Concurrent topology optimization based on multiphase materials under steady thermal conduction

Based on multiphase materials, a concurrent optimization model of macrostructures and porous microstructures is proposed. In this model, the minimized heat compliance is taken as objective function. Structural volume fraction and microstructure mass are taken as constraints. Macro design variables and micro phase design variables are introduced into macrostructures and microstructures independently, and are integrated into one system with elemental phase density. The punishment relationship between elemental phase density and thermal conductive coefficient is built through uniform interpolation model, and the sensitivity of objective function is deduced. To eliminate the checkerboard pattern and mesh-dependence problem, the heat compliance is filtered using a partial differential equation. The effects of material characteristics, heat loads, volume fraction and microstructure mass constraints are discussed with 2D problems. The numerical results indicate that the proposed method is reliable and efficient to the concurrent topology optimization of macrostructures and porous microstructures based on multiphase materials.