Nonlinear Finite Element Methods (ASEN 5107) Course Material

Nonlinear Finite Element Methods (ASEN 5107) - Fall 2007 Department of Aerospace Engineering Sciences University of Colorado at Boulder
Web site under complete revision: please be patient! *Note: Please do not download material until the link is marked with an asterisk ()** . Course outline and syllabus. HW preparation & submission guidelines. Fall 07 roster and e-mail addresses (not yet ready) Part 0: Preface Preface Index. Part I: Overview of Nonlinear Problems Chapter 1 Index. Overview. Chapter 2 Index. A Tour of Nonlinear Analysis. HW#1, due Thu Jan 25, posted. Solutions to HW#1 posted Chapter 3 Index. Residual Force Equations. Solutions to HW#2 in Ch 3 posted .* Chapter 4 Index. One-Parameter Residual Equations. HW#2 (Chs 3-4), due Thu Feb 1, posted.* Solutions to HW#2 in Ch 4 posted. Chapter 5 Index. Critical Points and Related Properties. HW#3 (Chs 5-6) due Thu Feb 8, posted. Solutions to HW#3 in Ch 5 Exercises posted* Chapter 6 Index. Conservative Systems. Solutions to to HW#3 in Ch 6 Exercises posted.* Part II: Formulation of Geometrically Nonlinear Finite Elements Chapter 7 Index. Review of Continuum Mechanics. HW#4, due Feb 15, posted. Solutions to Exercises in Ch 7 posted.* Chapter 8 Index. The TL Bar Element. Solutions to Exercises in Ch 8 posted.* Chapter 9 Index. The TL Timoshenko Plane Beam Element. HW#5, due Feb 22, posted. Contains tentative announcement of Midterm Quiz 1. Solutions to Exercises in Ch 9 posted.* Chapter 10 Index. Not to be covered Spring 2007. Chapter 11 Index. Not to be covered Spring 2007. Chapter 12 Index. CR Formulation Overview I. (Rewritten Chapter, ready) Chapter 13 Index. CR Formulation Overview II (Chapter under preparation) Provided for reference only - course will skip to next chapter. Chapter 14 Index. The CR Formulation: Space Bar. New Chapter. HW#6, due Th Mar 8, posted. Solutions posted although not complete. Chapter 15 Index. The CR Formulation: C1 Plane Beam. Part III: Nonlinear Solution Methods* Chapter 16 Index. Overview of Solution Methods. HW#7, due Th Mar 15, posted. Solutions posted.* Chapter 17 Index. Purely Incremental Methods: Load Control. Chapter 18 Index. Purely Incremental Methods: General Control. HW#8, due Th Mar 22 posted. Solutions posted. Chapter 19 Index. Will not be covered. Chapter 20 Index. Conventional Newton Methods. HW#9, due Th April 5, posted. Contains announcement of Take-home Midterm Quiz 2.* Solutions posted. Chapter 21 Index. Newton-Like Methods. Eqn numbers in Exercise 21.1 corrected 4/4/07. 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 (not assigned) posted.* Part IV: Stability Analysis Chapter 24 Index. Bifurcation: Linearized Prebuckling I. HW#9 (Chs 24-25) due April 19, posted. Contains announcement for take-home final exam. 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. HW#11 (Chs 27-28) , due April 26, posted. Solutions posted. Chapter 28 Index. Imperfections. HW#11 (Ch 27-28) , due April 26, posted under Ch 27 index. Solutions posted.* Chapter 29 Index Nonconservative Loading. Last HW: HW#12 (Chs 29-30) , due May 3, posted. HW Solutions posted.* Chapter 30 Index Dynamic Stability. HW Solutions posted.* Appendices Appendix H Index. The C1 TL Beam. Appendix R Index. The Mathematics of Finite Rotations. Appendix Z Index. References. Exams Exam Material Index. Take-home final exam posted.

