Topology optimization for microstructures of composite materials based on thermal conductivity

A new method is presented for thermal conductive microstructures of composite materials based on the technique of homogenization method and topology optimization. From the mathematical formulation of effective thermal conductivity for periodic microstructures, the effective conductivity matrix is evaluated by means of the finite element method. By defining the pseudo-density variable of each element in the design domain and constraining the total material cost, a topology optimization model with SIMP method is built to maximize either the effective thermal conductivity of the microstructure in specified directions or the thermal conduction efficiency of the macrostructure. The sensitivity of the objective function is then given. The optimal solution can be obtained by means of the dual optimization algorithm and perimeter constraint. Numerical results verify the validity of the proposed topology optimization method in the thermal conduction design of the microstructures.