential Equations (PDEs)
- Classify and solve different types of PDEs (Wave/Heat/Laplace)
- Apply separation of variables and transform methods
- Model physical phenomena using PDEs in engineering contexts

Syllabus

Complex Analysis
Fourier Analysis
Partial Differential Equations

References

[ZIL] Advanced Engineering Mathematics [6th ed.] by Dennis G. Zill
[KRE] Advanced Engineering Mathematics [9th ed.] by Erwin Kreyszig
[ONE] Advanced Engineering Mathematics [7th ed.] by Peter V. O’Neil
[DUF] Advanced Engineering Mathematics with MATLAB [4th ed.] by Dean G. Duffy
[YAN] Engineering Mathematics with MATLAB by Won Y. Yan et al.

Evaluation Scheme

Midterm Evaluation: 30 points
- Complex Analysis
Final Evaluation: 55 points
- Fourier Analysis + Partial Differential Equations
Continuous Evaluation: 15 points
- Based on exercises, quizzes, and participation during lectures and discussions.
Extracurricular Activities (optional): Up to 10 bonus points
- Awarded for participation in activities such as group , presentations, or relevant research outside the classroom.

Session Outline

Session	Date	Outline	Additional Resources
1	30 Shahrivar	Lecture 1 (U)¹	-
2	31 Shahrivar	Lecture 1	[ZIL]:17.1-17.8 & [KRE]: 13.1-13.7 & [ONE]: 19.1-19.5
3	6 Mehr	Lecture 2 (U)	-
4	7 Mehr	Lecture 2	[ZIL]:18.1-18.4 & [KRE]: 14.1-14.4 & [ONE]: 20.1-20.3
5	13 Mehr	Lecture 3 (U)	-
6	14 Mehr	Lecture 3	[ZIL]:19.4-19.6 & [KRE]: 16.2-16.4 & [ONE]: 22.1-22.3
7	20 Mehr	Lecture 4 (U)	-
8	21 Mehr	Lecture 4 + Lecture 5 (U)	[ZIL]:19.4-19.6 & [KRE]: 16.2-16.4 & [ONE]: 22.1-22.3
9	27 Mehr	Lecture 5	[ZIL]:20.1-20.3 & [KRE]: 17.1-17.4 & [ONE]: 23.1-23.2
10	28 Mehr	Ex. 1 + Ex. 2	-
11	25 Aban	Ex. 2 + Ex. 3	-
12	26 Aban	Ex. 4	-
13	27 Aban	Ex. 5	-
14	2 Azar	Lecture 6 (U)	-
15	9 Azar	Lecture 6	[ZIL]:12.1-12.4 & [KRE]: 11.1-11.5 & [ONE]: 13.1-13.6
16	10 Azar	Lecture 7	[ZIL]:13.1-13.2 & [KRE]: 12.1-12.2
17	11 Azar	Lecture 8 (U)	-
18	16 Azar	Lecture 8	[ZIL]:13.3-13.5 & [KRE]: 12.3-12.5
19	17 Azar	Lecture 9(U)	-
20	18 Azar	Lecture 9	[ZIL]:13.6-13.8 & [KRE]: 12.7-12.8
21	23 Azar	Lecture 10 (U)	-
22	24 Azar	Midterm	-
23	25 Azar	Lecture 10	[ZIL]:15.1-15.4 & [KRE]: 11.7-11.9 , 12.6, 12.11
24	30 Azar	Exc. 6	-
25	1 Dey	Exc. 7	-
26	2 Dey	Exc. 8	-
27	7 Dey	Exc. 8 + Exc. 9	-
28	8 Dey	Exc. 9	-

Module 1: Complex Analysis
- Lecture 1: Complex Numbers and Functions
  - Complex Numbers
  - Powers and Roots
  - Sets in the Complex Plane
  - Functions of a Complex Variable
  - Cauchy–Riemann Equations
  - Exponential and Logarithmic Functions
  - Trigonometric and Hyperbolic Functions
  - Inverse Trigonometric and Hyperbolic Functions
- Lecture 2: Complex Integration
  - Contour Integrals
  - Cauchy–Goursat Theorem
  - Independence of the Path
  - Cauchy’s Integral Formulas
- Lecture 3: Series
  - Sequences and Series
  - Taylor Series
  - Laurent Series
- Lecture 4: Residues
  - Zeros and Poles
  - Residues and Residue Theorem
  - Evaluation of Real Integrals
- Lecture 5: Conformal Mappings
  - Complex Functions as Mappings
  - Conformal Mappings
  - Linear Fractional Transformations
Module 2: Partial Differential Equations
- Lecture 6: Orthogonal Functions and Fourier Series
  - Orthogonal Functions
  - Fourier Series
  - Fourier Cosine and Sine Series
  - Complex Fourier Series
- Lecture 7: Boundary-Value Problems in Rectangular Coordinates - Part 1
  - Separable Partial Differential Equations
  - Classical PDEs and Boundary-Value Problems
- Lecture 8: Boundary-Value Problems in Rectangular Coordinates - Part 2
  - Heat Equation
  - Wave Equation
  - Laplace Equation
- Lecture 9: Boundary-Value Problems in Rectangular Coordinates - Part 3
  - Nonhomogeneous Boundary-Value Problems
  - Orthogonal Series Expansions
  - Fourier Series in Two Variables
- Lecture 10: Integral Transform Method
  - Error Function
  - Applications of the Laplace Transform
  - Fourier Integral
  - Fourier Transforms

Projects:

Additional Information

Prerequisites

Students are expected to have a basic understanding of:

Calculus II
Differential Equations
Introductory programming (optional)

Policies

Regular attendance is strongly recommended to stay on track with course material and acquire continuous evaluation score
Students are expected to arrive on time. Late arrivals may disrupt the class and could impact participation evaluation.
Collaboration on assignments, exercises, and projects is encouraged. However, all submissions must reflect individual understanding and adhere to academic integrity policies. Plagiarism or copying will not be tolerat

(U): Unfinished ↩︎

Heat and Mass Transfer

Tue, 12 Nov 2024 00:00:00 +0000

Course Information

Course Title: Heat and Mass Transfer
Course Code: 2014368
Credits: 3
Class Schedule:
- Days: Monday, Tuesday
- Time: 10:00-12:00
Class Location: Class 2, Class 30
Instructor: Seyed Sadjad Abedi-Shahri
- Email:
- Office Hours:

Lecture Materials: Provided weekly in .

Course Overview

A foundational engineering course covering heat and mass transfer principles, mechanisms, and applications. The course progresses systematically through conduction, convection, and mass transfer, incorporating selected biomedical examples to demonstrate real-world applications in biological systems.

Learning Objectives

Apply fundamental principles of heat and mass transfer
Solve steady-state and transient conduction problems in multiple dimensions
Analyze forced convection in external and internal flows
Evaluate natural convection scenarios
Derive and solve governing equations for transport phenomena
Use analytical and numerical methods for heat transfer problems
Apply heat and mass transfer principles to (bio)engineering design problems

Syllabus

Introduction to Heat Transfer
Introduction to Conduction
Steady-State Conduction
Transient Conduction
Introduction to Convection
External Flow Convection
Internal Flow Convection
Mass Transfer

References

[BER] Fundamentals of Heat and Mass Transfer [8th ed.] by Theodore L. Bergman, Adrienne S. Lavine
[CEN] Heat and Mass Transfer, Fundamentals & Applications [6th ed.] by Yunus A. Cengel, Afshin J. Ghajar
[DAT] Heat and Mass Transfer, A Biological Context [2nd ed.] by Ashim K. Datta

Evaluation Scheme

Midterm Evaluation: 40 points
- Modules 1 to 4
Final Evaluation: 45 points
- Modules 5 to 9
Continuous Evaluation: 15 points
- Based on exercises, quizzes, and participation during lectures and discussions.
Extracurricular Activities (optional): Up to 10 bonus points
- Awarded for participation in activities such as group , presentations, or relevant research outside the classroom.

