Constrained shape optimization problem in elastic mechanics : dedicated to Professor Dinh Nho Hao on the occasion of his 60th birthday

The main purpose of this article is to present a numerical method for geometrical shape optimization in the context of linear elastic structures. Our approach is based on the gradient method, where the shape derivative is computed by Cea's fast derivation method via Hadamard's boundary variation. In addition, we benefit the augmented Lagrangian method which combines the objective function and constraints into a penalty function to consider the given constrained optimization by solving an unconstrained problem. The regularity of moving mesh is ensured by topological gradient resmoothing techniques. Our numerical scheme converges to a (local) minimum solution, illustrated by several numerical experiments in the contexts of structural mechanics with the classical compliance objective function and volume constraint