A generalized objective function based on weight coefficient for topology-finding of tensegrity structures

This paper proposes a generalized objective function for the topology-finding of tensegrity structures to be able to assign selection priorities to different members and efficiently find multiple tensegrity structures through a single ground structure. The generalized objective function is constructed by the sum of the product of member internal forces and weight coefficients. The member weight coefficients can be defined and adjusted freely to change the selection priorities of different members in the topology-finding process. By adjusting the weight coefficients, different tensegrity structures can be generated. The weight coefficients can be determined by the designer according to the practical design requirements and preferences, e.g., member length limitations, member position requirements. In addition, a circular computing strategy is proposed for the weight coefficient adjustment to efficiently obtain a large number of tensegrity structures through a single ground structure. The topology design of typical regular tensegrity structures, as well as irregular ellipsoid tensegrity structures, are carried out to demonstrate the effectiveness of the proposed method. Furthermore, by using the proposed method, multiple novel tensegrity structures based on common Archimedes polyhedrons have been found; detailed information (e.g., member connectives, self-stress) are given as an open database for future investigation and applications.