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 83
... material derivative method We shall introduce a treatment based on a dynamic interpretation of the optimal shape design process . The method presented here is called the ma- terial derivative or shape derivative method . Material derivative ...
... material derivative method We shall introduce a treatment based on a dynamic interpretation of the optimal shape design process . The method presented here is called the ma- terial derivative or shape derivative method . Material derivative ...
Page 263
... material derivative method of continuum mechanics to account for changes in the shape of the domain . This method is generally known as the material derivative method ( Zolesio ( 1981a , 1981b , 1982a , 1982b ) ) . In this method the ...
... material derivative method of continuum mechanics to account for changes in the shape of the domain . This method is generally known as the material derivative method ( Zolesio ( 1981a , 1981b , 1982a , 1982b ) ) . In this method the ...
Page 264
... derivative approach with special local choice of the velocity field by means of shape functions ( nodal material derivative approach ) . As we have seen above ( Chapters 5 and 6 , Appendix II ) , when the material derivative approach is ...
... derivative approach with special local choice of the velocity field by means of shape functions ( nodal material derivative approach ) . As we have seen above ( Chapters 5 and 6 , Appendix II ) , when the material derivative approach is ...
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