On some applications of Generalized Geometric Projection to optimal 3D printing

Abstract

In recent years, Topology Optimization (TO) gained interest in the scientific community. It assists in finding the best arrangement of material in a design volume. The classical approach named ”Solid Isotropic Material with Penalization” (SIMP) associates a fictitious density to each finite element in the domain. While SIMP is described as an implicit approach which can lead to problems with dimensionality of variables, explicit methods adopt a geometric projection of simple elements (eg.: bars) to reduce the number of design variables. This simplifies the geometric interpretation of the optimal architecture. The major explicit methods were recently unified into a general framework, Generalized Geometric Projection (GGP).Currently it is quite challenging to take into account manufacturing constraints in the topology optimization design phase. Therefore this paper presents an application of the GGP Method to the design of products made by Additive Layer Manufacturing (ALM). Every printed layer constitutes a geometric element, involving design variables relative to position and width. Specific constraints of ALM, including bridge length and overhang angle, can be easily monitored by exploiting the geometric features of the combined elements.Examples in two dimensions will be reported, analyzing two academic benchmark problems. A comparison to other proven techniques is also detailed. An mean difference of 7.7% is observed for solutions with only overhang angle constraint, while a mean difference of 11% is observed for solutions with overhang angle and bridge length constraint. The presented work integrates design and manufacturing, directly identifying the path of the printed layers.