Session Outline

Session	Date	Outline	Additional Resources
1	23 Bahman	Lecture 1	[BER]: 1.1-1.7 & [CEN]: 1.1-1.15 & [DAT]: 1.1-1.9, 2.1-2.7
2	29 Bahman	Lecture 2	[BER]: 2.1-2.4 & [CEN]: 2.1-2.4 & [DAT]: 3.1-3.10
3	30 Bahman	Lecture 3 (U)¹	-
4	13 Esfand	Lecture 3 + Lecture 4 (U)	[BER]: 3.1-3.5 & [CEN]: 2.5-2.7, 3.1-3.5 & [DAT]: 4.1-4.4
5	14 Esfand	Lecture 4	[BER]: 3.6-3.7.1 & [CEN]: 3.6-3.7 & [DAT]: 4.5-4.8
6	20 Esfand	Lecture 5 (U)	-
7	21 Esfand	Lecture 5	[BER]: 4.1-4.6 & [CEN]: 3.8, 5.1-5.4
8	18 Farvardin	Lecture 6	[BER]: 5.1-5.3 & [CEN]: 4.1 & [DAT]: 5.1-5.2
9	19 Farvardin	Exc. 1 + Exc. 2 + Exc. 3	-
10	25 Farvardin	Lecture 7 (U)	-
11	26 Farvardin	Lecture 7	[BER]: 5.4-5.7, 5.10 & [CEN]: 4.2-4.3, 5.5 & [DAT]: 5.3-5.5
12	1 Ordibehesht	Exc. 4 + Exc. 5	-
13	2 Ordibehesht	Lecture 8	[CEN]: 6.1-6.5
14	8 Ordibehesh	Lecture 9 (U)	-
15	9 Ordibehesht	Lecture 9	[CEN]: 6.6-6.11
16	15 Ordibehesht	Exc. 6	-
17	16 Ordibehesht	Lecture 10 (U)	-
18	20 Ordibehesht	Exc. 7	-
19	22 Ordibehesht	Lecture 10	[CEN]: 7.1-7.3
20	23 Ordibehesht	Lecture 11 (U)	-
21	29 Ordibehesht	Lecture 11	[CEN]: 8.1-8.6
22	30 Ordibehesht	Lecture 12 (U)	-
23	5 Khordad	Review	-
24	6 Khordad	Midterm Exam	-
24	12 Khordad	Lecture 12	[CEN]: 14.1-14.5

Module 1: Introduction to Heat Transfer
- Lecture 1: Introduction to Heat Transfer
  - What is heat transfer?
  - Physical Origins and Rate Equations
  - Review of Thermodynamics
Module 2: Introduction to Conduction
- Lecture 2: Introduction to Conduction
  - The Conduction Rate Equation
  - The Thermal Properties of Matter
  - The Heat Diffusion Equation
  - Boundary and Initial Conditions
Module 3: Steady-State Conduction
- Lecture 3: One-Dimensional Conduction
  - The Plane Wall
  - An Alternative Conduction Analysis
  - Radial Systems
  - Conduction with Thermal Energy Generation
- Lecture 4: Applications of One-Dimensional, Steady-State Conduction
  - Heat Transfer from Extended Surfaces
  - The Bioheat Equation
- Lecture 5: Two-Dimensional Conduction
  - General Considerations and Solution Techniques
  - The Method of Separation of Variables
  - The Conduction Shape Factor and the Dimensionless Conduction Heat Rate
  - Finite-Difference Equations
Module 4: Transient Conduction
- Lecture 6: Lumped Systems
  - The Lumped Capacitance Method
  - Validity of the Lumped Capacitance Method
  - General Lumped Capacitance Analysis
- Lecture 7: Finite and Semi-Infinite Solids
  - Spatial Effects
  - The Plane Wall with Convection
  - Radial Systems with Convection
  - The Semi-Infinite Solid
  - Finite-Difference Methods
Module 5: Introduction to Convection
- Lecture 8: Physical Mechanism
  - Physical Mechanism of Convection
  - Classification of Fluid Flows
  - Velocity Boundary Layer
  - Thermal Boundary Layer
  - Laminar and Turbulent Flows
- Lecture 9: Governing Equations
  - Derivation of Differential Convection Equations
  - Solutions of Convection Equations for a Flat Plate
  - Nondimensionalized Convection Equations and Similarity
  - Functional Forms of Friction and Convection Coefficients
  - Analogies Between Momentum and Heat Transfer
Module 6: External Flow Convection
- Lecture 10: External Flow Convection
  - Drag and Heat Transfer in External Flow
  - Parallel Flow Over Flat Plates
  - Flow Across Cylinders and Spheres
Module 7: Internal Flow Convection
- Lecture 11: Internal Flow Convection
  - Average Velocity and Temperature
  - The Entrance Region
  - General Thermal Analysis
  - Laminar Flow in Tubes
  - Turbulent Flow in Tubes
Module 8: Mass Transfer
- Lecture 12: Mass Diffusion
  - Analogy Between Heat and Mass Transfer
  - Mass Diffusion
  - Boundary Conditions
  - Steady Mass Diffusion Through a Wall

Projects:

Additional Information

Prerequisites

Students are expected to have a basic understanding of:

Engineering Mathematics
Thermodynamics
Fluid Mechanics

Policies

Attendance is not mandatory but may influence your continuous evaluation score. Regular attendance is strongly recommended to stay on track with course material.
Students are expected to arrive on time. Late arrivals may disrupt the class and could impact participation evaluation.
Collaboration on assignments, exercises, and projects is encouraged. However, all submissions must reflect individual understanding and adhere to academic integrity policies. Plagiarism or copying will not be tolerated.

Announcements

The midterm will be held on 12 May 2025 (22 Ordibehesht 1404) from 08:00 to 10:00. Don’t forget to bring an engineering calculator.

(U): Unfinished ↩︎

TPIC 2024 - Oral Presentation

Fri, 08 Nov 2024 00:00:00 +0000

Deep Learning-Based Quantitative Assessment of Pulmonary Vascular Changes Using Histological Microscopy Images

Fri, 01 Nov 2024 00:00:00 +0000

Analysis of Hip Implants in Osteoporotic Patients Using the Finite Element Method for Optimal Selection Among Commercially Available Implants

Sat, 10 Aug 2024 00:00:00 +0000

Constructing Complex Shapes with Signed Distance Functions: The Heart Example

Sun, 07 Apr 2024 00:00:00 +0000

In this notebook, we’ll implement a signed distance function for a heart shape using Python and visualize it using matplotlib.

Function Definitions

The following functions are defined:

line_sdf: Calculates the signed distance from a point to a line segment.
circle_sdf: Calculates the signed distance from a point to a circle.
intersect_sdf: Calculates the signed distance field resulting from the intersection of two distance fields.
union_sdf: Calculates the signed distance field resulting from the union of two distance fields.

 1import numpy as np
 2import matplotlib.pyplot as plt
 3
 4def line_sdf(P, x1, y1, x2, y2):
 5 """
 6 Calculate the signed distance from a point P to a line segment
 7 defined by two endpoints (x1, y1) and (x2, y2).
 8 """
 9
10 a = np.array([x2 - x1, y2 - y1])
11 a = a / np.linalg.norm(a)
12 b = P - np.array([x1, y1])
13 d = np.dot(b, np.array([a[1], -a[0]]))
14 return d
15
16def circle_sdf(P, xc, yc, r):
17 """
18 Calculate the signed distance from a point P to a circle defined by its center (xc, yc) and radius r.
19 """
20 return np.sqrt((P[0] - xc) ** 2 + (P[1] - yc) ** 2) - r
21
22def intersect_sdf(d1, d2):
23 """
24 Calculate the signed distance field resulting from the intersection of two distance fields (d1 and d2).
25 """
26 return max(d1, d2)
27
28def union_sdf(d1, d2):
29 """
30 Calculate the signed distance field resulting from the union of two distance fields (d1 and d2).
31 """
32 return min(d1, d2)

Tangent Point Calculation

The find_tangent_point function finds the tangent point that has a specified distance from the bottom tip of the heart shape. This function is inspired by and .

 1def find_tangent_point(x1, y1, d1, x2, y2, d2):
 2 """
 3 Find the tangent point that has radius(d1) distance from center of circle
 4 and calculated distance (d2) from the bottom tip of the heart. The result is
 5 limited to desired tangent point.
 6 """
 7
 8 centerdx = x1 - x2
 9 centerdy = y1 - y2
10 R = np.sqrt(centerdx**2 + centerdy**2)
11
12 if not (abs(d1 - d2) <= R and R <= d1 + d2):
13 # No intersections
14 return []
15
16 d1d2 = d1**2 - d2**2
17 a = d1d2 / (2 * R**2)
18
19 c = np.sqrt(2 * (d1**2 + d2**2) / R**2 - (d1d2**2) / R**4 - 1)
20
21 fx = (x1 + x2) / 2 + a * (x2 - x1)
22 gx = c * (y2 - y1) / 2
23 # ix1 = fx + gx
24 ix2 = fx - gx
25
26 fy = (y1 + y2) / 2 + a * (y2 - y1)
27 gy = c * (x1 - x2) / 2
28 # iy1 = fy + gy
29 iy2 = fy - gy
30
31 return [ix2, iy2]

Heart Shape SDF

The heart_sdf function calculates the signed distance from a point to a heart shape defined by two circles and three line segments.

