Nonlinear Finite Element Methods (ASEN 6107) Course Material

Nonlinear Finite Element Methods (ASEN 6107) - Fall 2017 Department of Aerospace Engineering Sciences University of Colorado at Boulder
This is the public web site for the graduate course ASEN 6107: Nonlinear Finite Element Methods (NFEM). This doctoral and master-elective level course is part of the Aerospace Systems Focus Area of the graduate curriculum in the Department of Aerospace Engineering Sciences of the University of Colorado at Boulder. Normally offered every two years during the Spring semester (sometimes with 3 year gaps because of sabbaticals), both on-campus and remotely through CAETE. First taught in 1988. This website dates from 1999 and is continuously being revised. Related courses may be accessed at AFEM: Advanced Finite Element Methods (ASEN 6347) . Master & doctoral level AVVM: Advanced Variational Methods in Mechanics . Master and doctoral level (in preparation) FSI: Fluid Structure Interaction (ASEN 5509) . Advanced doctoral level IFEM: Introduction to Finite Element Methods (ASEN 5007) . Master & senior-elective level MFEMD: Matrix Finite Element Methods in Dynamics . Master & senior-elective level (in preparation) MFEMS: Matrix Finite Element Methods in Statics . Master & senior-elective level (in preparation) JSTR: Structures (ASEN 3112) . Junior undergraduate level, offered in D2L from 207 onward 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. Only briefly covered Chapter 2 Index. A Tour of Nonlinear Analysis. HW#1 posted, due 9/7. Solutions posted Chapter 3 Index. Residual Force Equations. HW#2 posted, due 9/14 Solutions posted Chapter 4 Index. One-Parameter Residual Equations. HW#2 solutions posted Chapter 5 Index. Critical Points and Related Properties. HW#3 posted, due 9/21. 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: Kinematics HW#4 posted, due 9/28. Solutions posted Chapter 8 Index. Review of Continuum Mechanics: Field Equations. HW#4 solutions posted Chapter 9 Index. TL Bar Elements: Formulation & Implementation. HW#5 posted, due 10/5. Solutions posted Chapter 10 Index. TL Bar Elements: Truss Analysis. HW#6 posted, due 10/19. Solutions posted Chapter 11 Index. The TL Plane Beam Element: Formulation. HW#6 solutions posted Chapter 12 Index. The TL Plane Beam Element: Implementation. Part III: Corotational, Geometrically Nonlinear Finite Elements Chapter 13 Index. CR Formulation Overview I. Chapter 14 Index. CR Formulation Overview II. Chapter 15 Index. Unified Kinematic Description: Space Bar. Chapter 16 Index. The CR Formulation: BE Plane Beam. Chapter 17 Index. Placeholder. Chapter 18 Index. Placeholder. Chapter 19 Index. Placeholder. Part IV: Solution Methods Chapter 20 Index. Overview of Solution Methods. HW#7 posted, due 10/26. solutions posted Chapter 21 Index. Purely Incremental Methods: Load Control. Chapter 22 Index. Purely Incremental Methods: General Control. HW#8 posted, due 11/2. solutions posted Chapter 23 Index. Purely Incremental Methods: Implementation. To be finished. Chapter 24 Index. Purely Incremental Methods: Benchmark Examples. Under construction. Chapter 25 Index. Conventional Newton Methods. Under complete renovation; dont print yet. Chapter 26 Index. Newton Methods: General Control and Variants. To be rewritten. Chapter 27 Index. Corrective Methods: Implementation. Under construction. Part V: Structural Stability Chapter 28 Index. Structural Stability: Basic Concepts. HW#10 posted, due 11/9. Solutions posted Chapter 29 Index. Linearized Prebuckling: Formulation. HW#11 posted, due 11/30. Solutions posted Chapter 30 Index. Linearized Prebuckling: Implementation. Chapter 31 Index. Linearized Prebuckling: Examples and Limitations. HW#10 solutions posted --> Chapter 32 Index. Qualitative Analysis of Critical Points. Chapter 33 Index. Nonlinear Bifurcation Analysis. HW#11 posted, due 12/6. solutions posted Chapter 34 Index. Imperfections. Chapter 35 Index. Nonconservative Loading: Overview. HW#12 (last HW) posted, due 12/14; Solutions posted Chapter 36 Index. Aero- and Hydrodynamic Loading. HW#12 solutions posted. Chapter 37 Index. Dynamic Stability: Formulation. Chapter 38 Index. Dynamic Stability: Examples. HW#12 solutions posted. 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 S Index. Accelerators and Line Search. Appendix T Index. Detecting and Traversing Critical Points. Appendix R Index. References. Old Chapters No Longer Covered Old Chapter 10 Index. Not to be covered. Old Chapter 11 Index. Not to be covered. Exam Material Exam Material Index. Midterm 1 posted Oct 7 afternoon, due on or before Oct 12 at class time. Solutions posted. Midterm 2 posted Nov 10 noon, due on or before Nov 16 at class time. Final Exam posted Wed Dec 13 afternoon, due Wed Dec 20 by 1pm.

