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 35
... of twist , 0. From the St Venant theory of torsion , the elastic deformation of the system is governed by the elliptic boundary value problem ( 2.27 ) ( 2.28 ) -Au = 2 u = 0 in Ω on an l Ω не T Figure 2.2 . where u is 35.
... of twist , 0. From the St Venant theory of torsion , the elastic deformation of the system is governed by the elliptic boundary value problem ( 2.27 ) ( 2.28 ) -Au = 2 u = 0 in Ω on an l Ω не T Figure 2.2 . where u is 35.
Page 133
... deformation of the body so that the point x , x = ( x1 , x2 ) of the undeformed body becomes the point x ' , x ' = ( x1 , x2 ) of the deformed body and x ' can be written as x ' = x + u ( x ) , where u = ( u1 , u2 ) denotes the vector ...
... deformation of the body so that the point x , x = ( x1 , x2 ) of the undeformed body becomes the point x ' , x ' = ( x1 , x2 ) of the deformed body and x ' can be written as x ' = x + u ( x ) , where u = ( u1 , u2 ) denotes the vector ...
Page 160
... deformation 2 ) scaled displacement field for initial body at nodal points 3 ) decrease of E versus iteration 4 ) triangulation of the optimal body before deformation 5 ) scaled displacement field of optimal body at nodal points ( same ...
... deformation 2 ) scaled displacement field for initial body at nodal points 3 ) decrease of E versus iteration 4 ) triangulation of the optimal body before deformation 5 ) scaled displacement field of optimal body at nodal points ( same ...
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