 1def heart_sdf(p, r=4):
 2 """
 3 Calculate the signed distance from a point P to a heart shape defined by two circles and three line segments.
 4
 5 The heart shape consists of two circles representing the left and right sides, and three line segments representing the bottom tip and the tangent lines connecting the circles.
 6
 7 Parameters:
 8 p (tuple): A tuple containing the coordinates (x, y) of the point P.
 9 r (float): The radius of the heart shape. Default is 4.
10
11 Returns:
12 float: The signed distance from the point P to the heart shape. Negative values indicate that the point is inside the heart shape, zero indicates that the point is on the boundary, and positive values indicate that the point is outside the heart shape.
13
14 Note:
15 The heart shape is constructed based on mathematical equations and geometric calculations. The function utilizes signed distance functions (SDFs) for circles and lines to determine the distance from the point P to various components of the heart shape.
16 """
17 # Some experimental ratio for the center of circles based on their radius
18 a = r * 3 / 4
19
20 circle1 = circle_sdf(p, -a, 0, r) # Left Circle
21 circle2 = circle_sdf(p, a, 0, r) # Right Circle
22
23 # Distance from bottom tip to center of circles
24 d2c = np.sqrt((a - 0) ** 2 + (0 - 2 * a - r) ** 2)
25
26 # Distance to tangent point of circle using Pythagorean theorem
27 d2t = np.sqrt(d2c**2 - r**2)
28
29 tpr = find_tangent_point(
30 a, 0, r, 0, -2 * a - r, d2t
31 ) # Tangent point on right circle
32
33 line1 = line_sdf(p, -tpr[0], tpr[1], 0, -2 * a - r)
34 line2 = line_sdf(p, 0, -2 * a - r, tpr[0], tpr[1])
35 line3 = line_sdf(p, tpr[0], tpr[1], -tpr[0], tpr[1])
36
37 # Create a triangle which base is the line that
38 # connects tangent points and the vertex point is heart bottom tip
39
40 dl = intersect_sdf(intersect_sdf(line1, line2), line3)
41
42 d = union_sdf(union_sdf(circle1, circle2), dl)
43
44 return d

Visualization

The plot_sdf function plots the signed distance function. This function is adopted from project.

 1def plot_sdf(SDF, BdBox=[-10, 10, -12, 8], n=300):
 2 """
 3 Plots the signed distance function.
 4 """
 5 x, y = np.meshgrid(
 6 np.linspace(BdBox[0], BdBox[1], n),
 7 np.linspace(BdBox[2], BdBox[3], n),
 8 )
 9 points = np.hstack([x.reshape((-1, 1)), y.reshape((-1, 1))])
10
11 sdf = np.fromiter(map(SDF, points), dtype=float)
12
13 inner = np.where(sdf <= 0, 1, 0)
14
15 _, ax = plt.subplots(figsize=(8, 6))
16 _ = ax.imshow(
17 inner.reshape((n, n)),
18 extent=(BdBox[0], BdBox[1], BdBox[2], BdBox[3]),
19 origin="lower",
20 cmap="Reds",
21 alpha=0.8,
22 )
23 ax.contour(x, y, sdf.reshape((n, n)), levels=[0], colors="gold", linewidths=2)
24 ax.set_xlabel("X", fontweight="bold")
25 ax.set_ylabel("Y", fontweight="bold")
26 ax.set_title("SDF Visualization", fontweight="bold", fontsize=16)
27 ax.set_aspect("equal")
28
29 plt.show()

Now let’s execute the plot_sdf function to visualize the signed distance function for the heart shape.

1plot_sdf(heart_sdf)

The full code, ready to copy and try, is also available at .

Exploring Boolean Operations in SDFs: Union, Difference, and Intersection

Mon, 18 Mar 2024 00:00:00 +0000

In our of Signed Distance Functions (SDFs), we unveiled their power in representing and manipulating geometric shapes. We also delved into the intricacies of SDFs for lines and rectangles. Now, let’s unlock the potential of Boolean operations on SDFs, enabling the creation of even more complex shapes.

Merging Shapes with Union: A Powerful Tool

The Union operation in SDFs allows us to combine two or more shapes, essentially merging them into a single new shape. Mathematically, the union of two SDFs, $SDF_1$ and $SDF_2$, representing shapes A and B respectively, can be expressed as:

$$ SDF_{Union}(P) = min(SDF_1(P), SDF_2(P)) $$

This operation essentially takes the minimum distance value from either SDF at each point (P). Points outside of both shape A or B will have a positive SDF value, indicating they lie outside the combined shape. Points within both shapes A and B will have a negative value, signifying their position inside the resulting union shape.

Union of Two Circles

The visualization of the union of two circles SDF is also available at using module.

Carving Shapes with Difference: Subtracting One from Another

The Difference operation in Signed Distance Functions (SDFs) enables us to sculpt one shape by subtracting another. Mathematically, the difference of $SDF1$ and $SDF2$, representing shapes A and B respectively, can be defined as:

$$ SDF_{Difference}(P)=max(SDF_1(P),−SDF_2(P)) $$

Here, the negative of $SDF_2$ is taken prior to the maximum operation. This action effectively reverses the sign of distances originating from shape B. Points lying outside both shapes, as well as points residing inside shape A but also within shape B, will yield a positive SDF value. This indicates that they belong to the exterior of the resultant shape after the difference operation. Points situated within shape A but outside shape B will generate a negative value, denoting their inclusion within the final difference shape.

Difference of Two Circles (Circle 1 - Circle 2)

The visualization of the difference of two circles SDF is also available at using module.

Finding the Common Ground: Intersection of Shapes

The Intersection operation in SDFs allows us to identify the region where two shapes overlap. Mathematically, the intersection of $SDF_1$ and $SDF_2$ can be expressed as:

$$ SDF_{Intersection}(P) = max(SDF_1(P), SDF_2(P)) $$

In this case, the maximum distance value is taken. Points outside both shapes A and B will have positive SDF values. Points inside either shape A or B (but not their overlap) will also have positive values. Points that lie within the overlapping region of both shapes A and B will have a negative SDF value, signifying their location within the intersection.

Intersection of Two Circles

The visualization of the intersection of two circles SDF is also available at using module.

A Composition of Lines: The SDF of a Rectangle

While we’ve explored circles and other shapes, it’s important to remember that even seemingly basic shapes can be constructed using SDFs and Boolean operations. Take a rectangle, for instance. We can define a rectangle as the intersection of four lines, each representing the distance to an edge:

The distance to the top edge of the rectangle.
The distance to the bottom edge.
The distance to the left edge.
The distance to the right edge.

Rectangle SDF

The visualization of the rectangle defined by intersection of 4 lines is also available at using module.

The order of these intersections does not matter. Taking the maximum distance (intersection) from all four lines simultaneously would define a rectangle. Alternatively, we can perform the intersection progressively.

This concept extends beyond rectangles. Any polygon can be defined similarly using the intersection of line SDFs representing distances to its edges.

Defining Complex Domains with SDF Boolean Operations

By mastering Boolean operations on SDFs, we unlock the ability to create mathematically defined representations of even intricate 2D domains. From simple geometric shapes to elaborate, user-defined patterns, these techniques empower us to model a vast array of scenarios. This opens doors for various applications, from scientific simulations to artistic expression, all leveraging the power of mathematics and code to define complex shapes and spaces.

Session 1: Introduction to Python

Fri, 15 Mar 2024 00:00:00 +0000

Session 1: Introduction to Python

Instructor :

Introduction to Programming

Programming is the process of creating a set of instructions or logic that can be understood and executed by a computer to perform a specific task or solve a problem. It involves breaking down complex problems into smaller, more manageable steps that the computer can follow.

