Two-scale concurrent design of lattice material microstructures and their macroscale distributions can effectively enlarge the design space, and thus achieve lightweight structures with desirable mechanical and multi-physics performances. Most of the existing inverse homogenization-based design methods do not take into consideration the connectivity issues of the microstructures. In practice, this may hinder the manufacturing and application of the optimized two-scale designs. To handle this issue, the present paper proposes a designable connective region method to obtain connectable microstructures in the context of two-scale concurrent structural topology optimization, considering structures composed of lattice materials with repetitive unit cells and prescribed porosity. On the microscale, the microstructures topologies are represented by the density model, and the effective material properties are computed with the homogenization method. On the macroscale, the distribution of different lattice materials is described with the discrete material optimization method, which can effectively reduce the amounts of macroscale elements with intermediate densities. The connectivity between any two types of the microstructures is naturally ensured by introducing pre-defined connective regions in the microstructural unit cells and keeping these regions sharing the same topology. This method can be conveniently implemented through microscale design variable linking and requires no evaluation of extra connectivity constraints and the corresponding sensitivities. It is exemplified by two-scale concurrent structural topology optimization for compliance minimization problems in two- and three-dimensional design domains. Numerical results show that this method is able to generate connectable lattice structures, which exhibits improved stiffness as compared with their uniform-lattice counterparts.

格构材料微观结构及其宏观分布的两尺度同时设计可以有效地扩大设计空间，从而实现具有理想的机械和多物理性能的轻量化结构。现有的大多数基于逆均质化的设计方法都没有考虑微结构的连通性问题。实际上，这可能会阻碍优化的两尺度设计的制造和应用。为了解决这个问题，本论文提出了一种可设计的连接区域方法，该方法考虑了由具有重复单元格和规定孔隙度的晶格材料组成的结构，在两尺度并行结构拓扑优化的背景下获得可连接的微观结构。在微观上 用密度模型表示微观结构的拓扑结构，并用均质化方法计算有效的材料性能。在宏观上，使用离散材料优化方法描述了不同晶格材料的分布，该方法可以有效地减少具有中等密度的宏观元素的数量。通过在微结构单元格中引入预定义的连接区域并保持这些区域共享相同的拓扑结构，自然可以确保任意两种类型的微结构之间的连通性。该方法可以通过微型设计变量链接方便地实现，并且不需要评估额外的连接限制和相应的灵敏度。它以二维并行结构拓扑优化为例，该优化用于二维和三维设计域中的合规性最小化问题。数值结果表明，该方法能够生成可连接的晶格结构，与均匀晶格结构相比，该结构显示出更高的刚度。