Nonlinear Finite Element Methods (ASEN 5107) - Fall 2007
Department of Aerospace Engineering Sciences
University of Colorado at Boulder

Web site under complete revision: please be patient!

Note: Please do not download material until the link is marked with an asterisk (*) .

*Course outline and syllabus.
*HW preparation & submission guidelines.
Fall 07 roster and e-mail addresses (not yet ready)

Part 0: Preface
Preface Index.

Part I: Overview of Nonlinear Problems
*Chapter 1 Index. Overview.
*Chapter 2 Index. A Tour of Nonlinear Analysis. HW#1, due Thu Jan 25, posted. Solutions to HW#1 posted
*Chapter 3 Index. Residual Force Equations. Solutions to HW#2 in Ch 3 posted .
*Chapter 4 Index. One-Parameter Residual Equations. HW#2 (Chs 3-4), due Thu Feb 1, posted. Solutions to HW#2 in Ch 4 posted.
*Chapter 5 Index. Critical Points and Related Properties. HW#3 (Chs 5-6) due Thu Feb 8, posted. Solutions to HW#3 in Ch 5 Exercises posted
*Chapter 6 Index. Conservative Systems. Solutions to to HW#3 in Ch 6 Exercises posted.

Part II: Formulation of Geometrically Nonlinear Finite Elements
*Chapter 7 Index. Review of Continuum Mechanics. HW#4, due Feb 15, posted. Solutions to Exercises in Ch 7 posted.
*Chapter 8 Index. The TL Bar Element. Solutions to Exercises in Ch 8 posted.
*Chapter 9 Index. The TL Timoshenko Plane Beam Element. HW#5, due Feb 22, posted. Contains tentative announcement of Midterm Quiz 1. Solutions to Exercises in Ch 9 posted.
Chapter 10 Index. Not to be covered Spring 2007.
Chapter 11 Index. Not to be covered Spring 2007.
*Chapter 12 Index. CR Formulation Overview I. (Rewritten Chapter, ready)
Chapter 13 Index. CR Formulation Overview II (Chapter under preparation) Provided for reference only - course will skip to next chapter.
*Chapter 14 Index. The CR Formulation: Space Bar. New Chapter. HW#6, due Th Mar 8, posted. Solutions posted although not complete.
*Chapter 15 Index. The CR Formulation: C1 Plane Beam.

Part III: Nonlinear Solution Methods
*Chapter 16 Index. Overview of Solution Methods. HW#7, due Th Mar 15, posted. Solutions posted.
*Chapter 17 Index. Purely Incremental Methods: Load Control.
*Chapter 18 Index. Purely Incremental Methods: General Control. HW#8, due Th Mar 22 posted. Solutions posted.
Chapter 19 Index. Will not be covered.
*Chapter 20 Index. Conventional Newton Methods. HW#9, due Th April 5, posted. Contains announcement of Take-home Midterm Quiz 2. Solutions posted.
*Chapter 21 Index. Newton-Like Methods. Eqn numbers in Exercise 21.1 corrected 4/4/07. 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 (not assigned) posted.

Part IV: Stability Analysis
*Chapter 24 Index. Bifurcation: Linearized Prebuckling I. HW#9 (Chs 24-25) due April 19, posted. Contains announcement for take-home final exam. 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. HW#11 (Chs 27-28) , due April 26, posted. Solutions posted.
*Chapter 28 Index. Imperfections. HW#11 (Ch 27-28) , due April 26, posted under Ch 27 index. Solutions posted.
*Chapter 29 Index Nonconservative Loading. Last HW: HW#12 (Chs 29-30) , due May 3, posted. HW Solutions posted.
*Chapter 30 Index Dynamic Stability. HW Solutions posted.

Appendices
Appendix H Index. The C1 TL Beam.
Appendix R Index. The Mathematics of Finite Rotations.
Appendix Z Index. References.

Exams
Exam Material Index. Take-home final exam posted.