ES 505- Variational Methods in Engineering

Fall 2003

Course Information

Topics:

Indicial Notation, scalars, vectors and tensors.

Problems of minimization and maximization.

Functionals. Classical problems in calculus of variations, Euler equations, Variational notation, Natural boundary conditions, Hamilton's principle, Lagrange equations.

Transformation of boundary value problems into the problem of calculus of variation.

Direct methods; Ritz method, Galerkin method, Kantorovich method, Weighted residual method.

References:

1. Methods of Applied Mathematics, F. B. Hildebrand, 2nd edition, 1965 Prentice-Hall, Inc.

2. Energy and Variational Methods in Applied Mechanics, J. N. Reddy, 1984

3. Energy Methods in Applied Mechanics, H. L. Langhaar, 1962

4. Solid Mechanics: A Variational Approach, Clive L. Dym, Irving H. Shames, 1973 McGraw-Hill

5. Foundations of Solid Mechanics, Y. C. Fung, 1965 Prentice-Hall, Inc.

6. Mathematics of Physics and Modern Engineering, Sokolnikoff and Redheffer, 1958 McGraw-Hill.

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