Design and form finding of cable net for a large cable–rib tension antenna with flexible deployable structures

•A new kind of cable net for a large cable–rib tension antenna is designed.•A form finding method is proposed for mesh antennas considering the deformation of deployable structure.•Node position updating is employed during form finding to gradually increase the surface accuracy.•Numerical simulations and experiment on 1.8 m prototype demonstrate the method. Cable net structures are important in the construction of large deployable space antennas. The shape and tension of a cable net must be properly designed for the operating requirements of a reflector in orbit. The application demand for large-scale space antennas highlights the problem of the flexible deformation of deployable structures. Thus, such deformation, which has a significant effect on surface accuracy, should be considered in the form finding design of cable nets. In this study, an approach considers the flexible deformation of deployable structures for identifying the desired shape for a cable net is proposed. First, the dimension of the triangles used for dividing the cable net of a cable–rib tension antenna is designed for the required accuracy, and the shape of the cable net is determined by introducing the sag effect in the design of boundary cables. Then, an approach that is based on force density and nonlinear finite element methods and ensures the appropriate node position and uniform tension of the cable net is proposed for the form finding problem. A feature of the developed method involves an optimization model that calculates the deformation of the deployable structure and iteratively modifies the node position to form the cable net. The genetic algorithm is employed for the acquisition of a set of optimal tensions with constraints. Finally, numerical examples and experimental test results are presented to validate the veracity and effectiveness of the proposed approach.