Topological sensitivity analysis with respect to a small hole located at the boundary of the domain

Article type: Research Article

Authors: Samet, Bessem

Affiliations: Ecole Supérieure des Sciences et Techniques de Tunis, Département de Mathématiques, 5, Avenue Taha Hussein-Tunis, B.P. 56, Bab Menara-1008, Tunisie. E-mail: bessem.samet@gmail.com

Abstract: The topological sensitivity analysis consists to study the variation of a shape functional with respect to emerging of small holes in the interior of the domain occupied by the body. In this paper, we consider the case of a hole located at the boundary of the domain. The topological asymptotic expansion is derived for the Laplace equation in three cases: Dirichlet condition, Neumann condition and Robin condition on the boundary of the hole.

Keywords: topological derivative, Laplace equation, singularity

DOI: 10.3233/ASY-2009-0957

Journal: Asymptotic Analysis, vol. 66, no. 1, pp. 35-49, 2010