Multi-objective Topology Optimization Design of Micro-structures

Abstract

This contribution proposes a methodology for the multi-objective synthesis and/or topology optimization of microstructures based on the topological derivative concept. The macroscopic properties are estimated by a standard multi-scale constitutive theory where the macroscopic responses are volume averages of their microscopic counterparts over a Representative Volume Element (RVE). We introduce a macroscopic cost functional that combines the mechanical and thermal effects in a single expression, allowing to design an RVE satisfying a specific thermo-mechanical macroscopic behavior. The algorithm is of simple computational implementation and relies in a level-set domain representation method. The effectiveness of the proposed methodology is illustrated by a set of finite element-based numerical examples.