Abstract: To construct functionally-graded structures with different shapes and properties,a variable parameter-based topology optimization of functionally-graded lattice structures with multi-domains was proposed,and a functionally-graded lattice structures with smooth continuity was constructed both within each domain and between different domains.The design domain was divided into multiple domains,and the Helmholtz PDE equation was used to filter the density of each domain,and different local volume constraint was imposed for each domain.Then the local volume constraint was integrated into the Solid Isotropic Material with Penalization (SIMP) based topology optimization method to achieve the construction of different functionally-graded lattices in each domain,while maintaining smooth continuity of structures in and between domains.The effectiveness of the proposed method was verified through the design and manufacture for the optimized functionally-graded lattice structures with the cantilever beam and the MBB beam.

Key words: topology optimization, functionally-graded structures, multi-domains, variable parameter

摘要： 为了在构件中构造形态多变和性能各异的功能梯度结构,提出一种多区域变参数的功能梯度结构拓扑优化方法,在保证构建结构单元连续性的同时,构建了多区域变参数的功能梯度结构。将设计域划分为多个区域,采用Helmholtz PDE方程对每个区域的密度变量进行过滤处理,然后施加不同的局部体积约束;将局部约束整合到传统变密度拓扑优化方法中,达到了不同区域生成不同功能梯度微结构的效果,同时区域之间的结构保持了良好的连续性。最后,通过悬臂梁和简支梁多区域功能梯度结构拓扑优化设计和制造,验证了所提方法的有效性。

关键词: 拓扑优化, 功能梯度结构, 多区域, 变参数