Self-supporting structure design for additive manufacturing by using a logistic aggregate function

Self-supporting designs that eliminate the need for structural supports can reduce manufacturing complexity caused by overhanging parts in additive manufacturing (AM). Traditionally, 45° is the minimum overhang angle required to ensure that designs can be manufactured without requiring any supporting structure. In this paper, a new self-supporting design method of AM based on topology optimization with overhang angle constraint is proposed. A self-supporting index established using a continuous logistic aggregate function is introduced to assess the supporting status of the specimen for AM process. This proposed self-supporting index is continuous and can be directly differentiated for sensitivity analysis without further mathematical transformations in the optimization formulation. Furthermore, it can be easily extended to a high-dimension aggregate (i.e., it can easily adapt to different overhang angles or self-supporting design domains). Numerical and fused deposition modeling (FDM) of a cantilever and MBB beam reveal that the self-supporting design can satisfy either general overhang angles or arbitrary orientation of AM deposition direction.