Basic tensegrity concepts and calculation methods

In this chapter, the fundamental notions about tensegrity systems are presented, together with the basic calculation methods. After giving a general introduction to the main tensegrity concepts, we dive into the analytical treatment of the statics and dynamics of tensegrity systems. In particular, we introduce the equilibrium and kinematic-compatibility equations and describe the four structural types to which tensegrity systems may belong, characterized by the presence or absence of selfstress states and internal mechanisms. We then pass to quasistatic processes and give the notions of prestress stability and superstability, which depend on the properties of the geometric stiffness and tangent stiffness operators. Notable examples are then reviewed to illustrate the nonlinear behavior of tensegrity systems. Dynamic processes are described next by deriving the motion equation, both for nonlinear large-displacement processes and, in its linearized form, for small-amplitude motions about a certain equilibrium configuration. The last part of the chapter introduces form-finding methods, and presents in details three of them with simple implementation: an analytical method for symmetric systems, the virtual cocoon method, and a marching algorithm to change the shape of a tensegrity system by controlling edge lengths. The latter method is then applied to the case study of a deployable ring for space antennas.