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 original 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

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