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 114
... approach ( introduced in Section 5.5 ) and algebraic approach ( Section 5.4 ) . To this end we shall suppose that ƒ is sufficiently smooth . We now begin with the material derivative approach . 6.3.1 . Design sensitivity analysis ...
... approach ( introduced in Section 5.5 ) and algebraic approach ( Section 5.4 ) . To this end we shall suppose that ƒ is sufficiently smooth . We now begin with the material derivative approach . 6.3.1 . Design sensitivity analysis ...
Page 263
... approaches . The first approach uses the discretized model , based on finite element analysis , and proceeds to carry out shape design sensitivity analysis by controlling finite element node movement and differentiating the algebraic ...
... approaches . The first approach uses the discretized model , based on finite element analysis , and proceeds to carry out shape design sensitivity analysis by controlling finite element node movement and differentiating the algebraic ...
Page 334
... approach 15 penalty functional 15 , 18 , 73 , 204 , 214 , 234 , 236 , 238-239 penalty method for approximating packaging problem 204-205 scalar case 59-63 state constrained problems 233-245 variational inequalities 19-24 , 59 , 214- 215 ...
... approach 15 penalty functional 15 , 18 , 73 , 204 , 214 , 234 , 236 , 238-239 penalty method for approximating packaging problem 204-205 scalar case 59-63 state constrained problems 233-245 variational inequalities 19-24 , 59 , 214- 215 ...
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