Programming languages are the tools used to communicate instructions to computers. They provide a structured way to express algorithms, which are sets of rules or procedures for solving problems. Different programming languages have their own syntax (rules for writing code) and semantics (meaning of the code).

Why Learn Programming?

Problem-solving: Programming teaches logical thinking and problem-solving skills.
Career opportunities: Programming skills are in high demand across various industries.
Automation: Programming allows you to automate repetitive tasks, saving time and increasing productivity.
Creation: Programming empowers you to create software applications, websites, games, and other digital products.
Understanding technology: Having a basic understanding of programming helps you better comprehend the technologies you use daily.

What is Python?

Python is a popular, high-level, general-purpose programming language known for its simplicity, readability, and versatility. It was created by Guido van Rossum in the late 1980s and first released in 1991.

Key Features of Python

Easy to learn: Python has a clean and straightforward syntax that emphasizes readability, making it easy for beginners to learn and understand.
Interpreted: Python is an interpreted language, which means that its code is executed line by line without the need for a separate compilation step, allowing for faster development and testing cycles.
Cross-platform: Python code can run on various operating systems, including Windows, macOS, and Linux, without requiring significant modifications.

Dynamically-typed: Python is a dynamically-typed language, which means that variable types are determined during runtime, providing flexibility and reducing development time.
Extensive libraries: Python has a vast collection of standard and third-party libraries and frameworks that cover a wide range of applications, from web development to data analysis, machine learning, and more.
Open-source: Python is an open-source language, which means its source code is freely available for use, modification, and distribution, fostering a strong community of developers.

Python Applications

Web Development: Python is widely used for building web applications and frameworks like Django, Flask, and Pyramid.
Data Analysis and Scientific Computing: Libraries like NumPy, Pandas, Matplotlib, and SciPy make Python a powerful tool for data analysis, manipulation, and visualization.
Artificial Intelligence and Machine Learning: Popular libraries like TensorFlow, Keras, and scikit-learn enable Python for AI and machine learning applications.

Automation and Scripting: Python’s simplicity and cross-platform compatibility make it an excellent choice for automating tasks and writing scripts.
Game Development: With libraries like Pygame and Panda3D, Python can be used to create games.
Education and Prototyping: Python’s readability and ease of use make it a popular choice for teaching programming and building prototypes.

Setting up the Python Environment

To start programming in Python, you need to set up the Python environment on your computer. This involves installing the Python interpreter and an Integrated Development Environment (IDE) or a code editor. In this bootcamp, we will be using the Anaconda distribution and the Spyder IDE.

Anaconda Distribution

Anaconda is a popular open-source distribution of Python and other data science packages. It comes bundled with Python, the Conda package manager, and various pre-installed libraries and tools for data science, machine learning, and scientific computing.

To install Anaconda, follow these steps:

Go to the official Anaconda website ( ) and download the latest version of Anaconda for your operating system (Windows, macOS, or Linux).
Run the downloaded installer and follow the prompts to complete the installation process.

After the installation is complete, you will have access to the Anaconda Navigator, which is a graphical user interface (GUI) that allows you to launch applications and manage conda packages, environments, and channels.

Spyder IDE

Spyder (Scientific Python Development Environment) is a powerful IDE that comes bundled with Anaconda. It provides a user-friendly interface for writing, debugging, and executing Python code, as well as advanced features such as code completion, code exploration, and integration with popular scientific libraries like NumPy, SciPy, and Matplotlib.

To launch Spyder, you can either:

Open the Anaconda Navigator and click on the “Launch” button next to the Spyder application.
Open the Anaconda Prompt (on Windows) or the terminal (on macOS/Linux) and type spyder.

The Spyder IDE consists of three main panels:

Editor: This is where you write and edit your Python code.
IPython Console: This is an interactive Python shell where you can run code and see the output immediately.
Variable Explorer: This panel displays the variables and their values in your current workspace.

Python Syntax

Python’s syntax is designed to be simple, readable, and easy to learn. Here’s a quick overview of some essential syntax elements:

Comments

1# This is a single-line comment
2
3"""
4This is a
5multi-line comment
6"""

Indentation

Python uses indentation to define code blocks instead of curly braces or keywords like begin and end. Proper indentation is crucial for Python code to run correctly.

1if condition:
2 # Indented block
3 statement1
4 statement2
5else:
6 # Indented block
7 statement3

Variables

Variables in Python don’t need to be explicitly declared. You can assign values to variables directly.

1x = 5 # Integer
2y = 3.14 # Float
3name = "Sadjad Abedi" # String
4is_true = True # Boolean

Data Types

Python supports several built-in data types, including:

Numbers

Python supports two main types of numbers: integers and floating-point numbers.

1x = 31 # Integer
2y = 3.14 # Float
3z = 1 + 3j # Complex number

Strings

Strings in Python are sequences of characters enclosed in single quotes (’), double quotes ("), or triple quotes (’’’ or """).

1name = "Sadjad Abedi"
2message = 'Hello, World!'
3multiline = """This is
4a multiline
5string."""

Lists

Lists are ordered collections of items, which can be of different data types.

1fruits = ["apple", "banana", "cherry"] # List of strings
2numbers = [1, 2, 3, 4, 5] # List of integers
3mixed = [1, "apple", 3.14, True] # Mixed data types

List Operations

1len(fruits) # Get the length of the list
2fruits[0] # Access the first element
3fruits[-1] # Access the last element
4fruits[1:3] # Get a slice (from index 1 to 3)
5fruits.append("orange") # Add an element to the end
6fruits.insert(1, "kiwi") # Insert an element at a specific index
7fruits.remove("banana") # Remove the first occurrence of an element
8fruits.pop(2) # Remove the element at a specific index

Basic Input/Output Operations

Python provides several built-in functions for handling input and output operations, allowing you to interact with users and work with files.

Input

The input() function is used to get user input from the console or terminal. It takes an optional prompt string as an argument and returns the user’s input as a string.

1name = input("Enter your name: ")
2print("Hello, " + name)

By default, input() returns a string.

If you need to work with other data types, such as integers or floats, you can use type conversion functions like int() or float().

1age = int(input("Enter your age: "))
2weight = float(input("Enter your weight (kg): "))

Output

The print() function is used to display output to the console or terminal.

1print("Hello, World!")

You can print multiple values by separating them with commas, and you can customize the separator and end characters using the sep and end parameters, respectively.

1print("Apple", "Banana", "Cherry", sep=", ") # Output: Apple, Banana, Cherry
2print("Hello", end="")
3print("World") # Output: HelloWorld

File Operations

Python provides several functions and methods for working with files, including reading from and writing to files.

Writing to a File

To write to a file, you first need to open it in write mode (“w”) or append mode (“a”). Then, you can use the write() method to write data to the file.

1file = open("data.txt", "w") # Open a file for writing
2file.write("Hello, World!")
3file.close() # Don't forget to close the file

Reading from a File

To read from a file, you need to open it in read mode (“r”). Then, you can use methods like read() or readline() to read the contents of the file.

1file = open("data.txt", "r")
2content = file.read() # Read the entire file
3print(content)
4file.close()

Alternatively, you can use a for loop to read the file line by line.

1file = open("data.txt", "r")
2for line in file:
3 print(line.strip()) # Strip leading/trailing whitespace
4file.close()

Python also provides a convenient with statement to automatically handle opening and closing files.

1with open("data.txt", "r") as file:
2 content = file.read()
3 print(content)

Questions?

Session 2: Control Flow and Functions

Fri, 15 Mar 2024 00:00:00 +0000

Session 2: Control Flow and Functions

Instructor :

Control flow statements in Python allow you to control the order of execution of your code based on certain conditions or loops. These statements are essential for creating dynamic and flexible programs.

Conditional Statements

Conditional statements allow you to execute different blocks of code based on certain conditions. Python uses the if, elif (else if), and else statements for this purpose.

`if` Statement

The if statement executes a block of code if the specified condition is True.

1x = 5
2
3if x > 0:
4 print("x is positive")

`elif` Statement

The elif statement allows you to check for additional conditions if the previous conditions were False.

1x = 0
2
3if x > 0:
4 print("x is positive")
5elif x < 0:
6 print("x is negative")
7else:
8 print("x is zero")

`else` Statement

The else statement is executed if all the previous conditions in the if and elif statements were False.

1age = 18
2
3if age < 13:
4 print("You are a child")
5elif age < 20:
6 print("You are a teenager")
7else:
8 print("You are an adult")

Loops

Loops are used to repeat a block of code multiple times. Python provides two types of loops: for loops and while loops.

`for` Loop

The for loop is used to iterate over a sequence (such as a list, tuple, string, or range) or other iterable objects.

1fruits = ["apple", "banana", "cherry"]
2
3for fruit in fruits:
4 print(fruit)

You can also use the range() function to generate a sequence of numbers for the for loop.

1for i in range(5):
2 print(i) # Output: 0 1 2 3 4

`while` Loop

The while loop executes a block of code as long as the specified condition is True.

1count = 0
2while count < 5:
3 print(count)
4 count += 1 # Increment the counter

Loops can be nested (one loop inside another loop) to create more complex patterns or iterate over multi-dimensional data structures.

1for i in range(3):
2 for j in range(2):
3 print(f"({i}, {j})")

Functions

Functions are reusable blocks of code that perform a specific task. They help organize code into logical units, improve code readability, and promote code reuse. In Python, functions are defined using the def keyword, followed by the function name, parentheses for arguments, and a colon.

Defining Functions

Here’s the basic syntax for defining a function:

1def function_name(parameters):
2 """
3 Docstring: A brief description of what the function does.
4 """
5 # Function body
6 # Code to be executed
7 return value

def is the keyword used to define a function.
function_name is the name you give to the function (follow naming conventions).
parameters are optional inputs that the function can accept (separated by commas).
The """Docstring""" is a multi-line string that provides a brief description of the function (optional but recommended).
The function body is the block of code that will be executed when the function is called.
The return statement is used to return a value from the function (optional).

Example:

1def greet(name):
2 """
3 Prints a greeting message with the provided name.
4 """
5 print(f"Hello, {name}!")
6
7greet("Alice") # Output: Hello, Alice!

Calling Functions

To use a function, you need to call it by its name, followed by parentheses and any required arguments.

1result = my_function(argument1, argument2)

Functions can return values using the return statement, which can be assigned to variables or used in expressions.

1def add_numbers(a, b):
2 """
3 Returns the sum of two numbers.
4 """
5 return a + b
6
7sum = add_numbers(3, 5)
8print(sum) # Output: 8

Scope and Namespaces

In Python, variables and functions have a scope, which determines their visibility and accessibility within the program. Understanding scope and namespaces is crucial for managing variable names and avoiding naming conflicts.

Scope

The scope of a variable or function refers to the region of the code where it is accessible. Python has several types of scope:

Local Scope: Variables defined within a function are local to that function and cannot be accessed outside of it. Their scope is limited to the function in which they are defined.

Global Scope: Variables defined outside of any function or class are global and can be accessed from anywhere in the program, including within functions.
Built-in Scope: Names that are part of the Python language itself, such as print, len, and range, have a built-in scope and are always available.

Example:

1x = 10 # Global variable
2
3def my_function():
4 y = 5 # Local variable
5 print(x) # Accessing global variable
6 print(y)
7
8my_function() # Output: 10, 5
9print(y) # Error: y is not defined (outside the function scope)

Namespaces

While scope determines the visibility and accessibility of variables and functions, namespaces are mapping structures that associate names (identifiers) with objects (variables, functions, etc.). Python maintains several namespaces:

Built-in Namespace: Contains names of built-in functions, exceptions, and other objects. This namespace is always available.

Global Namespace: Contains names defined at the top level of a module or script. Variables and functions defined outside any function or class reside in this namespace.
Local Namespace: Contains names defined inside a function or class. Variables and functions defined within a function or class reside in this namespace.

When Python tries to resolve a name (e.g., a variable or function), it searches the namespaces in the following order:

Local Namespace
Enclosing Namespaces (if nested functions or classes)
Global Namespace
Built-in Namespace

The scope of a variable or function determines which namespace it belongs to and where it can be accessed. The namespaces themselves are the structures that store and map these names to their corresponding objects.

Introducing CodeWars

CodeWars is an educational online platform that helps developers improve their coding skills through practice and gamification. It provides a vast collection of coding challenges, also known as “katas”, which cover a wide range of programming languages and concepts.

What are Katas?

Katas are coding challenges that range in difficulty from beginner to expert level. Each kata presents a problem statement and a set of requirements that you must fulfill by writing code that passes a series of test cases. Katas are designed to help you practice your problem-solving skills, learn new language features, and improve your coding proficiency.

Getting Started with CodeWars

To get started with CodeWars, follow these steps:

Sign Up: Visit the CodeWars website ( ) and create an account.
Choose a Language: Select the programming language you want to practice. CodeWars supports many popular languages, including Python, Java, JavaScript, C#, and more.

Browse Katas: Explore the available katas by difficulty level or topic. You can filter katas based on your preferences or search for specific keywords.
Attempt a Kata: Click on a kata to view its problem statement and requirements. CodeWars provides an online code editor where you can write and test your solution.

Submit Your Solution: Once you’ve written your code, submit it to the CodeWars platform. Your solution will be tested against a set of test cases, and you’ll receive feedback on whether it passed or failed.
Learn from Others: CodeWars allows you to view other users’ solutions to the same kata. You can learn from these solutions and gain insights into different problem-solving approaches.

Optionally, You can join the Clan “Scicho” by setting this name as clan name in your profile. You can also follow the instructor using this Link:

There is also a collection of katas that most fit your current proficiency:

Tutorial Videos

Questions?

Session 3: Data Structures

Fri, 15 Mar 2024 00:00:00 +0000

Session 3: Data Structures

Instructor :

Python provides several built-in data structures that allow you to organize and store data efficiently. In this session, we’ll explore data structures in Python.

Lists

Lists are ordered collections of items, which can be of different data types. They are mutable, meaning you can modify, add, or remove elements after creating the list.

Creating Lists

Lists are defined using square brackets [] and elements are separated by commas.

1fruits = ["apple", "banana", "cherry"]
2numbers = [1, 2, 3, 4, 5]
3mixed = [1, "apple", 3.14, True]

List Operations

Lists support various operations, such as indexing, slicing, concatenation, and more.

 1fruits = ["apple", "banana", "cherry"]
 2
 3print(len(fruits)) # Get the length of the list (Output: 3)
 4print(fruits[0]) # Access the first element (Output: "apple")
 5print(fruits[-1]) # Access the last element (Output: "cherry")
 6print(fruits[1:3]) # Get a slice (from index 1 to 3) (Output: ["banana", "cherry"])
 7fruits.append("orange") # Add an element to the end
 8fruits.insert(1, "kiwi") # Insert an element at a specific index
 9fruits.remove("banana") # Remove the first occurrence of an element
10fruits.pop(2) # Remove the element at a specific index

Lists are versatile and commonly used for storing and manipulating collections of data in Python.

Tuples

Tuples are ordered collections of items, similar to lists, but they are immutable, meaning you cannot modify, add, or remove elements after creating the tuple.

Creating Tuples

Tuples are defined using parentheses () and elements are separated by commas.

1point = (3, 4)
2person = ("John", 32, "Programmer")
3empty_tuple = ()

Alternatively, you can create tuples without parentheses if there is a comma separating the elements.

1point = 3, 4
2single_element_tuple = 1, # Note the trailing comma

Tuple Operations

Although tuples are immutable, you can perform various operations on them, such as indexing, slicing, and concatenation.

1person = ("John", 32, "Programmer")
2
3print(len(person)) # Get the length of the tuple (Output: 3)
4print(person[0]) # Access the first element (Output: "John")
5print(person[-1]) # Access the last element (Output: "Programmer")
6print(person[1:3]) # Get a slice (from index 1 to 3) (Output: (32, "Programmer"))

Tuples are commonly used for storing and handling collections of related but immutable data, such as coordinates, database records, or configuration settings.

Sets

Sets are unordered collections of unique elements. They are mutable, meaning you can add or remove elements after creating the set. Sets are useful for performing mathematical operations like union, intersection, and difference on collections of elements.

Creating Sets

Sets are defined using curly braces {} or the set() function.

1fruits = {"apple", "banana", "cherry"}
2numbers = set([1, 2, 3, 4, 4, 5]) # Duplicates are automatically removed

Set Operations

Sets support various operations, such as adding and removing elements, performing set operations, and more.

