Modeling of tensegrity-membrane systems

Tensegrity-membrane systems are a class of flexible multibody systems, which are composed of bars, tendons, and membranes. Due to advantages of lightweightness, multifunctionality and adaptability via control design, and the capacity of deployment inherited from tensegrity systems, tensegrity-membrane systems can be utilized in space applications such as solar sails and radar antennas. To study system's prestressing conditions, bars are treated as rigid bodies, and an energy-based method is used to determine the equations for static configurations of general tensegrity-membrane systems. For symmetric tensegrity-membrane systems with multiple stages, the equations for static configurations can be significantly simplified. Explicit analytic solutions for the equilibrium conditions of one-stage symmetric systems are derived. The system dynamics is studied based on the nonlinear finite element method, and the total Lagrangian formulation is implemented. Axial flexibility of bars is considered in the nonlinear finite element model. Simulations based on the dynamic relaxation technique are performed in order to validate the equilibrium determination method introduced in this article. Free vibration simulation results are also presented and discussions related to the deformation of bars, rigid bar assumption, and membrane behavior are included.