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 vii
... consider the shape optimization of the contact surface of a two - dimensional elastic body unilaterally supported by a rigid foundation . The problem is to redesign the contact surface in such a way that the total potential energy of ...
... consider the shape optimization of the contact surface of a two - dimensional elastic body unilaterally supported by a rigid foundation . The problem is to redesign the contact surface in such a way that the total potential energy of ...
Page 18
... consider more regular penalization like ( 1.43 ) 1 3 j ( v ) = { } ; ( v ̄ ) 3ds . Let us define the functional ( 1.44 ) - J ( y ) = ¦ || Vy || ô , n — ( f , y ) o , n , ƒ € Ľ2 ( N ) , where Vy grad y = ( 응 მყ მყ მთ 18.
... consider more regular penalization like ( 1.43 ) 1 3 j ( v ) = { } ; ( v ̄ ) 3ds . Let us define the functional ( 1.44 ) - J ( y ) = ¦ || Vy || ô , n — ( f , y ) o , n , ƒ € Ľ2 ( N ) , where Vy grad y = ( 응 მყ მყ მთ 18.
Page 51
... consider the stiffness of the bodies to be unchanged by the design process . The problem may be stated as ( P ) min sup \ * ( x ) α I where * is the solution stress to the contact problem for design a . As an alternative formulation of ...
... consider the stiffness of the bodies to be unchanged by the design process . The problem may be stated as ( P ) min sup \ * ( x ) α I where * is the solution stress to the contact problem for design a . As an alternative formulation of ...
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
adjoint algorithm Appendix applied approximation boundary value problem C₁ Céa compute constraints contact problems convex convex set cost functional defined denote design sensitivity analysis differentiable discrete domain elastic exist a subsequence Figure Find finite element follows formula given Gm(a H¹(Î Haslinger Haug Hlaváček I₁ Ir(an ITERATION jEJk Komkov Lagrange multipliers least one solution Lemma lim inf lim sup linear Lipschitz Lipschitz continuous lower semicontinuous mapping material derivative matrix method minimization Nečas Neittaanmäki nodes nonlinear nonlinear programming nonsmooth Numerical results obtain optimal control optimal design optimal pair optimal shape design parameter Pironneau Proof results for Example Section sensitivity analysis sequence shape design problems Shape optimization Sokolowski solves P(a subgradient subset T₁ Theorem triangulation un(an unilateral boundary value variational inequality vector w₁ Zolesio г₁