Variational Methods and Structural Optimization

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Description:

ME 697 Variational Methods and Structural Optimization 3-0-0-6

Mathematical preliminaries: Vector spaces, normed linear spaces, inner product spaces, functionals, Gåteaux variation, Fréchet differential; Calculus of variations: Motivating examples, first variation and Euler-Lagrange equations, second variation and sufficiency conditions for extremum, isoperimetric problems, global and local constraints, strong form and weak form of governing equations in mechanics, transversality conditions; One dimensional problems: Size optimization of bars and beams, stress constraints, eigenvalue problems for strings, bars and beams; Mathematical programming: Karush-Kuhn-Tucker (KKT) conditions, brief introduction to numerical optimization algorithms, application of mathematical programming to structural optimization problems; Structural optimization: Truss topology optimization, sensitivity analysis, topology optimization with frames and continuum elements, optimality criteria method for stiff structure, design of compliant mechanisms.

References:

I. M. Gelfand and S. V. Fomin, Calculus of Variations, Dover Publications, 2003.

R. Weinstock, Calculus o/ Variations with Applications to Physics and Engineering, Dover Publications, 1975.

A. S. Gupta, Calculus of Variations with Applications, Prentice-Hall of India Pvt. Ltd., New Delhi, 2008.

D. R. Smith, Variational Methods in Optimization, Dover Publications, 1998.

P. W. Christensen and A. Klarbring, An Introduction to Structural Optimization, Springer, 2009.

R. T. Haftka, and Z. Gurdal, Elements of Structural Optimization, Kluwer Academic Publishers, 1992.

M. P. Bendsøe, and O. Sigmund, Topology Optimization: Theory, Methods, and Applications, Springer, 2003.

P. Y. Papalambros and D. J. Wilde, Principles of Optimal Design, Cambridge University Press, 2000.

D. G. Luenberger, Optimization by Vector Space Methods, John-Wiley & Sons, 1969.