Stability conditions of tensegrity structures considering local and global buckling

Abstract

This study introduces an approach for assessing the stability of tensegrity structures by examining local and global buckling behaviors. We employ the minimal coordinate to parameterize the tensegrity configuration, incorporating nodal displacement and local bending deformation. A detailed formulation of the potential energy for tensegrity structures is presented under compression, tension, and bending. The formulation of the equilibrium equation is obtained using the principle of stationary total potential energy. Further, we study the stiffness characteristic of the structure by developing the tangent stiffness matrix. The equilibrium and stiffness of tensegrity structures with consideration of initially crooked members are derived. Our findings indicate that local and global buckling behaviors remain independent in perfect straight axial force member assumptions while they become coupled with consideration of initially crooked members. The critical buckling load of tensegrity structures under external load can be calculated by a generalized eigenvalue problem. The proposed method is also applicable to cable nets, trusses, and space frames.