Topological asymptotic analysis of the Kirchhoff plate bending problem

¹ Laboratoire d'analyse non linéaire et géométrie, Faculté des Sciences, 33 rue Louis Pasteur, 84000 Avignon, France. samuel.amstutz@univ-avignon.fr
² Laboratório Nacional de Computação Científica LNCC/MCT, Coordenação de Matemática Aplicada e Computacional, Av. Getúlio Vargas 333, 25651-075 Petrópolis – RJ, Brasil. novotny@lncc.br

Received: 16 October 2009
Revised: 15 February 2010

Abstract

The topological asymptotic analysis provides the sensitivity of a given shape functional with respect to an infinitesimal domain perturbation, like the insertion of holes, inclusions, cracks. In this work we present the calculation of the topological derivative for a class of shape functionals associated to the Kirchhoff plate bending problem, when a circular inclusion is introduced at an arbitrary point of the domain. According to the literature, the topological derivative has been fully developed for a wide range of second-order differential operators. Since we are dealing here with a forth-order operator, we perform a complete mathematical analysis of the problem.