Application of co-rotational method in geometrical nonlinear analysis of tensegrity structure and effect of pre-stress

Tensegrities are a kind of spatial structural system composed of cable (in tension) and strut (in compression). Stability of this system is provided by the self stress state between tensioned and compressed elements. In this paper, co-rotational method is used for study geometrical nonlinear analysis of tensegrity structure and analysis of the effect of pre-stress on it. This approach unlike other available approach in nonlinear static analysis, the major part of geometric non-linearity is treated by a co-rotational filter. The function of CR formulation is to extract relevant deformation quantities free or almost free from any rigid body motion in a given displacement field. One of advantage of the co-rotational approach is the fact that linear models can be easily used in the local coordinate system for modeling of nonlinear problems. The geometric non-linearity is incorporated in the transformation matrices relating local and global internal force vectors and tangent stiffness matrices. Three different numerical examples are studied using this approach. Results demonstrate that the deformations of tensegrity system are dependent on the value of pre-stress in tensegrity systems. The displacements of tensegrity system are decreased for fixed external tensile loading and increasing pre-tension force, however, for fixed pre-tension force and increasing external loading the displacements of tensegrity system are increased.