The shape and topological optimizations connection

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