Ch 1 - An Introduction to the Use of Finite Element Procedures
1.1 Introduction
1.2 Physical Problems, Mathematical Models, and the Finite Element Solution
1.3 Finite Element Analysis as an Integral Part of Computer-Aided Design
1.4 A Proposal on How to Study Finite Element Methods
Ch 2 - Vectors, Matrices, and Tensors
2.1 Introduction
2.2 Introduction to Matrices
2.3 Vector Spaces
2.4 Definition of Tensors
2.5 The Symmetric Eigenproblem
2.6 The Rayleigh Quotient and the Minimax Characterization
2.7 vector and Matrix Norms
2.8 Exercises
Ch 3 - Some Basic Concepts of Engineering Analysis and an Introduction to the Finite Element Method
3.1 Introduction
3.2 Solution of Discrete-System Mathematical Models
- 3.2.1 Steady-State Problems
- 3.2.2 Propagation Problems
- 3.2.3 Eigenvalus Problems
- 3.2.4 On the Nature of Solutions
- 3.2.5 Exercises
- 3.3.1 Differential Formulations
- 3.3.2 Variational Formulations
- 3.3.3 Weighted Residual Methods; Ritz Method
- 3.3.4 An Overview : The Differential and Galerkin Formulations, the Principle of Virtual Displacements, and an Introduction to the Finite Element Solution
- 3.3.5Finite Difference Differential and Energy Methods
- 3.3.6 Exercise
- 3.4.1 An introduction to Lagrange Multiplier and Penalty Methods
- 3.4.2 Exercises
