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 vii
... present various tech- niques for carrying out design sensitivity analysis . Furthermore , we give a procedure for solving optimal shape design problems by applying nonlinear programming algorithms . Several numerical examples are ...
... present various tech- niques for carrying out design sensitivity analysis . Furthermore , we give a procedure for solving optimal shape design problems by applying nonlinear programming algorithms . Several numerical examples are ...
Page 198
... present another kind of a state problem , namely the so - called free boundary value problem with constraints given in the interior of N. We consider the problem of controlling the shape of a coincidence set in connection with an ...
... present another kind of a state problem , namely the so - called free boundary value problem with constraints given in the interior of N. We consider the problem of controlling the shape of a coincidence set in connection with an ...
Page 297
... present another method , which treats the constraints more accurately . We no longer need any improvement function , subgradient ag- gregation for constraint functions or scaled multipliers , which implies that each iteration uses less ...
... present another method , which treats the constraints more accurately . We no longer need any improvement function , subgradient ag- gregation for constraint functions or scaled multipliers , which implies that each iteration uses less ...
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