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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.

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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.

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Tensegrity is a kind of spatial structural system composed of cable (in tension) and strut (in compression). Stability is provided by the self-stress state between tensioned and compressed elements. When this structure is subjected to external dynamic loading, it may become unstable due to low structural damping. In this study, the proportional damping is considered and dynamical equations of the tensegrity structure are derived based on the equilibrium configuration. In addition the mass of cable element is taken into account. In general, linearized dynamic model provides a good approximation for analyzing the nonlinear behavior of tensegrity structures around an equilibrium configuration. So, state space method is implemented to obtain the dynamic response of the tensegrity system. Two different tensegrity structures are numerically evaluated using this approach in order to show its efficiency. Results reveal how the dynamic analysis of a tensegrity structure is essential. When resonance occurs, the compressive and in-tension members of a tensegrity system may dynamically buckle and slack respectively. In addition, the results show that the computational time to evaluate a tensegrity structure using the state space method is shorter than that of Newmark algorithm.

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“Tensegrity” refers to a class of discrete structures with two force members (bars and cables) wherein bars only take tensile loads and cables only take compressive loads. The pre stressed members are interconnected so as to form a self equilibrium structure. Compared to a truss supporting the same external loading, a tensegrity structure has fewer members and could weigh less. Determining the stable topology (member connectivities), form (node coordinates) and size (cross sectional areas of members) of a tensegrity structure for weight minimization is a challenging task, as the governing equations are nonlinear and the conventional matrix analysis methods cannot be used. This article addresses the weight minimization of a class one tensegrity structure with a given number of bars and cables, anchored at certain nodes and supporting given load(s) at certain node(s). Member connectivities and their cross sectional areas and force densities are taken as design variables, whereas the members’ strength and buckling requirements and maximum nodal displacements constitute the constraints, along with the coordinates of the floating nodes to make the structure symmetric. Constraints are evaluated through the nonlinear shape design of the self equilibrium structure and the linear analysis of the loaded structure, assuming small displacements. Using a novel approach, optimization is simultaneously performed in multiple promising areas of the solution space, resulting in multiple, optimum solutions. The diversity of the solutions is demonstrated by applying the proposed approach to a number of structural design problem.