Advanced Variational Methods In Mechanics Course Material

Advanced Variational Methods In Mechanics (Course in Preparation) - Date TBA Department of Aerospace Engineering Sciences University of Colorado at Boulder
This is the public web site for the graduate core course (id TBA): Advanced Variational Methods in Mechanics (AVMM), which is under preparation. This master and doctoral level elective course will be 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. Selected Chapters of Parts I-III are taught as part of the AFEM graduate course (ASEN 6347) in the list below. Related courses may be accessed at AFEM: Advanced Finite Element Methods (ASEN 6347) . Master & doctoral level IFEM: Introduction to Finite Element Methods (ASEN 5007) . Master (core) & senior-elective level FSI: Fluid Structure Interaction (ASEN 5509) . Advanced doctoral 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) NFEM: Nonlinear Finite Element Methods (ASEN 6107) . Master & doctoral level JSTR: Structures (ASEN 3112) . Junior undergraduate level Part I: Introduction to Variational Calculus Chapter 1 Index. Variational Calculus Overview. Chapter 2 Index. The Basic Functional. Chapter 3 Index. Generalizations of the Basic Functional. Chapter 4 Index. General Variation of a Functional. Chapter 5 Index. Equality Constraints. Part II: Poisson Problems Chapter 6 Index. Decomposition of Poisson Problems. AFEM HW#1 & solutions (partly done) posted Chapter 7 Index. Weak and Variational Forms of Poisson's Equation. AFEM HW#2 & solutions posted Part III: The Variational Principles of Mechanics Chapter 8 Index. The Bernoulli-Euler Beam. HW#2 solutions posted Chapter 9 Index. Placeholder Chapter 10 Index. Three-Dimensional Linear Elastostatics. AFEM HW#3 & solutions posted Chapter 11 Index. The HR Variational Principle of Elastostatics. HW#3 solutions posted Chapter 12 Index. The Three-Field Variational Principle of Elastostatics Not covered Chapter 13 Index. Hybrid Variational Principles: Formulation. AFEM HW#4 & solutions posted Chapter 14 Index. Hybrid Variational Principles: 1D Application Examples. Will be covered this time Chapter 15 Index. Hybrid Variational Principles: 2D Application Examples. In progress. Not covered Chapter 16 Index. Placeholder Part IV: Parametrized Variational Principles Chapter 17 Index. Placeholder Chapter 18 Index. Placeholder Chapter 19 Index. Placeholder Chapter 20 Index. Placeholder Part V: Modified Equation Methods Chapter 21 Index. Placeholder Chapter 22 Index. Placeholder Chapter 23 Index. Placeholder Part VI: FIC-Based Variational Principles for 1D Solid-Fluid Problems Chapter 24 Index. Static Analysis (under construction) Chapter 25 Index. Spectral Analysis (under construction) Chapter 26 Index. Direct Time Integration (under construction) Part VII: FIC-Based Variational Principles for 2D Solid-Fluid Problems Chapter 27 Index. Invariant Higher Derivative Forms TBD Chapter 28 Index. Invariant Variational Forms TBD Chapter 29 Index. Static Analysis TBD Chapter 30 Index. Direct Time Integration TBD Part VIII: FIC-Based Variational Principles for 3D Solid-Fluid Problems Chapter 31 Index. Invariant Higher Derivative Forms TBD Chapter 32 Index. Invariant Variational forms TBD Chapter 33 Index. Static Analysis TBD Chapter 34 Index. Direct Time Integration TBD Part IX: FIC-Based Variational Principles for Diffusion-Absorption & Helmholtz Problems Chapter 35 Index. Computational Mechanics 2007 paper Chapter 36 Index. Placeholder Appendices Appendix A Index. Mathematical Background of Variational Calculus Appendix R Index. References (in progress).

Advanced Variational Methods In Mechanics (Course in Preparation) - Date TBA
Department of Aerospace Engineering Sciences
University of Colorado at Boulder

This is the public web site for the graduate core course (id TBA): Advanced Variational Methods in Mechanics (AVMM), which is under preparation. This master and doctoral level elective course will be 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. Selected Chapters of Parts I-III are taught as part of the AFEM graduate course (ASEN 6347) in the list below. Related courses may be accessed at
AFEM: Advanced Finite Element Methods (ASEN 6347) . Master & doctoral level
IFEM: Introduction to Finite Element Methods (ASEN 5007) . Master (core) & senior-elective level
FSI: Fluid Structure Interaction (ASEN 5509) . Advanced doctoral 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)
NFEM: Nonlinear Finite Element Methods (ASEN 6107) . Master & doctoral level
JSTR: Structures (ASEN 3112) . Junior undergraduate level

Part I: Introduction to Variational Calculus

Chapter 1 Index. Variational Calculus Overview.
Chapter 2 Index. The Basic Functional.
Chapter 3 Index. Generalizations of the Basic Functional.
Chapter 4 Index. General Variation of a Functional.
Chapter 5 Index. Equality Constraints.

Part II: Poisson Problems

Chapter 6 Index. Decomposition of Poisson Problems. AFEM HW#1 & solutions (partly done) posted
Chapter 7 Index. Weak and Variational Forms of Poisson's Equation. AFEM HW#2 & solutions posted

Part III: The Variational Principles of Mechanics

Chapter 8 Index. The Bernoulli-Euler Beam. HW#2 solutions posted
Chapter 9 Index. Placeholder
Chapter 10 Index. Three-Dimensional Linear Elastostatics. AFEM HW#3 & solutions posted
Chapter 11 Index. The HR Variational Principle of Elastostatics. HW#3 solutions posted
Chapter 12 Index. The Three-Field Variational Principle of Elastostatics Not covered
Chapter 13 Index. Hybrid Variational Principles: Formulation. AFEM HW#4 & solutions posted
Chapter 14 Index. Hybrid Variational Principles: 1D Application Examples. Will be covered this time
Chapter 15 Index. Hybrid Variational Principles: 2D Application Examples. In progress. Not covered
Chapter 16 Index. Placeholder

Part IV: Parametrized Variational Principles

Chapter 17 Index. Placeholder
Chapter 18 Index. Placeholder
Chapter 19 Index. Placeholder
Chapter 20 Index. Placeholder

Part V: Modified Equation Methods

Chapter 21 Index. Placeholder
Chapter 22 Index. Placeholder
Chapter 23 Index. Placeholder

Part VI: FIC-Based Variational Principles for 1D Solid-Fluid Problems

Chapter 24 Index. Static Analysis (under construction)
Chapter 25 Index. Spectral Analysis (under construction)
Chapter 26 Index. Direct Time Integration (under construction)

Part VII: FIC-Based Variational Principles for 2D Solid-Fluid Problems

Chapter 27 Index. Invariant Higher Derivative Forms TBD
Chapter 28 Index. Invariant Variational Forms TBD
Chapter 29 Index. Static Analysis TBD
Chapter 30 Index. Direct Time Integration TBD

Part VIII: FIC-Based Variational Principles for 3D Solid-Fluid Problems

Chapter 31 Index. Invariant Higher Derivative Forms TBD
Chapter 32 Index. Invariant Variational forms TBD
Chapter 33 Index. Static Analysis TBD
Chapter 34 Index. Direct Time Integration TBD

Part IX: FIC-Based Variational Principles for Diffusion-Absorption & Helmholtz Problems

Chapter 35 Index. Computational Mechanics 2007 paper
Chapter 36 Index. Placeholder

Appendices
Appendix A Index. Mathematical Background of Variational Calculus
Appendix R Index. References (in progress).