Nonlinear Finite Element Methods (ASEN 6107) Course Material

Nonlinear Finite Element Methods (ASEN 6107) - Spring 2012 Department of Aerospace Engineering Sciences University of Colorado at Boulder
This is the public web site for the graduate elective course ASEN 6107. This course is part of the Arospace Systems Focus Area of the graduate curriculum in the Department of Aerospace Engineering Sciences of the University of Colorado at Boulder. It is normally offered every two years during the Spring semester (sometimes with 3 year gaps because of sabbaticals). First offered in 1988. Course websites dates from 1998. 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. Chapter 2 Index. A Tour of Nonlinear Analysis. HW#1 & solutions posted Chapter 3 Index. Residual Force Equation HW#2 posted Chapter 4 Index. One-Parameter Residual Equations. Chapter 5 Index. Critical Points and Related Properties. HW#3 posted Chapter 6 Index. Conservative Systems. Part II: Total Lagrangian, Geometrically Nonlinear Finite Elements Chapter 7 Index. Review of Continuum Mechanics. HW#4 posted Chapter 8 Index. The TL Bar Element: Formulation. Chapter 9 Index. The TL Bar Element: Implementation. Chapter 10 Index. The TL Timoshenko Plane Beam Element: Formulation. Chapter 11 Index. The TL Timoshenko Plane Beam Element: Imp[lementation. 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. Chapter 15 Index. The CR Formulation: Space Beam. Chapter 16 Index. Solid Shell Element. Part IV: Solution Methods Chapter 17 Index. Overview of Solution Methods. Chapter 18 Index. Purely Incremental Methods: Load Control. Chapter 19 Index. Purely Incremental Methods: General Control. Chapter 20 Index. Conventional Newton Methods. Chapter 21 Index. Newton-Like Methods. Chapter 22 Index. Accelerators and Line Search. Chapter 23 Index. Detecting and Traversing Critical Points. Part V: Structural Stability Chapter 24 Index. Bifurcation: Linearized Prebuckling I. Chapter 25 Index. Bifurcation: Linearized Prebuckling II. 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 M Index. The Mathematics of Finite Rotations. Appendix R Index. References. Old Chapters No Longer Covered Old Chapter 10 Index. Not to be covered Spring 2012. Old Chapter 11 Index. Not to be covered Spring 2012.

Nonlinear Finite Element Methods (ASEN 6107) - Spring 2012
Department of Aerospace Engineering Sciences
University of Colorado at Boulder

This is the public web site for the graduate elective course ASEN 6107. This course is part of the Arospace Systems Focus Area of the graduate curriculum in the Department of Aerospace Engineering Sciences of the University of Colorado at Boulder. It is normally offered every two years during the Spring semester (sometimes with 3 year gaps because of sabbaticals). First offered in 1988. Course websites dates from 1998.

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.
Chapter 2 Index. A Tour of Nonlinear Analysis. HW#1 & solutions posted
Chapter 3 Index. Residual Force Equation HW#2 posted
Chapter 4 Index. One-Parameter Residual Equations.
Chapter 5 Index. Critical Points and Related Properties. HW#3 posted
Chapter 6 Index. Conservative Systems.

Part II: Total Lagrangian, Geometrically Nonlinear Finite Elements
Chapter 7 Index. Review of Continuum Mechanics. HW#4 posted
Chapter 8 Index. The TL Bar Element: Formulation.
Chapter 9 Index. The TL Bar Element: Implementation.
Chapter 10 Index. The TL Timoshenko Plane Beam Element: Formulation.
Chapter 11 Index. The TL Timoshenko Plane Beam Element: Imp[lementation.

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.
Chapter 15 Index. The CR Formulation: Space Beam.
Chapter 16 Index. Solid Shell Element.

Part IV: Solution Methods
Chapter 17 Index. Overview of Solution Methods.
Chapter 18 Index. Purely Incremental Methods: Load Control.
Chapter 19 Index. Purely Incremental Methods: General Control.
Chapter 20 Index. Conventional Newton Methods.
Chapter 21 Index. Newton-Like Methods.
Chapter 22 Index. Accelerators and Line Search.
Chapter 23 Index. Detecting and Traversing Critical Points.

Part V: Structural Stability
Chapter 24 Index. Bifurcation: Linearized Prebuckling I.
Chapter 25 Index. Bifurcation: Linearized Prebuckling II.
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 M Index. The Mathematics of Finite Rotations.
Appendix R Index. References.

Old Chapters No Longer Covered
Old Chapter 10 Index. Not to be covered Spring 2012.
Old Chapter 11 Index. Not to be covered Spring 2012.