Multiscale concurrent topology optimization for heat conduction with connectable microstructures

Thermal management has garnered increased attention with the advancement of equipment miniaturization. As an innovative structural design methodology, the multiscale concurrent topology optimization (MCTO) method for area-to-point heat conduction cases is gaining importance. However, the utilization of homogenization theory for designing multiscale structures tends to engender discontinuities among different microstructures. In this work, based on the material field series expansion (MFSE) method, a framework that addresses the issue of microstructural connectivity in the heat-conduction MCTO problem is proposed. Within this framework, various microstructures are defined in different regions of a single microscopic material field, thereby microstructural connectivity is well-ensured through the global correlation function. At the macroscopic, the design domain is partitioned into multiple material fields, with each material field evolving autonomously to yield the intricate architectures essential for heat conduction topology optimization on the macroscale. Additionally, the substantial reduction in the number of design variables, coupled with the implementation of the decoupled sensitivity analysis method, significantly improves the computational efficiency of the heat conduction MCTO process. Several 2D and 3D numerical examples with well-connected microstructures demonstrate the proposed optimization method's effectiveness and efficiency. Meanwhile, the parallelogram unit cell case, the relaxation microscopic volume fraction constraints case, and a complex 3D tee-branch pipe case are solved using the proposed method, showcasing lightweight and highly effective multiscale designs for realistic heat conduction cases.