Stiffness matrix based form-finding method of tensegrity structures

Abstract

A highly efficient form-finding method of tensegrity is presented on the basis of the structural stiffness matrix, which is defined as the derivative of the out-of-balance force vector with respect to the nodal coordinate vector. The stiffness matrix and the total potential energy of the structure are utilized to direct the rapid convergence of the structural configuration to the self-equilibrated and stable state. In the programmed procedure, we employ the stochastic selecting algorithm to exclude rigid-body motions, the restricted step algorithm to guarantee the positive definiteness of the structural stiffness matrix, and the line search algorithm to minimize the total potential energy. This form-finding method allows us to easily determine the self-equilibrated and stable configuration of a tensegrity from an arbitrary initial state. A number of representative examples are given to demonstrate its accuracy and efficacy for both regular and irregular tensegrity structures of large scale.