Form-finding of tensegrity structures using double singular value decomposition

Abstract

A numerical form-finding procedure of tensegrity structures is developed. The only required information is the topology and the types of members. The singular value decompositions of the force density and equilibrium matrices are performed iteratively to find the feasible sets of nodal coordinates and force densities which satisfy the minimum required deficiencies of these two matrices, respectively. An approach of defining a unique configuration of tensegrity structure by specifying an independent set of nodal coordinates is provided. An explanation is given for the preservation in self-equilibrium status of the tensegrity structures under affine transformation. Two- and three-dimensional examples are illustrated to demonstrate the efficiency and robustness of the proposed method in searching stable self-equilibrium configurations of tensegrity structures.