On the Topological Derivative in Shape Optimization

: In the paper the topological derivative for arbitrary shape functional is defined. Examples are provided for elliptic equations and the elasticity system in the plane. The topological derivative can be used for solving shape optimization problems in structural mechanics. Key-words: shape optimization, shape derivative, elasticity system, topological derivative, asymptotic expansion. (Resume : tsvp) Institut Elie Cartan, Laboratoire de Mathematiques, Universite Henri Poincare Nancy I, B.P. 239, 54506 Vandoeuvre l`es Nancy Cedex, France and Systems Research Institute of the Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland; e-mail: sokolows@iecn.u-nancy.fr y Systems Research Institute of the Polish Academy of Sciences, ul. Newelska 6, 01-447 Warszawa, Poland; e-mail: zochowsk@ibspan.waw.pl Unite de recherche INRIA Lorraine Technopole de Nancy-Brabois, Campus scientifique, 615 rue de Jardin Botanique, BP 101, 54600 VILLERS L ES NANCY (France) Telephone : (33)...