Global Length and Overhang Control for Level Set and Density Approaches via Perimeter Minimization

Abstract

Topology optimization is probably one of the most efficient techniques for structural design. However, running topology optimization without geometry control provides complex designs, which often are manufactured with additive manufacturing methods. Consequently, a fundamental aspect in topology optimization is to consider the following additive manufacturing constraints: minimal length scale and overhang. The aim of this paper is to propose a new numerical method to control globally such additive manufacturing constraints. The idea relies on penalizing a regularized version of the perimeter: an isotropic version for global length and an anisotropic version for overhang. Besides, we show that the method may be used with density and level set approaches. Several numerical examples, including compliant mechanisms and material design, show that some bars have been removed, decreasing the complexity of the shape, and vertical tendency orientation of boundaries is generally obtained.