Optimisation topologique de forme et raffinement de maillage

Abstract

We present the problem of topological optimization with fictitious materials. This approach leads to a formulation of blocking materials that is treated numerically by finite elements as a problem of non-linear elasticity. The computing time and the quality of the solution depend strongly on the mesh, because the topology is unknown and the problem is highly non-linear. For these reasons we use a local automatic mesh refinement method that allows to quickly determine an optimal topology on a coarse grid and then to refine the solution according to strong geometrical or numerical non-linearities. We test initially some refinement criteria related to the physics of the problem, such as the thickness or the thickness gradient, and then a criterion resulting from a posteriori error analysis developed by R. Verfürth.