Nonlinear Finite Element Methods (ASEN 6107) - Fall 2017
Department of Aerospace Engineering Sciences
University of Colorado at Boulder

This is the public web site for the graduate course ASEN 6107: Nonlinear Finite Element Methods (NFEM). This doctoral and master-elective level course is part of the Aerospace Systems Focus Area of the graduate curriculum in the Department of Aerospace Engineering Sciences of the University of Colorado at Boulder. Normally offered every two years during the Spring semester (sometimes with 3 year gaps because of sabbaticals), both on-campus and remotely through CAETE. First taught in 1988. This website dates from 1999 and is continuously being revised. Related courses may be accessed at
AFEM: Advanced Finite Element Methods (ASEN 6347) . Master & doctoral level
AVVM: Advanced Variational Methods in Mechanics . Master and doctoral level (in preparation)
FSI: Fluid Structure Interaction (ASEN 5509) . Advanced doctoral level
IFEM: Introduction to Finite Element Methods (ASEN 5007) . Master & senior-elective level
MFEMD: Matrix Finite Element Methods in Dynamics . Master & senior-elective level (in preparation)
MFEMS: Matrix Finite Element Methods in Statics . Master & senior-elective level (in preparation)
JSTR: Structures (ASEN 3112) . Junior undergraduate level, offered in D2L from 207 onward

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. Only briefly covered
Chapter 2 Index. A Tour of Nonlinear Analysis. HW#1 posted, due 9/7. Solutions posted
Chapter 3 Index. Residual Force Equations. HW#2 posted, due 9/14 Solutions posted
Chapter 4 Index. One-Parameter Residual Equations. HW#2 solutions posted
Chapter 5 Index. Critical Points and Related Properties. HW#3 posted, due 9/21. 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: Kinematics HW#4 posted, due 9/28. Solutions posted
Chapter 8 Index. Review of Continuum Mechanics: Field Equations. HW#4 solutions posted
Chapter 9 Index. TL Bar Elements: Formulation & Implementation. HW#5 posted, due 10/5. Solutions posted
Chapter 10 Index. TL Bar Elements: Truss Analysis. HW#6 posted, due 10/19. Solutions posted
Chapter 11 Index. The TL Plane Beam Element: Formulation. HW#6 solutions posted
Chapter 12 Index. The TL Plane Beam Element: Implementation.

Part III: Corotational, Geometrically Nonlinear Finite Elements
Chapter 13 Index. CR Formulation Overview I.
Chapter 14 Index. CR Formulation Overview II.
Chapter 15 Index. Unified Kinematic Description: Space Bar.
Chapter 16 Index. The CR Formulation: BE Plane Beam.
Chapter 17 Index. Placeholder.
Chapter 18 Index. Placeholder.
Chapter 19 Index. Placeholder.

Part IV: Solution Methods
Chapter 20 Index. Overview of Solution Methods. HW#7 posted, due 10/26. solutions posted
Chapter 21 Index. Purely Incremental Methods: Load Control.
Chapter 22 Index. Purely Incremental Methods: General Control. HW#8 posted, due 11/2. solutions posted
Chapter 23 Index. Purely Incremental Methods: Implementation. To be finished.
Chapter 24 Index. Purely Incremental Methods: Benchmark Examples. Under construction.
Chapter 25 Index. Conventional Newton Methods. Under complete renovation; dont print yet.
Chapter 26 Index. Newton Methods: General Control and Variants. To be rewritten.
Chapter 27 Index. Corrective Methods: Implementation. Under construction.

Part V: Structural Stability
Chapter 28 Index. Structural Stability: Basic Concepts. HW#10 posted, due 11/9. Solutions posted
Chapter 29 Index. Linearized Prebuckling: Formulation. HW#11 posted, due 11/30. Solutions posted
Chapter 30 Index. Linearized Prebuckling: Implementation.
Chapter 31 Index. Linearized Prebuckling: Examples and Limitations. HW#10 solutions posted -->
Chapter 32 Index. Qualitative Analysis of Critical Points.
Chapter 33 Index. Nonlinear Bifurcation Analysis. HW#11 posted, due 12/6. solutions posted
Chapter 34 Index. Imperfections.
Chapter 35 Index. Nonconservative Loading: Overview. HW#12 (last HW) posted, due 12/14; Solutions posted
Chapter 36 Index. Aero- and Hydrodynamic Loading. HW#12 solutions posted.
Chapter 37 Index. Dynamic Stability: Formulation.
Chapter 38 Index. Dynamic Stability: Examples. HW#12 solutions posted.

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 S Index. Accelerators and Line Search.
Appendix T Index. Detecting and Traversing Critical Points.
Appendix R Index. References.

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

Exam Material
Exam Material Index. Midterm 1 posted Oct 7 afternoon, due on or before Oct 12 at class time. Solutions posted.
Midterm 2 posted Nov 10 noon, due on or before Nov 16 at class time.
Final Exam posted Wed Dec 13 afternoon, due Wed Dec 20 by 1pm.