Nonlinear Finite Element Methods (ASEN 6107) - Spring 2014
Department of Aerospace Engineering Sciences
University of Colorado at Boulder

This is the public web site for the graduate course ASEN 6107: Nonlinear Finite Element Methods (NFEM). This doctoral and master-elective 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. Normally offered every two years during the Spring semester (sometimes with 3 year gaps because of sabbaticals), both on-campus and remotely through CAETE. First taught in 1988. This website dates from 1999 and is continuously being revised. Related courses may be accessed at
AFEM: Advanced Finite Element Methods (ASEN 6347) . Master & doctoral level
AVVM: Advanced Variational Methods in Mechanics . Master and doctoral level (in preparation)
FSI: Fluid Structure Interaction (ASEN 5509) . Advanced doctoral level
IFEM: Introduction to Finite Element Methods (ASEN 5007) . Master & senior-elective 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)
JSTR: Structures (ASEN 3112) . Junior undergraduate level

General Course Information. Syllabus, coursework, schedule ...
Web site under complete revision: please be patient!
Note: Please do not download material until the link is marked with an asterisk (*)

Part I: Fundamentals of Nonlinear Structural Analysis
Chapter 1 Index. Overview. Only briefly covered
Chapter 2 Index. A Tour of Nonlinear Analysis. HW#1 posted, due 1/23; solutions posted
Chapter 3 Index. Residual Force Equations. HW#2 posted, due 1/30; solutions posted
Chapter 4 Index. One-Parameter Residual Equations. HW#2 solutions posted
Chapter 5 Index. Critical Points and Related Properties. HW#3 posted, due 2/6; solutions posted
Chapter 6 Index. Conservative Systems. HW#3 solutions posted
Part II: Total Lagrangian, Geometrically Nonlinear Finite Elements
Chapter 7 Index. Review of Continuum Mechanics. HW#4 posted, due 2/13; solutions posted
Chapter 8 Index. TL Bar Elements: Formulation & Implementation HW#4 solutions posted
Chapter 9 Index. TL Bar Elements: Truss Analysis. HW#5 posted, due 2/20; reworked solutions posted
Chapter 10 Index. The TL Plane Beam Element: Formulation. HW#6 solutions posted
Chapter 11 Index. The TL Plane Beam Element: Implementation. HW#6 posted, due 3/6; solutions posted
Part III: Corotational, Geometrically Nonlinear Finite Elements
Chapter 12 Index. CR Formulation Overview I.
Chapter 13 Index. CR Formulation Overview II.
Chapter 14 Index. The CR Formulation: Space Bar. HW#7 posted, due 3/1; solutions posted
Chapter 15 Index. The CR Formulation: BE Plane Beam.
Chapter 16 Index. Placeholder.
Chapter 17 Index. Placeholder.
Part IV: Solution Methods
Chapter 18 Index. Overview of Solution Methods. HW#8 posted, due 3/20; solutions posted
Chapter 19 Index. Purely Incremental Methods: Load Control.
Chapter 20 Index. Purely Incremental Methods: General Control.
Chapter 21 Index. Purely Incremental Methods: Implementation. Only briefly covered in class, but source of HW#9 Exercises - HW#9 posted, due 4/3; solutions posted
Chapter 22 Index. Conventional Newton Methods. HW#10 posted, due 4/10; solutions posted
Chapter 23 Index. Newton Methods: General Control and Variants.
Chapter 24 Index. Corrective Methods: Implementation. In progress
Chapter 25 Index. Accelerators and Line Search. Not covered
Chapter 26 Index. Detecting and Traversing Critical Points. Not covered
Part V: Structural Stability
Chapter 27 Index. Bifurcation: Linearized Prebuckling I. HW#11 posted, due 4/24; solutions posted
Chapter 28 Index. Bifurcation: Linearized Prebuckling II. HW#11 solutions posted
Chapter 29 Index. Qualitative Analysis of Critical Points.
Chapter 30 Index. Nonlinear Bifurcation Analysis. HW#12 posted (last graded HW); solutions posted
Chapter 31 Index. Imperfections. HW#12 solutions posted
Chapter 32 Index. Nonconservative Loading: Overview. HW#13 posted (not to be graded or returned; intended only as exercise material for final exam); solutions posted
Chapter 33 Index. Aero- and Hydrodynamic Loading. Split off from old Ch 32. HW#13 solutions posted.
Chapter 34 Index. Dynamic Stability: Formulation.
Chapter 35 Index. Dynamic Stability: Examples. Split off from old Ch 33, now 34, HW#13 solutions posted.
Appendix A Index. The Mathematics of Finite Rotations.
Appendix B Index. Matrices for EICR Formulation.
Appendix C Index. Choice of Best CR Fit Frame.
Appendix D Index. CR Nomenclature.
Appendix H Index. The C1 TL Beam.
Appendix R Index. References.

Old Chapters No Longer Covered
Old Chapter 10 Index. Not to be covered Spring 2014.
Old Chapter 11 Index. Not to be covered Spring 2014.

Exam Material
Exam Material Index. Midterm 2 posted Fr April 11 noon, due Th April 17.
Final Exam posted Wed April 30 by 6pm.

Last update: May 2, 2014.

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