Optimized high thermal insulation by the topological design of hierarchical structures

This study proposes a new method for the topological design of hierarchical structures with high performance in thermal insulation. Firstly, a three-layer design strategy including macro-, meso- and micro-layers is presented. The macroscopic structures are formed by periodically arranged mesoscopic structures, whose topological configurations are determined by the material microstructures provided at the micro-level. The microstructures and mesoscopic structures are independent of the optimization, to ensure an efficiency of the hierarchical design process. Secondly, four classical microstructures are considered to provide the normalized equivalent thermal conductivities with arbitrary densities between 0 and 1. Then, the floating projection technique is employed to find the optimal topologies of the thermoelastic structures. The objective function is defined by maximizing the thermal compliance, subjected to the volume constraint that is added to the objective function through the Lagrange multiplier. The sensitivity analysis and algorithm implementation are given in detail. Finally, numerical examples are presented to illustrate the advantages of the proposed method to obtain hierarchical structures with high performance in thermal insulation.