Volume 17, Number 3, July-September 2011
|Page(s)||705 - 721|
|Published online||31 March 2010|
Topological asymptotic analysis of the Kirchhoff plate bending problem
Laboratoire d'analyse non linéaire et géométrie, Faculté
des Sciences, 33 rue Louis Pasteur, 84000 Avignon, France. firstname.lastname@example.org
2 Laboratório Nacional de Computação Científica LNCC/MCT, Coordenação de Matemática Aplicada e Computacional, Av. Getúlio Vargas 333, 25651-075 Petrópolis – RJ, Brasil. email@example.com
Revised: 15 February 2010
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.
Mathematics Subject Classification: 35J30 / 49Q10 / 49Q12 / 74K20 / 74P15
Key words: Topological sensitivity / topological derivative / topology optimization / Kirchhoff plates
© EDP Sciences, SMAI, 2010
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