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.
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