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Sensitivity analysis with respect to a local perturbation of the material property Powered by TCPDF (www.tcpdf.org) Abstract. In the present work, the notion of topological sensitivity is extended to the case of a local perturbation of the properties of the material constitutive of the domain. As a model example, we consider the problem −div (αεA∇uε) + βεuε(More)
The topological sensitivity analysis consists in studying the behavior of a shape functional when modifying the topology of the domain. In general, the perturbation under consideration is the creation of a small hole. In this paper, the topological asymp-totic expansion is obtained for the Laplace equation with respect to the insertion of a short crack(More)
The level-set method has been recently introduced in the field of shape optimization , enabling a smooth representation of the boundaries on a fixed mesh and therefore leading to fast numerical algorithms. However, most of these algorithms use a Hamilton-Jacobi equation to connect the evolution of the level-set function with the deformation of the contours,(More)
The aim of the topological sensitivity analysis is to determine an asymptotic expansion of a shape functional with respect to the variation of the topology of the domain. In this paper, we consider a state equation of the form div (A∇u) + k 2 u = 0 in dimensions 2 and 3. For that problem, the topological asymptotic expansion is obtained for a large class of(More)
The perimeter functional is known to oppose serious difficulties when it has to be handled within a topology optimization procedure. In this paper, a regularized perimeter functional Perε, defined for 2d and 3d domains, is introduced. On one hand, the convergence of Perε to the exact perimeter when ε tends to zero is proved. On the other hand, the(More)