Multi-scale topology optimization of periodic heat transfer structures with anisotropic multi-material based on the element-free Galerkin method

Purpose An efficient multi-scale topology optimization model of periodic heat transfer structures with anisotropic multi-material is proposed based on the element-free Galerkin method (EFGM). The effectiveness of the model is verified and the effects of multi-material category, design subdomain number, thermal conductivity factor and multi-material off-angle are studied. Design/methodology/approach The alternating active-phase algorithm is applied to achieve the optimal distribution of macroscopic multi-material, and the average relative densities of EFGM nodes at the same position of each design subdomain are kept the same to achieve macroscopic periodicity. The optimal topological configuration and periodicity of the microstructure are achieved by the homogenization. Findings The results indicate the multi-material category mainly affects the thermal conductivity performance of the macrostructure, different combinations of materials show different thermal conductivity properties, and the change of design subdomain number results in different periodic arrangements of macro and microstructures, with the increase of thermal conductivity factor and multi-material off-angle, the minimum thermal compliance of macrostructure decreases and more branching structures are generated. The recommended parameter ranges are 3–4 for multi-material category, 2.5–4 for thermal conductivity factor and 60°–90° for multi-material off-angle. Originality/value An efficient multi-scale topology optimization model of periodic heat transfer structures with anisotropic multi-material is proposed based on the EFGM. The heat dissipation performance of the periodic anisotropic multi-material structure can be effectively enhanced from different perspectives and scales, as well as the macro and micro topology structures with clear and smooth boundaries can be obtained without filtering technology.