Topology optimization of compatible thermal microstructures

Abstract

Thermal microstructures are arranged periodically or in gradients to create thermal management systems. Ensuring connectivity is a critical challenge in designing multiple thermal microstructures for multiscale applications. This is an important issue that has not yet been systematically studied in a quantitative manner. In this work, we introduce the concept of thermal compatibility. It refers to the ability of different microstructures to work together effectively in thermal systems. Thermal compatibility ensures efficient heat transfer while minimizing thermal resistance. To address this, we propose a novel framework incorporating thermal resistance into the topology optimization model with the constraint of predefined thermal conductivity tensors to generate compatible thermal microstructures. Our optimization model considers the compatibility of adjacent microstructures and extends to mutual compatibility. Moreover, it accounts for both isotropic and orthogonal anisotropic thermal microstructures. When the thermal microstructures exhibit good compatibility, the results from both full-scale and homogenization analyses are consistent. We further demonstrate the applicability of our method through two thermal-related multiscale design examples: thermal dissipation and thermal cloak design.