Structural topology optimization with four additive manufacturing constraints by two-phase self-supporting design

This paper studies the additive manufacturing (AM)-oriented minimum compliance structural topology optimization (TO) subject to four AM constraints: self-supporting constraint, connectivity constraint, solid-phase minimum length constraint, and void-phase minimum length constraint simultaneously. The essential novelty of this study is that we show that the connectivity constraint can be realized by imposing the void-phase self-supporting constraint. The corresponding proof is given in Appendix. The Elements Scheme (ES) method is used to construct the element-wise self-supporting constraint. By improving the constraint aggregating functions and aggregating a large number of element-wise self-supporting constraints on solid-phase and void-phase structures into three constraints, we propose a concise topology optimization formulation to effectively and simultaneously suppress the small overhang angle boundaries, hanging features (solid-phase upside-down triangles), voids with pointed tips (void-phase upside triangles), slim components, small voids, and enclosed voids in the optimized design. Numerical examples demonstrate the effectiveness of this formulation in comparison with other connectivity control methods.