Using co-rotational approach for analysing nonlinear dynamic tensegrity structures

In this paper, a new formulation is developed for nonlinear dynamic analysis of 2-D truss structures. This formulation is based on dynamics of co-rotational 2-D truss. The idea of co-rotational approach is to separate rigid body motions from pure deformations at the local element level. Using this approach, internal force vector and tangent stiffness matrix, inertia force vector and the tangent dynamic matrix are derived. Furthermore, the inertia force vector, tangent dynamic matrix, mass matrix and gyroscopic matrix are directly derived from the derivation of current orientation matrix with respect to global displacements or orientation matrixes. Using this new formulation, nonlinear response of any 2-D truss structures can be examined. Here, for example the response of tensegrity structures under dynamic loads are investigated. Tensegrity structures are a class of structural system composed of cable (in tension) and strut (in compression) components with reticulated connections, and assembled in a self-balanced fashion. These structures have nonlinear behaviour due to pre-stress forces. And their integrity is based on a balance between compression and tension. Two numerical examples are presented to illustrate the new formulation and results show that the new formulation has more convergence rate than the existing models.