Generalized Shape Optimization Using X-FEM and Level Set Methods

This paper presents an intermediate approach between parametric shape optimization and topology optimization. It is based on using the recent Level Set description of the geometry and the novel eXtended Finite Element Method (XFEM). The method takes benefit of the fixed mesh work using X-FEM and of the curves smoothness of the Level Set description. Design variables are shape parameters of basic geometric features. The number of design variables of this formulation is small whereas various global and local constraints can be considered. The Level Set description allows to modify the connectivity of the structure as geometric features can merge or separate from each other. However no new entity can be introduced. A central problem that is investigated here is the sensitivity analysis and the way it can be carried out efficiently. Numerical applications revisit the classical elliptical hole benchmark from shape optimization.