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

Multiscale Topology Optimization Method for Shell-infill Structures Based on Filtering/Projection Boundary Description

提出一种基于滤波/映射边界描述的壳-填充结构拓扑优化方法,用以实现壳-填充结构宏观拓扑构型和填充区域材料微观分布协同优化。该方法针对宏观单元密度引入两步Helmholtz滤波映射和空间梯度范数归一化,用以描述壳层区域和填充区域几何特征;基于惩罚的固体各向同性材料方法设计微观结构,基于均匀化理论分别获得壳层实体区域和填充孔隙区域等效弹性矩阵,在此基础上发展出融合壳-填充几何特征信息的材料插值模型;基于所提出的材料插值模型,建立以最小应变能为目标,双体积比约束下的多尺度拓扑优化模型并进行求解;以悬臂梁和MBB梁为算例,开展有壳/无壳设计、载荷工况、微结构体积分数和微结构的初始设计等不同因素对最终设计的影响,分析结果验证所发展算法的有效性。

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.