Homogenization-based optimum design of additively manufactured Voronoi cellular structures

Recently, cellular structures have gained researchers’ attraction owing to their diverse applications. Homogenization-based approaches are mostly applied to the design of cellular structures by using density-variable topology optimization (TO) with customized scaling laws. However, the employment of non-stochastic cellular structures, which is mostly applied in homogenization-based design, poses disadvantages in structural anisotropy and poor transitions between adjacent unit cells. In this study, a cellular structure design method relying on the homogenization-based approach and Voronoi tessellation, a type of stochastic cellular structure, is proposed. The density distribution of a given design domain is derived by performing homogenization-based TO with density variables. The optimized density field is used to derive two-dimensional wall-based (or 2.5D) microstructures by applying Voronoi tessellation and implicit modeling. Further, a novel technique for controlling the Voronoi wall thickness is proposed to effectively reduce the computation cost of Voronoi tessellation. The numerical validation by finite element analysis (FEA) shows the advantage of utilizing the Voronoi cellular structure in terms of structural stability with arbitrary load directions and robustness with local defects.