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 IIII are taught as part of the AFEM graduate course (ASEN 6347)
in the list below. Related courses may be accessed at 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 BernoulliEuler Beam. HW#2 solutions posted Chapter 9 Index. Placeholder Chapter 10 Index. ThreeDimensional Linear Elastostatics. AFEM HW#3 & solutions posted Chapter 11 Index. The HR Variational Principle of Elastostatics. HW#3 solutions posted Chapter 12 Index. The ThreeField 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: FICBased Variational Principles for 1D SolidFluid 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: FICBased Variational Principles for 2D SolidFluid 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: FICBased Variational Principles for 3D SolidFluid 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: FICBased Variational Principles for DiffusionAbsorption & 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).  
Last update: February 21, 2013.
This page constructed by Carlos Felippa: carlos.felippa@colorado.edu