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 36
... given by T = GRO , where G is the shear modulus of the material of the shaft and R is the torsional rigidity of the shaft given by R ( N ) = 2 [ u ( x ) dx . The problem of optimal shape design of N is given by ( 2.29 ) where min I ( N ...
... given by T = GRO , where G is the shear modulus of the material of the shaft and R is the torsional rigidity of the shaft given by R ( N ) = 2 [ u ( x ) dx . The problem of optimal shape design of N is given by ( 2.29 ) where min I ( N ...
Page 91
... given point . If gradients ( or sub- gradients ) are required by the optimization algorithm then the user must write similar subroutines to calculate them . Usually , all these things are re- quired at the same time at the given point ...
... given point . If gradients ( or sub- gradients ) are required by the optimization algorithm then the user must write similar subroutines to calculate them . Usually , all these things are re- quired at the same time at the given point ...
Page 167
... given friction In the previous section , the frictionless case was discussed . The present section deals with the simplest model involving friction , namely the so - called " given friction " model . = By the classical solution of the ...
... given friction In the previous section , the frictionless case was discussed . The present section deals with the simplest model involving friction , namely the so - called " given friction " model . = By the classical solution of the ...
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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Common terms and phrases
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