3D Shape Optimization with X-FEM and a Level Set Constructive Geometry Approach

This paper extends previous work on structural optimization with the eXtended Finite Element Method (X-FEM) and the Level Set description of the geometry. The proposed method takes advantage of fixed mesh approach by using an X-FEM structural analysis method and from the geometrical shape representation of the Level Set description. In order to allow the optimization of complex geometries represented with a Level Set description, we apply here a Constructive Solid Geometry (CSG) approach with the Level Set geometrical representation. Hence, this extension allows to optimize any boundary of the structure that is defined with a coumpound Level Set. Design variables are the parameters of basic geometric primitives which are described with a Level Set representation and/or the control points of the NURBS curves that act as the definition of an advanced Level Set primitive. The number of design variables of this formulation remains small whereas global (i.e. compliance or eigenfrequency) and local constraints (i.e. stresses) can be considered. Our results illustrate that fixed grid optimization with X-FEM coupled
to a Level Set geometrical description is a promising technique to achieve structural shape optimization.