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 ef- fective 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 do- main and constraining the total material cost,a topology optimization model with SIMP method is built to max- imize either the effective thermal conductivity of the microstructure in specified directions or the thermal con- duction 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 re- sults verify the validity of the proposed topology optimization method in the thermal conduction design of the microstructures.