Optimization of Manufacturable Porous Infill Structure Using Differentiable Voronoi Diagram

This paper presents a novel method for designing manufacturable porous infill structures using a Voronoi-based topology optimization framework. By integrating discrete Voronoi representations into density-based topology optimization in a differentiable manner, the method enables variable-thickness edge structures, with Euclidean distance fields generated from seed points. The material distribution and structural shape are determined by the seed point locations and the distance tensor, which serve as the design variables in this work. As the seed points are directly associated with the dual graph of the Voronoi diagram (VD), namely the Delaunay triangulation (DT), a constraint is formulated based on the DT to ensure the manufacturability of the infill structure. This is achieved by constraining all edge angles of the DT to satisfy the overhang requirement. Since 3D printers can fabricate overhanging structures up to a certain length, VD edges shorter than this threshold are exempt from the self-supporting constraint. To reduce the number of design variables and simplify the manufacturability constraint, a merging strategy is introduced to combine seed points that are sufficiently close during the optimization process. To ensure manufacturability of the outer surface, a set of seed points is additionally sampled on the outer boundary and kept fixed throughout optimization. The proposed method is validated on both regular and irregular 2D design domains, and the results demonstrate its capability to generate manufacturable porous infill structures with satisfactory mechanical performance.