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 oncampus 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 & seniorelective level (in preparation) MFEMS: Matrix Finite Element Methods in Statics Master & seniorelective 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 oncampus students. Solutions posted Chapter 3 Index. The Direct Stiffness Method II. HW#1 solutions posted Chapter 4 Index. Plane Truss Analysis by a CAS. Completely rewritten 9/16. HW#5 solutions posted Chapter 5 Index. Constructing MoM Members. HW#2 posted, due 9/8/16 for oncampus 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 oncampus students. Solutions posted Chapter 8 Index. Multifreedom Constraints I. HW#4 posted, due 9/22/16 for oncampus students. Has detailed info on Midterm 1. Solutions posted Chapter 9 Index. Multifreedom Constraints II. HW#4 solutions posted Chapter 10 Index. Superelements and GlobalLocal Analysis. HW#5 posted, due 10/4/16 for oncampus and BBA students. HW#5 solutions posted Part II: Mathematical Formulation of Finite Elements Chapter 11 Index. Variational Formulation of Bar Element. HW#6 posted, due 10/13/16 for oncampus students. HW#6 solutions posted Chapter 12 Index. Variational Formulation of Plane Beam Element. HW#6 solutions posted Chapter 13 Index. Advanced OneDimensional Elements. Not covered Chapter 14 Index. The Plane Stress Problem. HW#6 solutions posted Chapter 15 Index. ThreeNode Plane Stress Triangles. HW#7 posted, due 10/20/16 for oncampus students. Solutions posted. Chapter 16 Index. The Isoparametric Representation. HW#7 Solutions posted Chapter 17 Index. Isoparametric Quadrilaterals. HW#8 posted, due 10/27/16 for oncampus students; has info on Midterm 2. Solutions posted Chapter 18 Index. Shape Function Magic. HW#8 solutions posted Chapter 19 Index. FEM Convergence Requirements HW#9 posted, due 11/3/16 for oncampus and BBA students; has info on Midterm 2. Solutions posted Part III: Computer Implementation of Finite Elements Chapter 20 Index. Implementation of OneDimensional Elements. HW#10 posted, due 11/17/16 for both oncampus and BBA students. Solutions posted Chapter 21 Index. FEM Program for Space Trusses. HW#10 solutions posted Chapter 22 Index. FEM Programs for Frameworks. Not covered Chapter 23 Index. Implementation of isoP Quadrilateral Elements. HW#11 posted, due 12/3/16 for both oncampus and BBA students. Solutions posted Chapter 24 Index. Implementation of isoP Triangular Elements. HW#11 solutions posted Chapter 25 Index. The Assembly Process. HW#12 (last HW) due 12/08/16, posted. Contains information on final exam. 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. Linear Algebra: Matrix Calculus. Appendix E Index. Linear Algebra: Eigenproblems. Appendix F Index. Fitting Element Fields. 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. Appendix T Index. ThreeDimensional Continuum Mechanics. CAETE PPT files . Chapters 121, 2328. Exam Material Exam Material Index. Midterm exams 1 and 2, and their solutions posted. Final take home exam to be posted 12/7/16.  
Last update: December 6, 2016.
This page constructed by Carlos Felippa: carlos.felippa@colorado.edu