 1fruits = {"apple", "banana", "cherry"}
 2
 3fruits.add("orange") # Add an element to the set
 4fruits.remove("banana") # Remove an element from the set
 5fruits.discard("kiwi") # Remove an element if it exists (no error if not)
 6
 7numbers = {1, 2, 3, 4, 5}
 8even_numbers = {2, 4, 6, 8}
 9
10print(numbers | even_numbers) # Union (Output: {1, 2, 3, 4, 5, 6, 8})
11print(numbers & even_numbers) # Intersection (Output: {2, 4})
12print(numbers - even_numbers) # Difference (Output: {1, 3, 5})

Sets are useful for removing duplicates, performing mathematical operations on collections, and maintaining an unordered collection of unique elements.

Dictionaries

Dictionaries are unordered collections of key-value pairs. They are mutable, meaning you can add, modify, or remove key-value pairs after creating the dictionary. Dictionaries are useful for storing and retrieving data based on keys.

Creating Dictionaries

Dictionaries are defined using curly braces {} with key-value pairs separated by colons.

1person = {"name": "John", "age": 32, "occupation": "Programmer"}
2empty_dict = {}

Dictionary Operations

Dictionaries support various operations, such as accessing, adding, modifying, and removing key-value pairs.

1person = {"name": "John", "age": 32, "occupation": "Programmer"}
2
3print(person["name"]) # Access the value associated with the "name" key (Output: "John")
4person["age"] = 33 # Modify the value associated with the "age" key
5person["location"] = "USA" # Add a new key-value pair
6del person["occupation"] # Remove a key-value pair
7for key, value in person.items():
8 print(f"{key}: {value}") # Iterate over key-value pairs

Dictionaries are used for storing and retrieving data based on keys, representing structured data like objects or records, and implementing efficient lookup and retrieval operations.

List Comprehensions

List comprehensions in Python provide a concise and efficient way to create lists from existing iterables (such as lists, tuples, or strings) based on specific conditions or transformations. They offer a more readable and expressive syntax compared to traditional for loops and can often lead to more compact and optimized code.

Basic Syntax

The basic syntax for a list comprehension is as follows:

1new_list = [expression for item in iterable]

new_list: The new list created by the list comprehension.
expression: The operation or transformation applied to each item in the iterable.
item: The variable representing each element in the iterable.
iterable: The sequence (list, tuple, string, etc.) from which the elements are drawn.

Example:

1numbers = [1, 2, 3, 4, 5]
2squared_numbers = [x**2 for x in numbers]
3print(squared_numbers) # Output: [1, 4, 9, 16, 25]

In this example, the list comprehension creates a new list squared_numbers by squaring each element x in the numbers list.

Using Conditionals

List comprehensions can also include conditional statements to filter or transform elements based on specific conditions.

1numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
2even_numbers = [x for x in numbers if x % 2 == 0]
3print(even_numbers) # Output: [2, 4, 6, 8, 10]

In this example, the list comprehension creates a new list even_numbers by including only the elements x from numbers that are divisible by 2 (even numbers).

Nested Comprehensions

List comprehensions can be nested to create more complex expressions or work with multiple iterables.

1matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
2flattened = [num for row in matrix for num in row]
3print(flattened) # Output: [1, 2, 3, 4, 5, 6, 7, 8, 9]

In this example, the nested list comprehension[num for row in matrix for num in row] flattens the nested matrix list into a single list flattened.

Conditional Expression (Ternary Operator)

List comprehensions can also incorporate conditional expressions (ternary operators) to perform different operations based on conditions.

1numbers = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
2result = ["even" if x % 2 == 0 else "odd" for x in numbers]
3print(result) # Output: ['odd', 'even', 'odd', 'even', 'odd', 'even', 'odd', 'even', 'odd', 'even']

In this example, the list comprehension ["even" if x % 2 == 0 else "odd" for x in numbers] creates a new list result by appending the string “even” if x is even, and “odd” if x is odd.

List comprehensions are powerful and expressive tools that can significantly improve the readability and conciseness of your code when working with lists and iterables in Python. They can help you write more Pythonic and efficient code, especially when dealing with complex data transformations or filtering operations.

Questions?

Session 4: Introduction to Libraries and Modules

Fri, 15 Mar 2024 00:00:00 +0000

Session 4: Introduction to Libraries and Modules

Instructor :

Python provides a modular structure that allows you to organize your code into reusable components called modules and packages. These modules and packages can contain variables, functions, classes, and even other modules and packages.

This modular approach promotes code reuse, maintainability, and collaboration within the Python community.

Modules

A module in Python is a single file containing Python code, such as functions, classes, or variables. Modules help organize code into logical units and promote code reuse across different parts of your program or across different projects.

Packages

A package is a collection of modules organized into a directory structure. Packages allow you to hierarchically organize related modules, making it easier to manage and distribute larger code bases.

A package is essentially a directory that contains an __init__.py file, which marks the directory as a Python package. The __init__.py file can contain initialization code or be left empty.

Importing and Using Modules

To use a module or package in your Python code, you need to import it. The import statement allows you to access and use the code defined in the imported module or package.

Importing Modules

There are several ways to import modules in Python:

Import the entire module: import module_name
Import specific objects from a module: from module_name import object1, object2
Import a module with an alias: import module_name as alias
Import all objects from a module: from module_name import * (not recommended, as it can lead to naming conflicts)

Example:

1import math # Import the entire math module
2print(math.pi) # Access the pi constant from the math module
3
4from math import sqrt # Import the sqrt function from the math module
5print(sqrt(16)) # Use the imported sqrt function
6
7import random as rd # Import the random module with an alias
8print(rd.randint(1, 10)) # Use the randint function from the random module

Importing Packages

To import modules from a package, you need to use the package hierarchy in your import statement.

1import package_name.module_name
2from package_name.module_name import object1, object2

Installing External Libraries

Python has a vast ecosystem of external libraries and packages that provide additional functionality beyond the standard library. These external libraries can be installed using package managers like pip (Python Package Installer) or conda (Anaconda’s package manager).

To install an external library (e.g., NumPy or Matplotlib), you can open the Anaconda Prompt (on Windows) or the terminal (on macOS/Linux) and run the following command:

1conda install library_name

Replace library_name with the name of the library you want to install (e.g., numpy or matplotlib).

After installing a library, you can import and use it in your Python code like any other module or package.

Built-in Libraries

Python comes with a comprehensive standard library that provides a wide range of modules for various tasks. Here are a few examples of commonly used built-in modules:

math: This module provides access to mathematical functions and constants, such as pi, sin(), cos(), sqrt(), and more.
random: This module provides functions for generating random numbers and making random choices.
os: The os module allows you to interact with the operating system, including functions for file and directory operations, environment variables, and more.

re: The re module provides support for regular expressions, which are powerful patterns for text processing and manipulation.
datetime: This module supplies classes for working with dates, times, and time intervals, making it easier to perform date and time operations.
json: The json module allows you to encode and decode JSON (JavaScript Object Notation) data, which is a lightweight data interchange format.

Examples of `math` Module

1import math
2
3print(math.pi) # Output: 3.141592653589793 (pi constant)
4print(math.sqrt(16)) # Output: 4.0 (square root)
5print(math.sin(0)) # Output: 0.0 (sine function)
6print(math.cos(math.pi / 2)) # Output: 6.123233995736766e-17 (cosine function)
7print(math.floor(3.7)) # Output: 3 (floor function)
8print(math.ceil(3.2)) # Output: 4 (ceiling function)

Examples of `random` Module

 1import random
 2
 3print(random.random()) # Output: A random float between 0 and 1
 4print(random.uniform(1, 10)) # Output: A random float between 1 and 10
 5print(random.randint(1, 6)) # Output: A random integer between 1 and 6 (inclusive)
 6
 7my_list = [1, 2, 3, 4, 5]
 8print(random.choice(my_list)) # Output: A random element from the list
 9random.shuffle(my_list) # Shuffle the elements of the list in-place
10print(my_list) # Output: The shuffled list

Popular External Libraries

The Python ecosystem is enriched by a vast collection of external libraries and packages contributed by the community. These libraries offer specialized functionality for various domains. Here’s a description of some popular external libraries:

NumPy: A powerful library for numerical computing, providing support for large, multi-dimensional arrays and matrices, along with a vast collection of mathematical functions to operate on these arrays.
Matplotlib: A comprehensive data visualization library for creating static, animated, and interactive visualizations in Python, including plots, histograms, bar charts, scatter plots, and more.
Pandas: A high-performance, easy-to-use data manipulation and analysis library for working with structured (tabular, multidimensional, heterogeneous) and time-series data.

