Form-finding of tensegrity structures with multiple states of self-stress

Abstract

A numerical method is presented for form-finding of tensegrity structures with multiple states of self-stress. At the first stage, the range of feasible sets of the nodal coordinates and the force densities are iteratively calculated by the only known information of the topology and the types of members until the required rank deficiencies of the force density and equilibrium matrices are satisfied, respectively. The linear constraints on the force densities which are derived from the obtained configuration’s symmetry properties and/or directly assigned by designers are then utilized to define a single integral feasible force density vector in the second stage. An explanation on the null space of the force density matrix that generates the configurations of the tensegrities is rigorously given. Several numerical examples are presented to demonstrate the efficiency and robustness in searching new self-equilibrium stable configurations of tensegrity structures with multiple states of self-stress.