A multi-objective gradient-based approach for prestress and size optimization of cable domes

Cable domes represent a class of lightweight structures characterized by their significant aesthetic and architectural impact. Widely adopted for large-span roofing applications, such as arenas and stadiums, these structures may exhibit internal mechanisms that compromise their serviceability and load-bearing capacity. However, a state of self-equilibrated initial prestress can effectively stiffen these internal mechanisms, transforming an unserviceable structure into a serviceable one. Optimizing the prestress and size of cable domes is a challenging task, since these quantities affect the elastic and geometric stiffnesses of the structure. Structural weight and displacements are antagonist performance objectives, and their simultaneous optimization with constraints on the internal forces is a non-intuitive engineering problem. In the literature, so far multi-objective optimization studies for cable domes have relied only on gradient-free methods. This paper presents a novel gradient-based approach for the automated multi-objective optimization of cable domes, where the structural weight and displacements are simultaneously optimized. Constraints are imposed on the tension and compression forces in the cables and struts of the structures considered. The resulting multi-objective optimization problem is solved with a gradient-based approach based on sequential linear programming. The gradients of the objective and constraint functions are consistently calculated with adjoint sensitivity analyses. The proposed approach is assessed through reproducible numerical examples of design optimization of cable domes. The results show that the Pareto fronts of the problems considered are effectively computed with modest computational effort. The results are also in good agreement with those obtained with a genetic algorithm.