Nonlinear Finite Element Methods (ASEN 5107) - Fall 2004
Department of Aerospace Engineering Sciences
University of Colorado at Boulder
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*Course outline and syllabus.
HW preparation & submission guidelines.
*Fall 04 roster and e-mail list as of 9/16/04.
Part 0: Preface
Part I: Overview of Nonlinear Problems
*Chapter 1 Index. Overview.
*Chapter 2 Index. A Tour of Nonlinear Analysis. HW#1, due Thu Sep 2, posted. Solutions to HW#1 posted 9/14.
*Chapter 3 Index. Residual Force Equations. HW#2, due Thu Sep 14, posted. (also linked to Ch 4 index). Solutions posted 9/15.
*Chapter 4 Index. One-Parameter Residual Equations. Solutions to Exercises posted 9/15.
*Chapter 5 Index. Critical Points and Related Properties. HW#3, due Thu Sep 16, posted. (also linked to Ch 6 index). Solutions to HW#3 Exercises posted
*Chapter 6 Index. Conservative Systems. Solutions to to HW#3 Exercises posted.
Part II: Formulation of Geometrically Nonlinear Finite Elements
*Chapter 7 Index. Review of Continuum Mechanics. HW#4, due Sep 23, posted. Solutions to Exercises posted Oct 7.
*Chapter 8 Index. The TL Bar Element. Solutions to Exercises posted.
*Chapter 9 Index. The TL Timoshenko Plane Beam Element. HW#5, due Tuesday Oct 9, posted. Contains announcement of Midterm Quiz 1. Solutions to Exercises posted.
Chapter 10 Index. Not to be covered Fall 2004.
Chapter 11 Index. Not to be covered Fall 2004.
*Chapter 12 Index. CR Formulation Overview I. (Rewritten Chapter, ready)
*Chapter 13 Index. CR Formulation Overview II. (Rewritten Chapter, ready)
Chapter 14 Index. The CR Formulation: Bar, Triangle and Tetrahedron. (Chapter being rewritten)
Chapter 15 Index. The CR Formulation: Beams and Shells. (Chapter being rewritten)
Part III: Nonlinear Solution Methods
*Chapter 16 Index. Overview of Solution Methods.
*Chapter 17 Index. Purely Incremental Methods: Load Control.
*Chapter 18 Index. Purely Incremental Methods: General Control. HW#7, due Tu Nov 2 (Election Day) posted. Solutions posted.
Chapter 19 Index. Will not be covered.
*Chapter 20 Index. Conventional Newton Methods. Solutions posted.
*Chapter 21 Index. Newton-Like Methods. HW#8, due Th November 11, posted. Contains announcement of Take-home Midterm Quiz 2. Solutions posted.
Chapter 22 Index. Accelerators and Line Search. Not to be covered: provided as reference material only.
*Chapter 23 Index. Detecting and Traversing Critical Points. HW solutions posted.
Part IV: Stability Analysis
*Chapter 24 Index. Bifurcation: Linearized Prebuckling I. HW#9 (Chs 24-25) due December 2, posted. Solutions posted.
*Chapter 25 Index. Bifurcation: Linearized Prebuckling II. HW solutions posted.
*Chapter 26 Index. Qualitative Analysis of Critical Points.
*Chapter 27 Index. Nonlinear Bifurcation Analysis.
*Chapter 28 Index. Imperfections. HW#10 (Ch 27-28) , due Dec 6, posted.
*Chapter 29 Index Nonconservative Loading.
*Chapter 30 Index Dynamic Stability.
Appendix H Index. The C1 TL Beam.
*Appendix R Index. The Mathematics of Finite Rotations.
Appendix Z Index. References.
*Exam Material Index. Take-home final exam posted.
Last update: December 9, 2004.
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