Level set-based multiscale topology optimization for a thermal cloak design problem using the homogenization method

TL;DR

This paper introduces a multiscale topology optimization approach using level set and homogenization methods to design composite materials that function as thermal cloaks, optimizing microstructures for desired thermal properties.

Contribution

It presents a novel multiscale topology optimization framework combining level set and homogenization techniques for thermal cloak design.

Findings

Optimized microstructures effectively achieve thermal cloaking.

The method successfully evaluates effective thermal conductivity.

Examples demonstrate the validity of the optimized designs.

Abstract

Artificially designed composite materials consist of microstructures, that exhibit various thermal properties depending on their shapes, such as anisotropic thermal conductivity. One of the representative applications of such composite materials for thermal control is the thermal cloak. This study proposed a topology optimization method based on a level set method for a heat conduction problem to optimally design composite materials that achieve a thermal cloak. The homogenization method was introduced to evaluate its effective thermal conductivity coefficient. Then, we formulated a multiscale topology optimization method for the composite materials in the framework of the homogenization method, where the microstructures were optimized to minimize objective functions defined using the macroscopic temperature field. We presented examples of optimal structures in a two-dimensional problem and discussed the validity of the obtained structures.