A novel application framework for self-supporting topology optimization

Abstract

This paper presents an application framework that provides a complete process to design an optimized self-supporting structure, ready to be fabricated via additive manufacturing without the usage of additional support structures. Such supports in general have to be created during the fabricating process so that the primary object can be manufactured layer by layer without collapse; this process is very time-consuming and waste of material. The main approach resolves this issue by formulating the self-supporting requirements as an explicit quadratic continuous constraint in a topology optimization problem, or specifically, requiring the number of unsupported elements (in terms of the sum of squares of their densities) to be zero. Under the formulation, the required sensitivity of the self-supporting constraint with respect to the design density can be derived straightforward and is only linearly dependent on the density of the element itself. In addition, a novel discrete convolution operator is particularly designed to detect the unsupported elements. The approach works for cases of general overhang angles, and the produced optimized structures have close target compliance to those of the reference structures obtained without considering the self-supporting constraint, as demonstrated by various 2D and 3D benchmark examples.