SciPy: A collection of mathematical algorithms and convenience functions for scientific and technical computing, including modules for optimization, linear algebra, integration, interpolation, and more.
Scikit-learn: A machine learning library that provides simple and efficient tools for data mining and data analysis, including classification, regression, clustering, dimensionality reduction, and more.
TensorFlow: A powerful library for machine learning and deep learning, used for building and deploying neural networks and other machine learning models.

Requests: A simple and elegant library for making HTTP requests, handling cookies, file uploads, and more.
Django: A high-level Python web framework that encourages rapid development and clean, pragmatic design for web applications.
Flask: A lightweight, flexible, and minimalist Python web framework for building web applications.

Introducing NumPy (for Numerical Computing)

NumPy (Numerical Python) is a fundamental library for scientific computing in Python. It provides support for large, multi-dimensional arrays and matrices, as well as a vast collection of mathematical functions to operate on these arrays efficiently.

NumPy is widely used in various fields, including data analysis, machine learning, scientific computing, and more. It serves as the foundation for many other scientific libraries in the Python ecosystem, such as Pandas, SciPy, and Matplotlib.

NumPy Arrays

The core data structure in NumPy is the ndarray (N-dimensional array). NumPy arrays are efficient, homogeneous (containing elements of the same data type), and provide a wide range of operations and functions to work with them.

1import numpy as np
2
3# Creating NumPy arrays
4a = np.array([1, 2, 3, 4, 5]) # 1D array
5b = np.array([[1, 2], [3, 4]]) # 2D array
6c = np.zeros((3, 4)) # 3x4 array filled with zeros
7d = np.ones((2, 3, 4)) # 2x3x4 array filled with ones
8e = np.arange(10) # 1D array with values from 0 to 9
9f = np.linspace(0, 1, 5) # 1D array with 5 evenly spaced values between 0 and 1

 1# Array operations
 2print(a + 2) # Output: [3 4 5 6 7] (Element-wise addition)
 3print(a * b) # Output: [[ 1 4]
 4 # [ 9 16]] (Element-wise multiplication)
 5print(np.sqrt(a)) # Output: [1. 1.41421356 1.73205081 2. 2.23606798] (Square root)
 6print(np.sum(b)) # Output: 10 (Sum of all elements)
 7print(np.mean(a)) # Output: 3.0 (Mean of the elements)
 8
 9# Array indexing and slicing
10print(b[0, :]) # Output: [1 2] (First row of b)
11print(b[:, 1]) # Output: [2 4] (Second column of b)
12print(b[1, 1]) # Output: 4 (Element at row 1, column 1 of b)

1# Array reshaping
2g = a.reshape(1, 5) # Reshaping 1D array a into a 2D array with shape (1, 5)
3print(g) # Output: [[1 2 3 4 5]]
4
5# Array concatenation
6h = np.concatenate((a, e), axis=0) # Concatenate a and e along the first axis
7print(h) # Output: [1 2 3 4 5 0 1 2 3 4 5 6 7 8 9]

Introducing Matplotlib (for Data Visualization)

Matplotlib is a comprehensive data visualization library in Python. It provides a wide range of tools and functions for creating static, animated, and interactive visualizations in various formats, including plots, histograms, bar charts, scatter plots, and more.

Basic Plotting

Matplotlib provides a MATLAB-like interface for creating plots. Here’s an example of creating a simple line plot:

 1import matplotlib.pyplot as plt
 2import numpy as np
 3
 4# Generate some data
 5x = np.linspace(0, 10, 100)
 6y = np.sin(x)
 7
 8# Create a figure and axes
 9fig, ax = plt.subplots()
10
11# Plot the data
12ax.plot(x, y)
13
14# Add labels and title
15ax.set_xlabel('X')
16ax.set_ylabel('Y')
17ax.set_title('Sine Wave')
18
19# Display the plot
20plt.show()

Plot Customization

Matplotlib offers extensive customization options for plots, allowing you to adjust colors, line styles, markers, legends, and more.

 1import matplotlib.pyplot as plt
 2import numpy as np
 3
 4# Generate some data
 5x = np.linspace(-10, 10, 100)
 6y1 = x**2
 7y2 = x**3
 8
 9# Create a figure and axes
10fig, ax = plt.subplots()
11
12# Plot the data
13ax.plot(x, y1, color='r', label='Square')
14ax.plot(x, y2, color='g', linestyle='--', marker='o', label='Cube')
15
16# Add labels, title, and legend
17ax.set_xlabel('X')
18ax.set_ylabel('Y')
19ax.set_title('Polynomial Plots')
20ax.legend()
21
22# Display the plot
23plt.show()

Other Visualization Types

Matplotlib supports various types of visualizations beyond line plots, including:

Scatter plots
Bar charts
Histograms
Pie charts
3D plots
Contour plots
Image plots

 1import matplotlib.pyplot as plt
 2import numpy as np
 3
 4# Generate some data
 5data = np.random.normal(0, 1, 1000)
 6
 7# Create a figure and axes
 8fig, ax = plt.subplots()
 9
10# Plot a histogram
11ax.hist(data, bins=20, edgecolor='black')
12
13# Add labels and title
14ax.set_xlabel('Value')
15ax.set_ylabel('Frequency')
16ax.set_title('Histogram')
17
18# Display the plot
19plt.show()

Reading and Writing Files

Working with files is a fundamental aspect of many programming tasks. Python provides built-in functions and modules for reading and writing files, allowing you to interact with various file formats and perform file operations efficiently.

Reading Files

Python provides the open() function to open files for reading or writing. Here’s an example of reading the contents of a text file:

 1# Open a file in read mode
 2file = open('example.txt', 'r')
 3
 4# Read the entire file
 5content = file.read()
 6print(content)
 7
 8# Read a single line
 9line = file.readline()
10print(line)
11
12# Read all lines into a list
13lines = file.readlines()
14print(lines)
15
16# Close the file
17file.close()

It’s recommended to use the with statement when working with files, as it ensures the file is properly closed after the operations are completed, even in the case of exceptions or errors.

1# Open a file using the with statement
2with open('example.txt', 'r') as file:
3 # Read the file contents
4 content = file.read()
5 print(content)

Writing Files

Writing to files is similar to reading, but you need to open the file in write mode (w) or append mode (a).

1
2# Open a file in write mode (will create the file if it doesn't exist)
3with open('output.txt', 'w') as file:
4 file.write('This is a new line\n')
5 file.write('This is another line\n')
6
7# Open a file in append mode
8with open('output.txt', 'a') as file:
9 file.write('This line is appended\n')

Working with Other File Formats

Python’s standard library and third-party libraries provide support for working with various file formats, such as CSV, JSON, Excel, and more.

 1# Working with CSV files
 2import csv
 3
 4# Open a CSV file and read its contents
 5with open('data.csv', 'r') as file:
 6 reader = csv.reader(file)
 7 for row in reader:
 8 print(row)
 9
10# Open a CSV file and write data to it
11with open('output.csv', 'w', newline='') as file:
12 writer = csv.writer(file)
13 writer.writerow(['Name', 'Age', 'City'])
14 writer.writerow(['John', 25, 'New York'])
15 writer.writerow(['Jane', 30, 'London'])

Questions?

Mathematics of 2D Shapes: Line and Rectangle SDFs Unveiled

Fri, 15 Dec 2023 00:00:00 +0000

In our of Signed Distance Functions (SDFs), we demystified their role in representing and manipulating geometric shapes. Now, let’s delve deeper into the mathematical intricacies of SDFs, focusing specifically on lines and rectangles in 2D geometry.

