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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Theory and Applications J. Haslinger, Pekka Neittaanmäki. 6.3 . Design sensitivity analysis and numerical examples 6.3.1 . Design sensitivity analysis - material derivative approach 6.3.2 . Design sensitivity analysis - algebraic ...
Theory and Applications J. Haslinger, Pekka Neittaanmäki. 6.3 . Design sensitivity analysis and numerical examples 6.3.1 . Design sensitivity analysis - material derivative approach 6.3.2 . Design sensitivity analysis - algebraic ...
Page 79
... design sensitivity analysis . In the algebraic approach ( Section 5.4 ) we compute the variation of I ; with respect to the movement of the design variables aj . In Section 5.5 we apply the so - called material derivative approach to the ...
... design sensitivity analysis . In the algebraic approach ( Section 5.4 ) we compute the variation of I ; with respect to the movement of the design variables aj . In Section 5.5 we apply the so - called material derivative approach to the ...
Page 263
... design sensitivity analysis in discrete cases . For the numerical realization of optimal shape design algorithms see Arora and Beanzinger ( 1986 ) ( uses of AI in design optimization ) , Arora and Thanedar ( 1986 ) ( computational ...
... design sensitivity analysis in discrete cases . For the numerical realization of optimal shape design algorithms see Arora and Beanzinger ( 1986 ) ( uses of AI in design optimization ) , Arora and Thanedar ( 1986 ) ( computational ...
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