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 & solutions posted Chapter 4 Index. One-Parameter Residual Equations. HW#2 solutions posted Chapter 5 Index. Critical Points and Related Properties. HW#3 & 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 & sol posted Chapter 8 Index. The TL Plane Bar Element: Formulation. HW#4 solutions posted Chapter 9 Index. The TL Plane Bar Element: Implementation. HW#5 posted Chapter 10 Index. The TL Plane Beam Element: Formulation. Chapter 11 Index. The TL Plane Beam Element: Implementation. HW#6 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 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 Chapter 19 Index. Purely Incremental Methods: Load Control. Chapter 20 Index. Purely Incremental Methods: General Control. HW#9 posted Chapter 21 Index. Purely Incremental Methods: Implementation. Not covered Chapter 22 Index. Conventional Newton Methods. HW#10 posted, also under Ch 27 Chapter 23 Index. Newton-Like Methods. Not covered Chapter 24 Index. Placeholder. 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#10 posted, also under Ch 22 Chapter 28 Index. Bifurcation: Linearized Prebuckling II. Chapter 29 Index. Qualitative Analysis of Critical Points. Chapter 30 Index. Nonlinear Bifurcation Analysis. HW#11 posted (last HW) Chapter 31 Index. Imperfections. Chapter 32 Index. Nonconservative Loading. Chapter 33 Index. Dynamic Stability. 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 2012. Old Chapter 11 Index. Not to be covered Spring 2012. Exam Material Exam Material Index. Midterm 1 & solutions posted. Final Exam posted Th Apr 26 noon.

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 & solutions posted
Chapter 4 Index. One-Parameter Residual Equations. HW#2 solutions posted
Chapter 5 Index. Critical Points and Related Properties. HW#3 & 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 & sol posted
Chapter 8 Index. The TL Plane Bar Element: Formulation. HW#4 solutions posted
Chapter 9 Index. The TL Plane Bar Element: Implementation. HW#5 posted
Chapter 10 Index. The TL Plane Beam Element: Formulation.
Chapter 11 Index. The TL Plane Beam Element: Implementation. HW#6 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
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
Chapter 19 Index. Purely Incremental Methods: Load Control.
Chapter 20 Index. Purely Incremental Methods: General Control. HW#9 posted
Chapter 21 Index. Purely Incremental Methods: Implementation. Not covered
Chapter 22 Index. Conventional Newton Methods. HW#10 posted, also under Ch 27
Chapter 23 Index. Newton-Like Methods. Not covered
Chapter 24 Index. Placeholder.
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#10 posted, also under Ch 22
Chapter 28 Index. Bifurcation: Linearized Prebuckling II.
Chapter 29 Index. Qualitative Analysis of Critical Points.
Chapter 30 Index. Nonlinear Bifurcation Analysis. HW#11 posted (last HW)
Chapter 31 Index. Imperfections.
Chapter 32 Index. Nonconservative Loading.
Chapter 33 Index. Dynamic Stability.

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 2012.
Old Chapter 11 Index. Not to be covered Spring 2012.

Exam Material
Exam Material Index. Midterm 1 & solutions posted.
Final Exam posted Th Apr 26 noon.