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 25
... finite element method To avoid unnecessarily complicating matters , we will assume the domain NC R2 is polygonal . That is , the boundary IC R2 of N is made up of straight segments . It is known that a smooth domain ... finite element method.
... finite element method To avoid unnecessarily complicating matters , we will assume the domain NC R2 is polygonal . That is , the boundary IC R2 of N is made up of straight segments . It is known that a smooth domain ... finite element method.
Page 263
... finite element method , finite dif- ference method or boundary element method , the backbone for the numerical realization of optimal shape design problems is constituted by nonlinear pro- gramming algorithms . As every function ...
... finite element method , finite dif- ference method or boundary element method , the backbone for the numerical realization of optimal shape design problems is constituted by nonlinear pro- gramming algorithms . As every function ...
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... finite element approximation , and numerical solution of optimal shape design problems . The authors explain the mathematical basis of optimal shape design , and give examples of the calculations involved . In the first chapters they ...
... finite element approximation , and numerical solution of optimal shape design problems . The authors explain the mathematical basis of optimal shape design , and give examples of the calculations involved . In the first chapters they ...
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