De-homogenization of optimal 2D topologies for multiple loading cases

This work presents an extension of the highly efficient de-homogenization method for obtaining high-resolution, near-optimal 2D topologies optimized for minimum compliance subjected to multiple load cases. We perform a homogenization-based topology optimization based on stiffness optimal Rank-N microstructure parameterizations to obtain stiffness optimal multi-scale designs on relatively coarse grids. To avoid relatively thin microstructure features, we regularize the design by introducing a material indicator field which results in well-defined widths and structural boundaries. In order to avoid singularities from the multiple load case problem, the orientations of the microstructures are further regularized. Subsequently, we derive a single-scale interpretation of stiffness optimal multi-scale designs on a fine grid using de-homogenization. The single-scale interpretation can be derived without costly postprocessing analysis on the fine grid, as an implicit boundary formulation is used.