Abstract: In the traditional topology optimization,aiming at the problem that the solving scale would be increased caused by unidirectional processing for middle density elements and the oversized initial design domain,a spatial expansion topological optimization based on Bi-Directional Interpolation Model (BDIM) was presented.The mathematical model of BDIM was established,and the spatial expansion strategy was constructed based on boundary element sensitivity.A method to decrease the solving scale of spatial expansion topological optimization was proposed,and the numerical examples were presented to demonstrate its feasibility.The numerical results indicated that BDIM only for sensitivity was more global than BDIM for sensitivity and rigidity,included the traditional Solid Isotropic Microstructures with Penalization (SIMP) model.It could get a clear boundary optimization result without filtering,and also had a smaller objective design value and less iteration.Spatial expansion topological optimization was significant for actual engineering structure design in the limited space.

Key words: bi-directional interpolation model, topological optimization, spatial expansion, variable density method, engineering structure design

摘要： 针对传统拓扑优化中对中间密度单元处理的单向性及初始设计域选择过裕而使求解规模增大的问题,提出一种基于双向插值模式的空间扩张拓扑优化。建立了双向插值模式拓扑优化问题的数学模型,构建了基于边界单元敏度信息的空间扩张策略,并提出降低空间扩张拓扑优化问题求解规模的技术,最后通过算例验证了其可行性。算例表明,利用空间扩张策略仅对敏度进行插值的模式相对于基于刚度和敏度进行双向插值的模式和传统带惩罚指数的固体各向同性微结构模式,在优化设计中更具有全局性,不用过滤便可以高效地得到边界清晰的拓扑优化结果,且具有较小的目标设计值和较少的迭代步数。

关键词: 双向插值模式, 拓扑优化, 空间扩张, 变密度法, 工程结构设计