Multimember Unit–Based Topology Optimization of Cable-Supported Grid Structures

Cable-supported grid structures, integrating rigid and flexible components, represent a lightweight and efficient structural form. Conventional topology design methods based on single-member units often produce incomplete upper grids and lower cable-supported structures containing redundant, irregular, and discontinuous cables, which complicate practical construction. This paper proposes a multimember unit–based topology optimization model grounded in graph theory. The approach preserves grid integrity while selecting cable topologies from predefined arrangements, ensuring the engineering feasibility of the optimized designs. The model supports coupled topology optimization, allowing cables and bars to be arranged simultaneously, an approach not found in existing literature. By preprocessing member groups, the method effectively accommodates slidable nodes, a challenge that conventional approaches cannot address. Additionally, the multimember unit–based formulation improves computational efficiency over the single-member unit–based approach. The efficacy of the proposed method is demonstrated through several numerical examples and validated by finite-element analysis.