A study on X-FEM in continuum structural optimization using a level set model

In this paper, we implement the extended finite element method (X-FEM) combined with the level set method to solve structural shape and topology optimization problems. Numerical comparisons with the conventional finite element method in a fixed grid show that the X-FEM leads to more accurate results without increasing the mesh density and the degrees of freedom. Furthermore, the mesh in X-FEM is independent of the physical boundary of the design, so there is no need for remeshing during the optimization process. Numerical examples of mean compliance minimization in 2D are studied in regard to efficiency, convergence and accuracy. The results suggest that combining the X-FEM for structural analysis with the level set based boundary representation is a promising approach for continuum structural optimization.