Topology optimization for periodic thermal conductive material using SIMP method

In order to obtain periodic material microstructure under macroscopic thermal conduction condition, the optimal topological model of periodic structure was built by solid isotropic material with penalization (SIMP) method. The volume fraction was referred as constraint and minimized thermal compliance was taken as optimization objective in this model. To satisfy the periodic constraint, the designable domain was divided into a certain number of identical unit cells and the thermal compliance was reallocated. The filtered variable implicitly as a solution of a partial differential equation (PDE) was applied to eliminate the checkerboard patterns and mesh-dependence problems efficiently. The optimal topological configurations were analyzed and compared with different numbers of unit cells and different load cases. The numerical results indicate that proposed periodic model is valid in design of periodic material microstructure with macroscopic steady state thermal conduction condition. Microstructure configurations are different when number of unit cells changes and it reflects the influences of size effect to periodic material design. With an increasing number of unit cells, the optimal results gradually converge to the results using homogenization method.