The optimal initial self-stress design for tensegrity grid structures

To achieve the optimal feasible force density vector of a given geometry configuration tensegrity grid structure, an efficient procedure is presented for optimal initial self-stress design of tensegrity grid structures by consecutively solving two linear homogeneous systems in conjunction with a minimization problem. An optimization approach is utilized to seek the global minimum of the problem, leading to a set of force densities which guarantee the non-degeneracy condition for the force density matrix. The evaluation of the eigenvalues of tangent stiffness matrix is also introduced to check the stability of the tensegrity grid structures. Finally, two numerical examples have been investigated comprehensively in this paper to prove the capability of the proposed method in initial self-stress design of tensegrities satisfying either stability or super stability. Furthermore, division of number of member group has been discussed in detail for the purpose of demonstrating the efficiency of the proposed method in seeking initial force densities of tensegrity grid structures according to the need of an actual project.