Notes on Basics of EFI - Part 1

Course Overview

• Duration: 8 weeks
• Structure: 6 modules per week, one lecture each day (Monday to Friday)
• Total: 48 lectures (20-25 minutes each)
• Assignments: Mostly multiple-choice questions related to finite element analysis (FEA) theory

Recommended Textbook

• Title: Introduction to the Finite Element Method
• Author: J. N. Reddy
• Strengths: Easy to understand; clear explanations without compromising on mathematics

Importance of Finite Element Analysis (FEA)

• FEA solves differential equations which are mathematically intensive
• Widely used across various engineering disciplines (Mechanical, Civil, Aerospace, etc.) and scientific fields
• Helpful in solving complex physical phenomena (e.g. heat transfer, stress analysis, fluid dynamics)

Key Concepts in FEA

1. Theory of Finite Element Method:

   • Starts with 1D problems, leads to understanding complex geometries
   • Transition to 2D and 3D problems is based on similar principles

2. Differential Equations:

   • Use to capture physical phenomena (e.g. bending, heat transfer)
   • Challenges with integration - generally more complex than differentiation
   • FEA provides an approximate solution to these equations

3. General and Flexible Approach:

   • Can solve various types of differential equations (linear, non-linear)
   • Systematic and structured process suitable for automation
   • Applicable to a wide range of physical problems

Steps in Applying Finite Element Method

1. Develop Governing Equations:

   • Create equilibrium equations based on applied forces and stress-strain relationships
   • Use laws of geometry to relate curvature and displacement

2. Methods to Solve Governing Equations:

   • Exact Solutions: Satisfy both differential equations and boundary conditions; often not feasible
   • Approximate Solutions:
     • Analytical Solutions: Provide formulas for unknown variables
     • Numerical Solutions: Provide numerical values at various points

3. Weighted Integral Approach:

   • Weight the error across the domain and set it to zero for an approximate solution

4. Finite Difference Method:

   • An alternative numerical method that expresses derivatives as differences
   • Converts partial differential equations into algebraic equations

Conclusion

• This session covered basic introductions to FEA including the theoretical foundation and steps to apply the method.
• Next class will build upon these concepts.