Additive manufacturing constraints in Topology optimization

Additive manufacturing has motivated the development of new constraints in topology optimization to ensure the manufacturability of optimized designs. This work reviews and compares several important classes of constraints, considering both density-based and level-set methods. First, the perimeter constraint and its anisotropic extension are discussed as ways to control the complexity of boundaries and the orientation of features, which is relevant for directional manufacturing processes. The overhang constraint directly addresses the need to limit unsupported regions, a key issue in layer-by-layer fabrication. Minimum length scale control ensures the elimination of excessively small features that are impractical to fabricate and helps avoid mesh dependency. Connectivity constraints play a crucial role in guaranteeing that optimized structures remain manufacturable and free of disconnected components. In this context, we propose solving an auxiliary problem that enforces connectivity by penalizing or eliminating isolated regions, thus ensuring structural integrity. Both density and level-set formulations are examined, highlighting how these constraints can be integrated and the advantages and limitations of each approach. The study emphasizes that an appropriate combination of these constraints is essential to bridge the gap between mathematically optimal designs and physically realizable additive manufacturing components.