Finite Element Approximation for Optimal Shape Design: Theory and ApplicationsExplains 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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Page vi
... solution does not depend smoothly , in general , on the control , i.e. it is not possible to differentiate the solution of the state problem with respect to variation of the boundary . Hence shape sensitivity analysis is a crucial ...
... solution does not depend smoothly , in general , on the control , i.e. it is not possible to differentiate the solution of the state problem with respect to variation of the boundary . Hence shape sensitivity analysis is a crucial ...
Page 67
... solution a * to ( P ) . Due to the equivalence of ( Ph ) and ( P ) the existence of a solution a to ( Ph ) follows . Moreover , we shall give in Theorem 4.2 an answer to the question : What is the relation between ( P ) and ( Ph ) when ...
... solution a * to ( P ) . Due to the equivalence of ( Ph ) and ( P ) the existence of a solution a to ( Ph ) follows . Moreover , we shall give in Theorem 4.2 an answer to the question : What is the relation between ( P ) and ( Ph ) when ...
Page 168
... solution of ( P ( a ) ) . The existence of a solution ( PF ) can be established in the same way as in Section 7.3 . Thus we have Theorem 7.4 . Let Uad be given by ( 7.68 ) . Then there exists at least one solution of Problem ( PF ) . In ...
... solution of ( P ( a ) ) . The existence of a solution ( PF ) can be established in the same way as in Section 7.3 . Thus we have Theorem 7.4 . Let Uad be given by ( 7.68 ) . Then there exists at least one solution of Problem ( PF ) . In ...
Contents
Preliminaries | 1 |
Abstract setting of optimal shape design problem and | 28 |
Optimal shape design of systems governed by a unilateral | 53 |
Copyright | |
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algorithm Appendix applied approximation boundary value problem C₁ Céa Computer constraints contact problems convex convex set cost functional defined denote design sensitivity analysis differentiable discrete domain elastic element method exist a subsequence Figure Find finite element finite element method follows formula given Glowinski Gm(a H¹(Î Haslinger Haug Hlaváček Ir(an ITERATION jEJk ji Eli Komkov Lagrange multipliers Lemma lim inf lim sup linear Lipschitz continuous lower semicontinuous matrix minimization Nečas Neittaanmäki nodes nonlinear programming nonsmooth Numerical results obtain optimal control optimal design optimal pair optimal shape design parameter Pironneau Proof results for Example Section sequence shape design problems Shape optimization Sokolowski solves P(a structural design structural optimization subgradient subset T(Un T₁ Theorem triangulation un(an variational inequality vector w₁ Zolesio г₁