Finite element approximation for optimal shape design: theory and applications
Explains how to speed the optimal shape design process using a computer. Outlines the problems inherent in optimal shape design and discusses methods of their solution. Concentrates on finite element approximation and describes numerical realization of optimization techniques. Treats optimal design problems via the optimal control theory when the state systems are governed by variational inequalities. Provides useful background information, followed by numerous approaches to optimal shape design, all supported by illustrative examples. Appendices provide algorithms and numerous examples and their calculations are included.
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Abstract setting of optimal shape design problem and
Optimal shape design of systems governed by a unilateral
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adjoint algorithm Appendix applied approximation boundary conditions boundary value problem Chapter constraints contact problems convex set cost functional defined denote design sensitivity analysis differentiable discrete domain elastic exist a subsequence f Find fi(a Figure finite element fixed follows formula ft(a G K(a G R2 G Rn G U*d given gradient Green's formula Haslinger Haug Hilbert space Hlavacek initial iterations Komkov Lagrange multipliers Lemma liminf limsup linear Lipschitz Lipschitz continuous lower semicontinuous mapping material derivative method minimize Moreover Necas Neittaanmaki nodal nodes nonlinear programming nonsmooth Numerical results obtain optimal control optimal pair optimal shape design parameter Pironneau Proof respect results for Example satisfying Section sequence sequential quadratic programming shape design problems shape optimization Sokolowski solves P(a stress subgradient sufficiently small Tc(a Theorem triangulation u(ft unilateral boundary value variational inequality vector Zolesio