Determination of active members and zero-stress states for symmetric prestressed cable–strut structures

Abstract

A prestressed cable–strut structure is generally flexible and exhibits strong coupling between its stress state and configuration. The zero-stress state offers the basis for design and analysis of cable–strut structures and has significant influence on the prestress state and the load state. Here, a computational method is proposed for seeking zero-stress states of symmetric cable–strut structures. By evaluating distributed static indeterminacy and symmetry representations using group theory, the active member with proper importance index and high-order symmetry is chosen from different types of members. Moreover, natural lengths and the involved elongations of the members are established from the initial prestresses and geometric properties. Then, based on the Newton method and the Moore–Penrose inverse theory, internal forces of the members are actively reduced. The structural configuration and tangent stiffness matrix are iteratively updated during the whole process from the prestress state to the zero-stress state. The feasibility and accuracy of the proposed approach are verified by some numerical examples, whereas the results are compared with analytical solutions and FEM simulation. The results show that one zero-stress configuration is associated with a specific prestress state, and the process between zero-stress state and prestress state is reversible. This work has theoretical significance for the design of novel cable–strut structures and provides a reference for the construction process of prestressed cable–strut structures in practical applications.