The Significance of Line SDFs

A Line Signed Distance Function (SDF) assigns a real number to each point in space, representing the distance from that point to the nearest point on a specified line. The sign of this distance indicates whether the point lies to the left or right of the line. Mathematically, the signed distance from a point $ P(x,y) $ to a line $L$ defined by two points $ (x_1, y_1) $ and $ (x_2, y_2) $ on it can be calculated in three steps:

Vector Representation:
- Define vector $ \mathbf{a} $ as the direction vector of the line: $$ \mathbf{a} = \begin{bmatrix} x_2 - x_1 \ y_2 - y_1 \end{bmatrix} $$
- Normalize $ \mathbf{a} $ to obtain a unit vector $ \hat{\mathbf{a}} $: $$ \hat{\mathbf{a}} = \frac{\mathbf{a}}{|\mathbf{a}|} $$
Position Vector:
- Define vector $ \mathbf{b} $ as the position vector from any point on the line $L$ to point $ P $: $$ \mathbf{b} = \begin{bmatrix} x - x_1 \ y - y_1 \end{bmatrix} $$
Dot Product:
- Calculate the dot product of $ \mathbf{b} $ and a vector perpendicular to $ \mathbf{a} $: $$ d = \mathbf{b} \cdot \begin{bmatrix} a_y \ -a_x \end{bmatrix} $$

Understanding Line SDF Values

Positive SDF: Points to the right of the line (when facing along the line’s direction) will have a positive SDF value.
Negative SDF: Points to the left of the line will have a negative SDF value.
Zero SDF: Points lying on the line will have an SDF value of zero.

The visualization of line SDF is available at using module.

Unraveling Rectangle SDFs

Continuing our exploration of signed distance functions (SDFs), let’s delve into rectangles. A rectangle can be defined by its bottom-left corner coordinates $(x_1, y_1)$ and top-right corner coordinates $(x_2, y_2)$. The signed distance function $d_{\text{Rectangle}}$ for a point $P = (x, y)$ to this rectangle is expressed as:

$$ d_{\text{Rectangle}}(P) = \max\left(x_1 - x, x - x_2, y_1 - y, y - y_2, 0\right) $$

The function accounts for the distances to each side of the rectangle, considering negative distances for points inside the rectangle and positive distances for points outside. The overall signed distance is determined by taking the maximum among these distances.

Directionality Matters

For rectangles, the order of corner points matters, affecting the orientation of the SDF. Ensure consistency in the order to maintain a coherent representation.

The visualization of rectangle SDF is available at using module.

Other 2D Shapes with Known SDFs

In addition to , and , various other 2D shapes have well-defined SDFs. While we won’t delve deep into them in this post, some noteworthy shapes include ellipses, triangles, and regular polygons.

By understanding the mathematics behind SDFs for lines and rectangles, we pave the way for more advanced explorations into 2D geometry and computational modeling. Stay tuned for future posts as we continue our journey through the captivating world of implicit geometry.

Feel free to experiment with the provided mathematical expressions and incorporate visual illustrations to enhance your understanding. Mathematics becomes a powerful tool when coupled with visualization.

Happy exploring!

Demystifying Signed Distance Functions

Sun, 10 Dec 2023 00:00:00 +0000

Demystifying Signed Distance Functions

In the realm of mathematics and computer graphics, signed distance functions (SDFs) play a pivotal role in representing and manipulating geometric shapes. Unlike traditional polygonal meshes, which store vertices and connectivity information, SDFs define shapes implicitly, offering a powerful and flexible approach to 3D modeling and simulation.

What is a Signed Distance Function?

At its core, an SDF is a mathematical function that assigns a real number to each point in space, representing the distance from that point to the nearest boundary of a specified shape. This distance value carries a sign, indicating whether the point lies inside, outside, or on the boundary of the shape.

Properties of Signed Distance Functions

Non-parametric Representation: SDFs describe shapes without explicit geometric data, making them ideal for representing complex shapes and adapting to deformations.
Global Shape Representation: SDFs provide a global representation of a shape, allowing for efficient proximity queries and intersection detection crucial for computational geometry.
Differentiable: SDFs are differentiable, enabling smooth transitions between different shape representations and their derivatives, a key aspect in mesh generation.

Applications of Signed Distance Functions

Mesh Generation for Physics Simulations: SDFs are widely used in physics simulations to represent objects and their interactions, enabling the creation of high-quality meshes representing objects with complex shapes, realistic collision detection and physics calculations.
Level of Detail (LOD): SDFs facilitate efficient LOD management by allowing for the creation of high-quality representations at various levels of detail.
Procedural Modeling: SDFs are the foundation of procedural modeling techniques, enabling the creation of organic and complex shapes from simple mathematical rules.
Graphics Rendering: SDFs play a crucial role in ray tracing algorithms, enabling ray casting and intersection detection for realistic graphics rendering.

Understanding the Mathematical Significance

In mathematical terms, the sign of the distance values generated by the SDF holds crucial information about the relative position of a point to the shape:

Negative Values: Points with negative SDF values lie inside the shape’s boundary. The magnitude of the negative value represents how far inside the point is relative to the nearest surface.
Positive Values: Points with positive SDF values are located outside the shape. Similar to negative values, the magnitude indicates the distance from the point to the nearest surface outside the shape.
Zero Value: A point with an SDF value of zero resides exactly on the shape’s boundary.

Mathematically, the SDF function can be represented as follows for a given point $P$ in space:

$$ SDF(P) = \text{Distance from } P \text{ to the nearest surface} $$

The sign of $SDF(P)$ provides a concise indication of whether the point $P$ is inside, outside, or on the boundary of the represented shape.

This mathematical understanding is foundational for computational geometry algorithms and plays a pivotal role in mesh generation processes, guiding the placement of vertices and defining the geometry of the resulting mesh.

Mathematical Example: SDF for a Circle

Consider a two-dimensional space ($x, y$) and a circle centered at the origin with a radius of $r$. The SDF for this circle ($SDF_{\text{circle}}$) at a given point $(x, y)$ can be expressed as follows:

$$ SDF_{\text{circle}}(x, y) = \sqrt{x^2 + y^2} - r $$

In this equation:

$SDF_{\text{circle}}(x, y)$ is the signed distance function for the circle.
$\sqrt{x^2 + y^2}$ calculates the Euclidean distance from the point $(x, y)$ to the origin.
$r$ is the radius of the circle.

Now, let’s break down the sign of $SDF_{\text{circle}}(x, y)$ based on the relative position of the point to the circle:

If $SDF_{\text{circle}}(x, y) < 0$, the point $(x, y)$ is inside the circle.
If $SDF_{\text{circle}}(x, y) > 0$, the point $(x, y)$ is outside the circle.
If $SDF_{\text{circle}}(x, y) = 0$, the point $(x, y)$ is exactly on the boundary of the circle.

This mathematical example illustrates how the SDF values can be computed for a simple geometric shape like a circle, forming the basis for more complex computations in computational geometry and mesh generation.

Example Python Code: Creating a Circle SDF

The following Python code defines an SDF function for a circle:

1import numpy as np
2
3def circle_sdf(x, y, center = [0,0], radius = 80):
4 return np.sqrt((x - center[0])**2 + (y - center[1])**2) - radius

This function takes two-dimensional coordinates as input and returns the distance from the point to the circle’s boundary.

Signed Distance Function Visualization

The visualization of circle SDF is also available at using module.

pyPolyMesher: Polygonal mesh generator

Sat, 09 Dec 2023 00:00:00 +0000

Introduction

PyPolyMesher is a powerful Python library designed for polygon mesh generation, drawing inspiration from the renowned . Leveraging the flexibility and efficiency of Python, this library empowers users to effortlessly create polygonal meshes using signed distance functions of different domains.

Features

Seamlessly generate structured quadrilateral elements from specified points.
Effortlessly create unstructured polygon elements using randomly generated points.
Comprehensive SDF support for all example domains featured in the original program.
Easily generate the SDF for new domains with user-friendly functionality.
Import polygon-shaped domains directly from dxf files.

Explore the file for detailed insights into features and usage.

License

Distributed under the GPLv3 License. Refer to for mdetailed licensing information.

Contact

Project Link:

QTREEMESH: Generating QuadTree Mesh from Images

Fri, 08 Dec 2023 00:00:00 +0000

Introduction

QTREEMESH is a Python package that simplifies the generation of Quadtree meshes from images. Quadtree structures, known for their efficiency in spatial data representation, find applications in image processing and finite element analysis. This package provides an intuitive interface for seamlessly generating Quadtree meshes, enabling various image processing and analysis techniques.

Features (v0.1.2)

Perform QuadTree decomposition of images
Generate QuadTree mesh
Export as vtk format
Generate FEM-friendly mesh (handling hanging nodes)

License

Distributed under the MIT License. See for more information.

Contact

Project Link:

A Scaled Boundary Finite Element Formulation for Solving Plane-Strain Viscoelastic Problems

Tue, 01 Nov 2022 00:00:00 +0000

Numerical analysis of human head with implant under impact

Tue, 29 Dec 2020 00:00:00 +0000