Topology optimization of material microstructures using energy-based homogenization method under specified initial material layout

Due to multiple local optimums in the society of periodic material microstructure deign using topology optimization, it is widely recognized that the initial microstructure configuration can significantly influence the optimal design. This study investigates the effect of different initial material layouts of microstructure unit cell upon the optimal design, and proposes a microstructure initialization scheme to alleviate the dependency of the optimal design on its initial design. The effective elastic properties of microstructures are evaluated by the efficient energy-based homogenization method. Topology optimization models are formulated to seek the best microstructures with the extreme properties or desired properties under the prescribed volume constraints. Several typical numerical examples are presented to demonstrate the effectiveness of the proposed scheme. Numerical results show that the proposed scheme can reduce the sensitivity of the optimal design upon optimization parameters and be beneficial to achieve a stable and rapid convergence.