The shape and topological optimizations connection

In 1973, Jean Cea introduced a topological shape optimization algorithm based on a fixed point method. The recent topological gradient concept provides a mathematical justification of Cea's powerful method. The aim of the topological gradient is to compute the sensitivity of a cost function when we drill a little hole in the domain. Some optimality conditions are derived when classical shape gradient and topological gradient are used simultaneously, and numerical results are shown both in Mechanics and Electromagnetics. (C) 2000 Published by Elsevier Science S.A. All rights reserved.