基于滤波/映射边界描述的壳-填充结构多尺度拓扑优化方法

In order to realize the optimal macroscopic layout and microscopic properties of shell-infill structures, a multiscale topology optimization method of the porous structures based on filtering/projection boundary description is proposed. Firstly, the shell interface is described by introducing a two-step Helmholtz filtering/projection and normalized spatial gradient norm. Secondly, the topology of microstructure is designed by the classic solid isotropic material with penalization (SIMP) method, and the effective properties of microstructure are evaluated by the energy-based homogenization method (EBHM), and then the material interpolation model of the structure is established. Furthermore, a multiscale topology optimization model is built and solved to minimize the compliance under two volume constraints. Based on the cantilever beam and the MBB beam structure example, the shell-infill design and the design without shell are compared from the micro-scale optimization degree, and the influences of the loading conditions, the volume fraction of the microstructure and the initial design of the microstructure on the structure are also explored. The results of several numerical examples demonstrate the effectiveness of the proposed method.