Table of Contents
- Preface
- My Goals
- Target Audience
- Prerequisite
- Textbook
- References
CHAPTER 2: APPROXIMATION OF FUNCTION
- What is FEM?
- Approximation of Function
CHAPTER 3: METHOD OF WEIGHTED RESIDUAL
- Mathematical Theory
- General Expression of Galerkin Method
- Least Square Method (Off the Topic)
CHAPTER 5: EXAMPLE OF GALERKIN METHOD AND MATRIX FORMULATION
- The 2nd-Order PDE Problem
- Matrix Formulation
CHAPTER 6: SHAPE FUNCTIONS AND GRAPHICAL EXPLANATION
- Shape Functions
- Graphical Idea
CHAPTER 7: EXAMPLE PROBLEM (1-DIMENSIONAL, 3-DEGREE OF FREEDOM)
- Objective
- Problem
- Exact Solution
- Piece-wise Linear Shape Function
- Stiffness Matrix
- Force Vector
- Matrix Form
- Solve Matrix Form by Gauss-Jordan Elimination
- Solve Matrix Form by Excel Spreadsheet
- Under Constrained Problem – What if d4 is unknown?
CHAPTER 8: PIECE-WISE LINEAR FINITE ELEMENT SPACE
- Global Coordinate System
- Element Point of View
- Shape Function in Element Space
- Local and Global Location
- Other Important Equations for Future References
- Assembling Global Matrix Forms
- Change Integral from Global to Elemental Coordinate System
- Example
CHAPTER 9: EULER-BERNOULLI’S BEAM THEOREM
- Euler-Bernoulli’s Beam in FEM form
- Can We Use Piece-wise Linear Shape Functions?
- Piece-wise Cubic Shape Function
- Hermite Shape Function
- Local Stiffness Matrix
- Local Force Vector
- Example (Simple General Case with Constant p)
- Example 1 (Constant E, I, h, and p)
- Example 2 (Variable h)
- Example 3 (Variable p)
- Example 4 (Variable E)
- Example 5 (Variable I)
- Example 6 (Variable All)
- More General Formula with F and M in Elements
- Example 7 (Variable All with Forces and Moments)
- Force and Moment at Both Ends
CHAPTER 10: 2D SCALAR PROBLEM (HEAT CONDUCTION)
- Contents – TBD
CHAPTER 11: 2D TENSOR PROBLEM (STRESS DISTRIBUTION)
- Contents – TBD
CHAPTER 12: ISOPARAMETRIC ELEMENT
- Mathematical Definition
- Example of Isoparametric Element – Bilinear Quadrilateral Element
CHAPTER 13: ELEMENT MAPPING
- Mapping Conditions
- Jacobian Determinant
CHAPTER 14: HIGHER-ORDER ELEMENT
- Lagrange Polynomial
CHAPTER 15: GAUSSIAN QUADRATURE
- Contents – TBD
CHAPTER 16: GAUSSIAN QUADRATURE - EXAMPLE PROBLEM
- Contents – TBD
CHAPTER 17: FINAL EXAM
- Contents – TBD
CHAPTER 18: APPENDIX A: DEMONSTRATION OF VARIOUS PLATE ELEMENTS
- CST CTRIA3
- LST CTRIA6
- Bilinear Quadrilateral CQUAD4
- Bilinear Quadrilateral CQUAD8