Density and level set-XFEM schemes for topology optimization of 3-D structures

As the capabilities of additive manufacturing techniques increase, topology optimization provides a promising approach to design geometrically sophisticated structures. Traditional topology optimization methods aim at finding conceptual designs, but they often do not resolve sufficiently the geometry and the structural response such that the optimized designs can be directly used for manufacturing. To overcome these limitations, this paper studies the viability of the extended finite element method (XFEM) in combination with the level-set method (LSM) for topology optimization of three dimensional structures. The LSM describes the geometry by defining the nodal level set values via explicit functions of the optimization variables. The structural response is predicted by a generalized version of the XFEM. The LSM–XFEM approach is compared against results from a traditional Solid Isotropic Material with Penalization method for two-phase “solid–void” and “solid–solid” problems. The numerical results demonstrate that the LSM–XFEM approach describes crisply the geometry and predicts the structural response with acceptable accuracy even on coarse meshes.