The optimization design of the microstructures and their macro distribution in porous composite structures (PCS) offers significant potential for achieving both lightweight and functional performance. This paper proposes a novel optimization design framework for PCS with varying densities and multiple microstructures. Initially, components topology optimization (TO-Components) using ordered SIMP interpolation is applied to determine the type and density distribution of void, solid and porous materials. Following this, element stress state analysis calculates the stress-to-density ratio (se) for each porous material element. A two-level k-means++ clustering method, based on se and density, then replaces the widely used manual partitioning, enabling optimal subregion division for the specified number of microstructure types. This approach identifies representative unit cells (RUCs) for the subsequent topology optimization of RUCs (TO-RUCs). The TO-RUCs process designs the microstructures of each RUC using homogenization theory to minimize strain energy. Three benchmark numerical examples take only 1 to 2 min to complete the full-scale design. Additionally, the scalability of the design for both uniform and variable density PCS is explored. The comparison examples demonstrate that the proposed method reduces optimization time by an order of magnitude while maintaining consistent full-scale compliance, using the same material quantity, compared to existing methods. Finally, additive manufacturing and mechanical testing of the optimized structures confirm the performance benefits.

中文翻译：

---

基于聚类的多尺度拓扑优化框架，用于多孔复合结构的高效设计


多孔复合材料结构 （PCS） 中微观结构及其宏观分布的优化设计为实现轻量化和功能性能提供了巨大的潜力。本文为具有不同密度和多种微结构的 PCS 提出了一种新的优化设计框架。最初，使用有序 SIMP 插值进行组件拓扑优化 （TO-Components） 来确定空隙、固体和多孔材料的类型和密度分布。在此之后，单元应力状态分析会计算每个多孔材料单元的应力密度比 （se）。然后，基于 se 和密度的两级 k-means++ 聚类方法取代了广泛使用的手动分区，从而为指定数量的微结构类型实现最佳子区域划分。这种方法确定了代表性晶胞 （RUC），用于 RUC （TO-RUC） 的后续拓扑优化。TO-RUCs 工艺使用均质化理论设计每个 RUC 的微观结构，以最小化应变能。三个基准数值示例只需 1 到 2 分钟即可完成全尺寸设计。此外，还探讨了均匀密度和可变密度 PCS 设计的可扩展性。比较示例表明，与现有方法相比，使用相同材料量，所提出的方法将优化时间缩短了一个数量级，同时保持了一致的满量程柔度。最后，优化结构的增材制造和机械测试证实了性能优势。