An Improved Form-Finding Method for Calculating Force Density with Group Theory

A form-finding method for symmetric tensegrity structure is proposed based on the eigenvalue minimization problem of force density matrix in this paper. The topology is the only premise condition about the structure. The problem to solve force density in the self-equilibrium tensegrity structure is transformed into a linear optimization problem, which the force density matrix under the rank deficiency condition. The constraints of the objective function can be established by the characteristics of member forces and the group theory. Then the nodal coordinates can be determined by eigenvalue decomposition once the force densities is obtained. In order to to show the efficiency of the proposed method, several simulations of tensegrity structures which include plane and spatial are demonstrated. It can be found that the form-finding process of symmetric tensegrity structure in the proposed method has the characteristics of rapid speed and high precision.