Static and dynamic analyses of tensegrity structures. Part 1. Nonlinear equations of motion

Abstract In order to present basic equations for static and dynamic analyses of a class of truss structures called tensegrity structures, large-deformation kinematics and kinetics were presented in both Eulerian and Lagrangian formulations. The two sets of equations of motion yield the same values even if different stress and strain measures were employed for their computation. The Eulerian formulation was implemented in an updated Lagrangian finite element code using Newton’s method with consistently linearized equations of motion. By utilizing the linearized Lagrangian equations of motion at pre-stressed initial configurations, harmonic modal analyses of a three-bar tensegrity module and a six-stage tensegrity beam were conducted. In the second part of the paper, linearized equations were utilized to investigate the equilibrium configurations of basic tensegrity modules and the stiffness of pre-stressed tensegirty structures.