Two-scale concurrent topology optimization of lattice structures with connectable microstructures

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.