FORM-FINDING ANALYSIS OF IRREGULAR TENSEGRITY STRUCTURES BY MATRIX ITERATION

This paper proposed a novel form-finding method for irregular tensegrity structures base on matrix iteration. On the basis of two different forms of structural equilibrium equations, the estimated elemental self-stresses and nodal coordinates were constructed via the singular value decomposition of equilibrium matrix and eigenvalue decomposition of force density matrix, respectively. The configuration of tensegrity that satisfies the specified coordinates was determined through the iterative computation of self-stresses and nodal coordinates, and the constraint condition was introduced in the construction of the estimated nodal coordinates simultaneously. The detailed algorithm procedure was listed and the convergent criterion was also defined. In the end, several illustrated examples were given to prove the validity of the algorithm. Numerical examples and physical models showed that the proposed form-finding method was correct and efficient. The form-finding algorithm could be applied to find tensegrity structures that satisfied the given geometrical forms, and the creation of novel irregular tensegrity, as long as the topological relation and several known coordinate of nodes were given.