Introduction to Finite Element Methods (ASEN 5007)
Fall 2016
Department of Aerospace Engineering Sciences
University of Colorado at Boulder

This is the public web site for the graduate core course ASEN 5007: Introduction To Finite Element Methods (IFEM). This master level course is part of the Aerospace Systems Focus Area of the graduate curriculum in the Department of Aerospace Engineering Sciences of the University of Colorado at Boulder. Offered yearly during the Fall Semester, both on-campus and remotely through CAETE. First taught in 1987. This website dates from 1998 and is continuously being revised. Related courses may be accessed at
AFEM: Advanced Finite Element Methods (ASEN 6347) Master & doctoral level
AVMM: Advanced Variational Methods in Mechanics Master & doctoral level (in preparation)
FSI: Fluid Structure Interaction (ASEN 5509) Doctoral level
MFEMD: Matrix Finite Element Methods in Dynamics Master & senior-elective level (in preparation)
MFEMS: Matrix Finite Element Methods in Statics Master & senior-elective level (in preparation)
NFEM: Nonlinear Finite Element Methods (ASEN 6107) Master & doctoral level
IAST: Intro to Aerospace Structures (ASEN 3112) Junior undergraduate level

General Course Information. Syllabus, coursework, schedule, roster ...

Part 0: Preface
Preface Index.

Part I: Finite Element Discretization and the Direct Stiffness Method
Chapter 1 Index. Overview. Not covered
Chapter 2 Index. The Direct Stiffness Method I. HW#1 posted, due 9/1/16 for on-campus students. Solutions posted
Chapter 3 Index. The Direct Stiffness Method II. HW#1 solutions posted
Chapter 4 Index. Plane Truss Analysis by a CAS. Covered in 9/22/16; rewrite in progress. Exercise 4.1 to be part of HW#5
Chapter 5 Index. Constructing MoM Members. HW#2 posted, due 9/8/16 for on-campus students. Solutions posted
Chapter 6 Index. Finite Element Modeling: Introduction.
Chapter 7 Index. Finite Element Modeling: Mesh, Loads, BCs. HW#3 posted, due 9/15/16 for on-campus students. Solutions posted
Chapter 8 Index. Multifreedom Constraints I. HW#4 posted, due 9/22/16 for on-campus students. Has detailed info on Midterm 1.
Chapter 9 Index. Multifreedom Constraints II.
Chapter 10 Index. Superelements and Global-Local Analysis. HW#5 posted, due 9/22/16 for on-campus students.

Part II: Mathematical Formulation of Finite Elements
Chapter 11 Index. Variational Formulation of Bar Element.
Chapter 12 Index. Variational Formulation of Plane Beam Element.
Chapter 13 Index. Advanced One-Dimensional Elements. Not covered
Chapter 14 Index. The Plane Stress Problem.
Chapter 15 Index. Three-Node Plane Stress Triangles.
Chapter 16 Index. The Isoparametric Representation.
Chapter 17 Index. Isoparametric Quadrilaterals.
Chapter 18 Index. Shape Function Magic.
Chapter 19 Index. FEM Convergence Requirements
Chapter 21 Index. FEM Program for Space Trusses.
Chapter 22 Index. FEM Programs for Frameworks. Not covered
Chapter 23 Index. Implementation of iso-P Quadrilateral Elements.
Chapter 24 Index. Implementation of iso-P Triangular Elements.
Chapter 25 Index. The Assembly Process.
Chapter 26 Index. Solving FEM Equations. Not covered
Chapter 27 Index. A Complete Plane Stress FEM Program. For demos.
Chapter 28 Index. Stress Recovery.
Chapter 29 Index. Fitting Fields Over Triangles (in progress) Not covered
Chapter 30 Index. Thermomechanical Effects. Not covered

Part IV: Intro to Dynamics and Vibrations
This Part has been moved to the MFEMD web site.

Appendices & Miscellaneous Stuff
Appendix A Index. Linear Algebra: Vectors.
Appendix B Index. Linear Algebra: Matrices.
Appendix C Index. Continuum Mechanics Summary.
Appendix D Index. Linear Algebra: Determinants, Inverses, Rank.
Appendix E Index. Linear Algebra: Eigenproblems.
Appendix F Index. Matrix Calculus.
Appendix G Index. Graphics Utilities.
Appendix H Index. History of MSA -> FEM.
Appendix M Index. From IOMoDE to FOMoDE (advanced stuff).
Appendix O Index. The Origins of the Finite Element Method.
Appendix P Index. Partitioned Matrices and the Schur Complement.
Appendix Q Index. Miscellaneous FEM Formulation Topics.
Appendix R Index. References (in progress).
Appendix S Index. Spatial Applications of Matrices.
CAETE PPT files . Chapters 1-21, 23-28.

Exam Material
Exam Material Index. Midterm exams 1 and 2, and their solutions posted. Final take home exam posted 12/9/15.

Last update: September 21, 2016.

This page constructed by Carlos Felippa: