Structural topology optimization with the XFEM and level sets

The extended finite element method (XFEM) and the level set method are used as a vehicle for topology optimization. The 0 level set (black contours in the bottom right) define the geometry of the beam. The structural response (left) is computed using the XFEM on a uniform structured mesh (top right). The optimization algorithm manipulates the level set field to minimize the displacement of the tip of the beam. Up to 50% of the design domain may be filled with material. The video shows the evolution of the design process.

Dave Makhija
University of Colorado at Boulder