Equilibrium Analysis of Tensegrity Structures with Elastic Ties

Abstract

In this paper, the equilibrium analysis of a passive tensegrity structure with elastic con- necting ties is addressed. The problem is modeled as a constrained optimization of the total po- tential energy of the system and the Lagrange multiplier method is used to deduce the equilibrium equations. The homotopy continuation method is used to completely solve the resulting nonlin- ear polynomial system and all the equilibrium positions are identified. Furthermore, the stabil- ity analysis of the equilibrium configurations is carried out using the second order condition and higher order condition for cases where the second order condition fails. One numerical example is provided to demonstrate the analysis.