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 vi
... smooth . The contents of this book are organized as follows . Chapter 1 contains some fundamental results for subsequent reference . The aim of Chapter 2 is , firstly , to formulate and to give results concern- ing the existence of a ...
... smooth . The contents of this book are organized as follows . Chapter 1 contains some fundamental results for subsequent reference . The aim of Chapter 2 is , firstly , to formulate and to give results concern- ing the existence of a ...
Page 51
... smooth . As a consequence of the restriction to small separations one may consider the stiffness of the bodies to be unchanged by the design process . The problem may be stated as ( P ) min sup X * ( x ) α τ where * is the solution ...
... smooth . As a consequence of the restriction to small separations one may consider the stiffness of the bodies to be unchanged by the design process . The problem may be stated as ( P ) min sup X * ( x ) α τ where * is the solution ...
Page 242
... smooth functions ( the SQP - algorithm for example ) can also reduce the value of functions with occasional discontinuities in their derivatives . This is usually sufficient because , due to the nonconvexity of J , we can find only a ...
... smooth functions ( the SQP - algorithm for example ) can also reduce the value of functions with occasional discontinuities in their derivatives . This is usually sufficient because , due to the nonconvexity of J , we can find only a ...
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