Book review: "Variational Methods in Shape Optimization Problems"
Andrzej Myśliński (2006)
Control and Cybernetics
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Andrzej Myśliński (2006)
Control and Cybernetics
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Cherif Amrouche, Šárka Nečasová, Jan Sokołowski (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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Material and shape derivatives for solutions to the Dirichlet Laplacian in a half-space are derived by an application of the speed method. The proposed method is general and can be used for shape sensitivity analysis in unbounded domains for the Neumann Laplacian as well as for the elasticity boundary value problems.
Marc Dambrine, Djalil Kateb (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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The level set method has become widely used in shape optimization where it allows a popular implementation of the steepest descent method. Once coupled with a ersatz material approximation [Allaire , (2004) 363–393], a single mesh is only used leading to very efficient and cheap numerical schemes in optimization of structures. However, it has some limitations and cannot be applied in every situation. This work aims at exploring such a limitation. We estimate the systematic...
Bijan Mohammadi (2010)
Control and Cybernetics
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François Jouve, Grégoire Allaire, Frédéric de Gournay (2008)
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 to...
G. Allaire, C. Dapogny, G. Delgado, G. Michailidis (2014)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the optimal distribution of several elastic materials in a fixed working domain. In order to optimize both the geometry and topology of the mixture we rely on the level set method for the description of the interfaces between the different phases. We discuss various approaches, based on Hadamard method of boundary variations, for computing shape derivatives which are the key ingredients for a steepest descent algorithm. The shape gradient obtained for a sharp interface involves...
Dorin Bucur, Ioana Durus, Edouard Oudet (2008)
Control and Cybernetics
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(2005)
Control and Cybernetics
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Grégoire Allaire, Frédéric de Gournay, François Jouve, Anca-Maria Toader (2005)
Control and Cybernetics
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