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
Part I: Introduction to Variational Principles Chapter 1 Index. Overview Chapter 2 Index. Placeholder Chapter 3 Index. Placeholder Chapter 4 Index. Placeholder Chapter 5 Index. Placeholder Part II: Poisson Problems Chapter 6 Index. Decomposition of Poisson Problems Chapter 7 Index. Weak and Variational Forms of Poisson's Equation Part III: The Variational Principles of Mechanics Chapter 8 Index. The Bernoulli-Euler Beam Chapter 9 Index. Placeholder Chapter 10 Index. Three-Dimensional Linear Elastostatics Chapter 11 Index. The HR Variational Principle of Elastostatics Chapter 12 Index. The Three-Field Variational Principle of Elastostatics Chapter 13 Index. Hybrid Variational Principles: Formulation Chapter 14 Index. Hybrid Variational Principles: Application Examples Chapter 15 Index. Placeholder 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: FIRC-Based Variational Principles for 1D Solid-Fluid Problems Chapter 21 Index. Static Analysis (under construction) Chapter 22 Index. Spectral Analysis (under construction) Chapter 23 Index. Direct Time Integration (under construction) Part VI: FIRC-Based Variational Principles for 2D Solid-Fluid Problems Chapter 24 Index. Invariant Higher Derivative Forms TBD Chapter 25 Index. Invariant Variational Forms TBD Chapter 26 Index. Static Analysis TBD Chapter 27 Index. Direct Time Integration TBD Part VII: FIRC-Based Variational Principles for 3D Solid-Fluid Problems Chapter 28 Index. Invariant Higher Derivative Forms TBD Chapter 29 Index. Invariant Variational forms TBD Chapter 30 Index. Static Analysis TBD Chapter 31 Index. Direct Time Integration TBD Chapter 32 Index. Placeholder Chapter 33 Index. Placeholder Chapter 34 Index. Placeholder Part VIII: FIRC-Based Variational Principles for Diffusion-Absorption & Helmholtz Problems Chapter 35 Index. Computational Mechanics 2007 paper Chapter 36 Index. Placeholder Appendices 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

Part I: Introduction to Variational Principles

Chapter 1 Index. Overview
Chapter 2 Index. Placeholder
Chapter 3 Index. Placeholder
Chapter 4 Index. Placeholder
Chapter 5 Index. Placeholder

Part II: Poisson Problems

Chapter 6 Index. Decomposition of Poisson Problems
Chapter 7 Index. Weak and Variational Forms of Poisson's Equation

Part III: The Variational Principles of Mechanics

Chapter 8 Index. The Bernoulli-Euler Beam
Chapter 9 Index. Placeholder
Chapter 10 Index. Three-Dimensional Linear Elastostatics
Chapter 11 Index. The HR Variational Principle of Elastostatics
Chapter 12 Index. The Three-Field Variational Principle of Elastostatics
Chapter 13 Index. Hybrid Variational Principles: Formulation
Chapter 14 Index. Hybrid Variational Principles: Application Examples
Chapter 15 Index. Placeholder
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: FIRC-Based Variational Principles for 1D Solid-Fluid Problems

Chapter 21 Index. Static Analysis (under construction)
Chapter 22 Index. Spectral Analysis (under construction)
Chapter 23 Index. Direct Time Integration (under construction)

Part VI: FIRC-Based Variational Principles for 2D Solid-Fluid Problems

Chapter 24 Index. Invariant Higher Derivative Forms TBD
Chapter 25 Index. Invariant Variational Forms TBD
Chapter 26 Index. Static Analysis TBD
Chapter 27 Index. Direct Time Integration TBD

Part VII: FIRC-Based Variational Principles for 3D Solid-Fluid Problems

Chapter 28 Index. Invariant Higher Derivative Forms TBD
Chapter 29 Index. Invariant Variational forms TBD
Chapter 30 Index. Static Analysis TBD
Chapter 31 Index. Direct Time Integration TBD
Chapter 32 Index. Placeholder
Chapter 33 Index. Placeholder
Chapter 34 Index. Placeholder

Part VIII: FIRC-Based Variational Principles for Diffusion-Absorption & Helmholtz Problems

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

Appendices
Appendix R Index. References (in progress).