Multi-material thermomechanical topology optimization with applications to additive manufacturing: Design of main composite part and its support structure

Abstract

This paper presents a density-based topology optimization formulation for the design of multi-material thermoelastic structures. The formulation is written in the form of a multi-objective topology optimization problem that considers two competing objective functions, one related to mechanical performance (mean compliance) and one related to thermal performance (either thermal compliance or temperature variance). To solve the optimization problem, we present an efficient design variable update scheme, which we have derived in the context of the Zhang–Paulino–Ramos (ZPR) update scheme by Zhang et al. (2018). The new update scheme has the ability to solve non-self-adjoint topology optimization problems with an arbitrary number of volume constraints, which can be imposed either to a subset of the candidate materials, or to sub-regions of the design domain, or to a combination of both. We present several examples that explore the ability of the formulation to obtain candidate Pareto fronts and to design support structures for additive manufacturing. Enabled by the ZPR update scheme, we are able to control the complexity and the length scale of the support structures by means of regional volume constraints.