Concurrent Optimization of Unit-Cell Topology and Tessellating Orientation for Finite Periodic Structures

Finite periodic layout for multicomponent systems signifies a compelling design strategy for constructing complex larger structures through assembling repeating representative unit-cells with various orientations. In addition to better transportability, handleability and replaceability, design with structural segmentation has been considered particularly valuable for additive manufacturing of large workpiece due to limited printing dimension of machine. However, existing design optimization of periodic structures has been largely restricted to simple translational placements of unit-cells, sophisticated tessellation with differently oriented topological unit-cells remains underexplored. This paper presents an efficient and adaptable topology optimization framework for concurrently optimizing periodic structures comprised of repeating topological unit-cells and their tailored orientations. By introducing a weighting factor associated with different orientation states of unit-cells, a dominant orientation for each unit-cell can gradually emerge in the course of optimization process. The proposed procedure combines the solid isotropic material with penalization (SIMP) model for topology optimization of unit-cell and the discrete material optimization (DMO) technique for the optimization of its orientation. The optimization objective is to minimize structural compliance subject to volume fraction constraint. Through sensitivity analysis, optimality criteria can be applied to simultaneously optimize a representative unit-cell (RUC) topology and the orientation weighting factors in the periodic macrostructure. Several 2D and 3D examples are investigated to demonstrate significant enhancement in compliance reduction of up to 34% compared to conventional periodic design without orientation optimization. This represents a notable improvement in finite periodic structural optimization, particularly leveraging the topology optimization to tailor unit-cell orientation rather than relying on brute-force search approaches. Our methodology paves a new avenue for designing more efficient and readily manufacturable lightweight structures with enhanced performance metrics.