Shape optimization of a nonlinear elliptic system
Andrzej Myśliński (1993)
Kybernetika
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Andrzej Myśliński (1993)
Kybernetika
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Zdeněk Kestřánek (1988)
Aplikace matematiky
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Shape optimization problems are optimal design problems in which the shape of the boundary plays the role of a design, i.e. the unknown part of the problem. Such problems arise in structural mechanics, acoustics, electrostatics, fluid flow and other areas of engineering and applied science. The mathematical theory of such kind of problems has been developed during the last twelve years. Recently the theory has been extended to cover also situations in which the behaviour of the system...
Frédéric de Gournay, Grégoire Allaire, François Jouve (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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The goal of this paper is to study the so-called worst-case or robust optimal design problem for minimal compliance. In the context of linear elasticity we seek an optimal shape which minimizes the largest, or worst, compliance when the loads are subject to some unknown perturbations. We first prove that, for a fixed shape, there exists indeed a worst perturbation (possibly non unique) that we characterize as the maximizer of a nonlinear energy. We also propose a stable algorithm...