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 masterelective 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 oncampus 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 & seniorelective 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) 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. OneParameter 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. Appendices 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.
This page constructed by Carlos Felippa: carlos.felippa@colorado.edu