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Introduction to Finite Element Method – Lecture Notes

TOC

Part 0: Preface

Preface  Part I: Finite Element Discretization and the Direct Stiffness Method
1  Overview.
2  The Direct Stiffness Method I
3  The Direct Stiffness Method II
4  Analysis of Example Truss by a CAS
5  Constructing MoM Members
6  Finite Element Modeling: Introduction
7  Finite Element Modeling: Mesh, Loads, BCs
8  Multifreedom Constraints I
9  Multifreedom Constraints II
10  Superelements and Global-Local Analysis

Part II: Mathematical Formulation of Finite Elements
11  Variational Formulation of Bar Element
12  Variational Formulation of Plane Beam Element
13  Advanced One-Dimensional Elements
14  The Plane Stress Problem
15  Three-Node Plane Stress Triangles
16  The Isoparametric Representation
17  Isoparametric Quadrilaterals
18  Shape Function Magic
19  FEM Convergence Requirements
20  Implementation of One-Dimensional Elements
21  FEM Program for Space Trusses
22  FEM Programs for Trusses and Frames
23  Implementation of iso-P Quadrilateral Elements
24  Implementation of iso-P Triangular Elements
25  The Assembly Process
26  Solving FEM Equations
27  A Complete Plane Stress FEM Program
28  Stress Recovery
28  Fitting Fields Over Triangles
30  Thermomechanical Effects.

Part IV: Intro to Dynamics and Vibrations
31  Dynamics & Vibrations Overview
32  Lumped and Consistent Mass Matrices
33  Customized Mass Matrices

Appendices & Miscellanea
A  Vector Algebra Refresher
B  Matrix Algebra Refresher
C  A Continuation of Appendix B
D  Matrix Calculus Summary
F  Geometric Applications of Matrices
G  Oldies but Goodies
H  History of MSA -> FEM
M  Miscellaneous Advanced Topics

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