Topology optimization for additive manufacturing with length scale, overhang, and building orientation constraints

This paper presents a density-based topology optimization approach considering additive manufacturing limitations. The presented method considers the minimum size of parts, the minimum size of cavities, the inability of printing overhanging parts without the use of sacrificial supporting structures, and the printing directions. These constraints are geometrically addressed and implemented. The minimum size on solid and void zones is imposed through a well-known filtering technique. The sacrificial support material is reduced using a constraint that limits the maximum overhang angle of parts by comparing the structural gradient with a critical reference slope. Due to the local nature of the gradient, the chosen restriction is prone to introduce parts that meet the structural slope but that may not be self-supporting. The restriction limits the maximum overhang angle for a user-defined printing direction, which could reduce structural performance if the orientation is not properly selected. To ease these challenges, a new approach to reduce the introduction of such non-self-supporting parts and a novel method that includes different printing directions in the maximum overhang angle constraint are presented. The proposed strategy for considering the minimum size of solid and void phases, maximum overhang angle, and printing direction, is illustrated by solving a set of 2D benchmark design problems including stiff structures and compliant mechanisms. We also provide MATLAB codes in the appendix for educational purposes and for replication of the results.