Geometric Optimization and Structural Analysis of Cable-Braced Gridshells on Freeform Surfaces

In freeform surface grid structures, quadrilateral meshes offer high visual transparency and simple joint connections, but their structural stability is relatively limited. To enhance stability, designers often introduce additional structural elements along the diagonals of the quadrilateral mesh, forming double-layer quadrilateral grid systems such as cable-braced gridshells. However, current design methodologies do not support the simultaneous optimization of both layers. As a result, the two layers are often designed independently in practical applications, leading to complex joint detailing that compromises construction efficiency, architectural aesthetics, and overall structural performance. To address these challenges, this study presents a weighted multi-objective geometry optimization framework based on a Guided-Projection algorithm. The proposed method integrates half-edge data structure and multiple geometric and structural constraints, enabling the simultaneous optimization of quadrilateral mesh planarity (i.e., panels lying on flat planes) and the orthogonality (i.e., angles approaching 90°) of diagonal cable layouts. Through multiple case studies, the method demonstrates significant improvements in panel planarity and cable orthogonality. The results also highlight the algorithm’s rapid convergence and high computational efficiency. Finite element analysis further validates the structural benefits of the optimized configurations, including reduced peak axial forces in cables, more uniform cable force distribution, and enhanced overall stiffness and buckling resistance. In conclusion, the method improves structural stability, constructability, and design efficiency, offering a practical tool for optimizing freeform cable-braced gridshells.