Nonlinear Finite Element Methods (ASEN 6107) Course Material

Nonlinear Finite Element Methods (ASEN 6107) - Fall 2010 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 10 roster and e-mail addresses. From CUConnect as of 1/19/10. 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 21, posted. Solutions to HW#1 posted Chapter 3 Index. Residual Force Equations. HW#2 (Chs 3-4), due Thu Jan 28, posted. (Also posted under Chapter 4 Index)* Solutions to HW#2 in Ch 3 posted . Chapter 4 Index. One-Parameter Residual Equations. HW#2 (Chs 3-4), due Thu Jan 28, 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 4, posted.* Solutions to HW#3 in Ch 5 Exercises posted Chapter 6 Index. Conservative Systems. HW#3 (Chs 5-6) due Thu Feb 4, posted.* Solutions 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 11, posted.* Chapter 8 Index. The TL Bar Element. Chapter 9 Index. The TL Timoshenko Plane Beam Element. Chapter 10 Index. Not to be covered Spring 2010. Chapter 11 Index. Not to be covered Spring 2010. 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. Chapter 15 Index. The CR Formulation: C1 Plane Beam. 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. Chapter 19 Index. Will not be covered. Chapter 20 Index. Conventional Newton Methods. Solutions posted. Chapter 21 Index. Newton-Like Methods. Chapter 22 Index. Accelerators and Line Search. Not to be covered: provided as reference material only. Chapter 23 Index. Detecting and Traversing Critical Points. Part IV: Stability Analysis Chapter 24 Index. Bifurcation: Linearized Prebuckling I. Chapter 26 Index. Qualitative Analysis of Critical Points. Chapter 27 Index. Nonlinear Bifurcation Analysis. Chapter 28 Index. Imperfections. Chapter 29 Index Nonconservative Loading. Chapter 30 Index Dynamic Stability. Appendices Appendix H Index. The C1 TL Beam. Appendix R Index. The Mathematics of Finite Rotations. Appendix Z Index. References. Exams Exam Material Index.

Nonlinear Finite Element Methods (ASEN 6107) - Fall 2010
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 10 roster and e-mail addresses. From CUConnect as of 1/19/10.

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 21, posted. Solutions to HW#1 posted
*Chapter 3 Index. Residual Force Equations. HW#2 (Chs 3-4), due Thu Jan 28, posted. (Also posted under Chapter 4 Index) Solutions to HW#2 in Ch 3 posted .
*Chapter 4 Index. One-Parameter Residual Equations. HW#2 (Chs 3-4), due Thu Jan 28, 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 4, posted. Solutions to HW#3 in Ch 5 Exercises posted
*Chapter 6 Index. Conservative Systems. HW#3 (Chs 5-6) due Thu Feb 4, posted. Solutions 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 11, posted.
*Chapter 8 Index. The TL Bar Element.
*Chapter 9 Index. The TL Timoshenko Plane Beam Element.
Chapter 10 Index. Not to be covered Spring 2010.
Chapter 11 Index. Not to be covered Spring 2010.
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.
Chapter 15 Index. The CR Formulation: C1 Plane Beam.

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.
Chapter 19 Index. Will not be covered.
Chapter 20 Index. Conventional Newton Methods. Solutions posted.
Chapter 21 Index. Newton-Like Methods.
Chapter 22 Index. Accelerators and Line Search. Not to be covered: provided as reference material only.
Chapter 23 Index. Detecting and Traversing Critical Points.

Part IV: Stability Analysis
Chapter 24 Index. Bifurcation: Linearized Prebuckling I.
Chapter 26 Index. Qualitative Analysis of Critical Points.
Chapter 27 Index. Nonlinear Bifurcation Analysis.
Chapter 28 Index. Imperfections.
Chapter 29 Index Nonconservative Loading.
Chapter 30 Index Dynamic Stability.

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

Exams
Exam Material Index.