Geometric Constraints for the Topology Optimization of Structures Made of Primitives

Abstract

This paper presents a topology optimization method for the design of 2and 3-dimensional structures composed of bars in which the joining locations and the angles between adjacent bars can be controlled through optimization constraints. The topology optimization is performed using the geometry projection method, whereby the parametric description of the bars is smoothly mapped onto a fixed finite element mesh for analysis. By directly designing the geometric parameters of the bars as opposed to, for example, the element-wise densities or nodewise level set values of conventional topology optimization approaches, this method readily facilitates constraints on the geometry. This ability is leveraged in this work to impose a minimum angle between adjacent members, and to define regions of the geometry in which connections between components may be allowed or prevented so as to produce designs that are readily manufacturable. Even though these geometric constraints are presented in the context of the design with isotropic components, they can be readily extended to design with primitives made of anisotropic materials. The applicability of this methodology is demonstrated by several numerical examples.