Three-dimensional projection-based topology optimization for prescribed-angle self-supporting additively manufactured structures

Additive Manufacturing (AM) professionals often throw around the notion that complexity is free. Indeed, complexity is much easier and potentially cheaper to achieve through AM than through traditional manufacturing, but it is not free. Upon attempting to manufacture complex designs, it is quickly found that certain features, or topologies, are more manufacturable than others, with sacrificial support material required for many complex designs. This will significantly increase machining costs. Topology Optimization (TO) is a freeform computational design methodology which is ideal for designing lightweight structures through a combination of modeling and rigorous optimization. While AM can realize many complex topologies, there still remain AM manufacturing limitations (such as overhangs), which require customized TO design algorithms beyond freeform TO. In this work, a projection-based TO methodology is presented to design for 3D self-supporting structures - i.e. structures that do not require sacrificial support material. The foundation of the presented methodology is a 2D overhang projection framework. In addition to expanding the methodology to three dimensions, the algorithm is drastically improved through (1) adopting a new overhang mapping scheme which allows for exact specification of allowable overhang angle, and (2) implementing an adjoint approach to sensitivity calculations to speed up calculation drastically and to allow for scalability. Using several examples, it is shown that the presented methodology generates self-supporting structures (given a prescribed printable overhang angle) which are entirely manufacturable without any added sacrificial support material. Upon printing a couple topologies with mixed success, further customization of the algorithm is proposed for situations where multiple directional dependent overhang angles are possible in a single AM system.