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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.
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Frederic Golay. Optimisation topologique de forme et raffinement de maillage. Revue Européenne des Éléments Finis, HERMÈS / LAVOISIER, 2004, 13 (8), pp.881-897. ⟨10.3166/reef.13.881-897⟩. ⟨hal-00979097⟩



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