Éléments finis stochastiques étendus pour le calcul de structures à géométrie aléatoire : application à la prise en compte de la corrosion de structures en région littorale

摘要

In a structural analysis, the incorporation of uncertainties related to material properties, loading or geometry seems today essential if oneseeks to obtain reliable numerical predictions. Stochastic finite element method allows solving this kind of problem when the uncertainties dealwith material properties or loading. However, there is still no available efficient strategy to deal with uncertainties on the geometry although itcould have a great interest in various applications such as corrosion modeling in a random environment. The aim of this thesis is to develop acomputational strategy which allows taking into account these geometrical uncertainties.The proposed method, called X-SFEM, is based on an extension to the stochastic framework of the deterministic X-FEM method. It lies on animplicit representation of the random geometry by the level sets technique and on a Galerkin approximation for the construction and the resolution ofthe problem. The method is presented for problems with random shape, where only the boundary is random, and for problems of random material interface. For this latter kind of problem, we proposed a new enrichment strategy of the approximation space based on the partition of unity method and which is well adapted to the stochastic framework. We present the various developments carried out for this work and we show the efficiency of the method with several numerical examples. Finally, we proposed an application of the X-SFEM method to a mechanical problem of a structuralcomponent submitted to marine corrosion impact.