### Introduction to Finite Element Methods (ASEN 5007), Department of Aerospace Engineering Sciences, University of Colorado at Boulder

One of the best resources for FEA pdfs is the Colorado University structural analysis course. The coursework had been built up over a number of years, starting in 1987. The website itself was relatively ancient having been launched way back in 1998. Now sadly it seems to have been removed from the Public Domain. The data here is a copy of that website from a moment in time, wherein the *o**riginal content is the construction of *Carlos Felippa.

The notes have a focus on how to actually write FEA software. Hence there are in-depth sections to do with assembly of simple single element models and more complex multi element models. Quite a few worked, numerical examples are provided along with code snippets written for Matlab.

A fantastic resource for students and engineers.

**Part 0: Preface **

Preface.

**Part I: Finite Element Discretization and the Direct Stiffness Method **

Chapter 1 Overview

*Chapter 2 The Direct Stiffness Method I

*Chapter 3 The Direct Stiffness Method II

*Chapter 4 Analysis of Example Truss by a CAS

*Chapter 5 Constructing MoM Members

*Chapter 6 Finite Element Modeling: Introduction.

*Chapter 7 Finite Element Modeling: Mesh, Loads, BCs

*Chapter 8 Multifreedom Constraints I

*Chapter 9 Multifreedom Constraints II

*Chapter 10 Superelements and Global-Local Analysis

**Part II: Formulation of Finite Elements **

*Chapter 11 Variational Formulation of Bar Element

*Chapter 12 Variational Formulation of Plane Beam Element

Chapter 13 Advanced One-Dimensional Elements

*Chapter 14 The Plane Stress Problem

Chapter 15 The Linear Plane Stress Triangle

Chapter 16 The Isoparametric Representation

Chapter 17 Isoparametric Quadrilaterals

Chapter 18 Shape Function Magic

Chapter 19 FEM Convergence Requirements

**Part III: Computer Implementation of Finite Elements **

Chapter 20 Implementation of One-Dimensional Elements

Chapter 21 FEM Program for Space Trusses

Chapter 22 FEM Programs for Trusses and Frames

Chapter 23 Implementation of iso-P Quadrilateral Elements

Chapter 24 Implementation of iso-P Triangular Elements

Chapter 25 The Assembly Process

Chapter 26 Solving FEM Equations

Chapter 27 A Complete Plane Stress FEM Program

Chapter 28 Stress Recovery

Chapter 29 Thermomechanical Effects

**Part IV: Intro to Dynamics and Vibrations**

Chapter 30 Dynamics & Vibrations Overview

Chapter 31 Lumped and Consistent Mass Matrices

Chapter 32 Customized Mass Matrices

**Appendices & Miscellanea **

Appendix A Linear Algebra: Vectors

Appendix B Linear Algebra: Matrices

Appendix C Continuum Mechanics Summary

Appendix D Linear Algebra: Determinants, Inverses and Ranks

Appendix E Linear Algebra: Eigenproblems

Appendix F Matrix Calculus

Appendix G Graphic Utilities

Appendix H An outline of MSA History

Appendix M Converting IOMoDE to FOMoDEA

Appendix O The Origins of the Finite Element Method

Appendix P Partitioned Matrices and the Schur Complement

Appendix Q Miscellaneous FEM Formulation Topics

Appendix S Spatial Applications of Matrices

References References