Heat flux manipulation by using a single-variable formulated multi-scale topology optimization method

Abstract

This paper proposes a novel multi-scale topology optimization method to obtain a design that cannot be achieved by single-scale topology optimization for heat flux manipulation in heat conduction problems. The optimal designs are derived using a multi-scale topology optimization method for shielding, concentrating, and reversing the heat flux over the objective domain. A single variable formulation is proposed to avoid underestimating the material property. The micro-scale design variables are updated by the method of moving asymptotes with design sensitivity derived by the adjoint variable method. The validity and effectiveness of this method are shown by comparing the performance measure and the computing time to the single-scale topology optimization method. The results show that the multi-scale approach achieved better performance over the various composition ratios of the high-conductive material than the single-scale method and converged about 20 times faster.