Displaying similar documents to “Design-dependent loads in topology optimization”

Optimal design in small amplitude homogenization

Grégoire Allaire, Sergio Gutiérrez (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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This paper is concerned with optimal design problems with a special assumption on the coefficients of the state equation. Namely we assume that the variations of these coefficients have a small amplitude. Then, making an asymptotic expansion up to second order with respect to the aspect ratio of the coefficients allows us to greatly simplify the optimal design problem. By using the notion of -measures we are able to prove general existence theorems for small amplitude optimal design...

On an optimal shape design problem in conduction

José Carlos Bellido (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we analyze a typical shape optimization problem in two-dimensional conductivity. We study relaxation for this problem itself. We also analyze the question of the approximation of this problem by the two-phase optimal design problems obtained when we fill out the holes that we want to design in the original problem by a very poor conductor, that we make to converge to zero.

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.