Displaying similar documents to “Local minimizers of functionals with multiple volume constraints”

Numerical minimization of eigenmodes of a membrane with respect to the domain

Édouard Oudet (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we introduce a numerical approach adapted to the minimization of the eigenmodes of a membrane with respect to the domain. This method is based on the combination of the Level Set method of S. Osher and J.A. Sethian with the relaxed approach. This algorithm enables both changing the topology and working on a fixed regular grid.

A penalty method for topology optimization subject to a pointwise state constraint

Samuel Amstutz (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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This paper deals with topology optimization of domains subject to a pointwise constraint on the gradient of the state. To realize this constraint, a class of penalty functionals is introduced and the expression of the corresponding topological derivative is obtained for the Laplace equation in two space dimensions. An algorithm based on these concepts is proposed. It is illustrated by some numerical applications.

A level set method in shape and topology optimization for variational inequalities

Piotr Fulmański, Antoine Laurain, Jean-Francois Scheid, Jan Sokołowski (2007)

International Journal of Applied Mathematics and Computer Science

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The level set method is used for shape optimization of the energy functional for the Signorini problem. The boundary variations technique is used in order to derive the shape gradients of the energy functional. The conical differentiability of solutions with respect to the boundary variations is exploited. The topology modifications during the optimization process are identified by means of an asymptotic analysis. The topological derivatives of the energy shape functional are employed...

Shape and topology optimization of the robust compliance via the level set method

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...

Design-dependent loads in topology optimization

Blaise Bourdin, Antonin Chambolle (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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We present, analyze, and implement a new method for the design of the stiffest structure subject to a pressure load or a given field of internal forces. Our structure is represented as a subset S of a reference domain, and the complement of S is made of two other “phases”, the “void” and a fictitious “liquid” that exerts a pressure force on its interface with the solid structure. The problem we consider is to minimize the compliance of the structure S , which is the total work of the...