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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... contact problems 7.1 . Introduction to elasticity .... 114 115 .. 117 119 .123 .123 124 • 129 - elastic case 133 . 133 135 .... 136 145 7.2 . Variational formulation of contact problems 7.3 . Setting of the optimal shape problem ...
... contact problems 7.1 . Introduction to elasticity .... 114 115 .. 117 119 .123 .123 124 • 129 - elastic case 133 . 133 135 .... 136 145 7.2 . Variational formulation of contact problems 7.3 . Setting of the optimal shape problem ...
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... problem may be stated as ( P ) min sup X * ( x ) α τ where * is the solution stress to the contact problem for design a . As an alternative formulation of problem ( P ) , consider the problem min J ( u ( a ) ) α ( P ' ) subject to a dx ...
... problem may be stated as ( P ) min sup X * ( x ) α τ where * is the solution stress to the contact problem for design a . As an alternative formulation of problem ( P ) , consider the problem min J ( u ( a ) ) α ( P ' ) subject to a dx ...
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... contact problems the situation is rather different . In correspondence with unilateral conditions ( 7.16 ) , we ... contact problem is then defined as follows : ( 7.19 ) Find uЄ K : J ( u ) ≤ J ( v ) V v E K. This is equivalent to ...
... contact problems the situation is rather different . In correspondence with unilateral conditions ( 7.16 ) , we ... contact problem is then defined as follows : ( 7.19 ) Find uЄ K : J ( u ) ≤ J ( v ) V v E K. This is equivalent to ...
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