Stability Conditions for General Tensegrity with Rigid Bodies

Abstract

This study develops stability conditions for general tensegrity regarding the three stability criteria (e.g., prestress stability, general stability, and super stability) based on an energy approach. The coupling relations of specific nodal degrees of freedom caused by the rigid bodies are described by a set of constraint functions and incorporated into the potential energy function by the Lagrangian multiplier method. Stiffness matrices of general tensegrity systems are derived from the augmented potential energy function. It shows that the stability of general tensegrity can be evaluated through the stiffness matrices expressed in the constrained motion space generated by the constraint functions. Elegant formulations are developed for the evaluation of the three types of stability conditions for general tensegrity systems. Moreover, it turns out that the formulations developed in this study will degenerate into those for the stability analysis of classic tensegrity if no rigid bodies exist in the system, which indicates that the proposed approach is a general framework for the stability analysis of any type of tensegrity systems.