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The form-finding analysis is a crucial step for determining the stable self-equilibrated states for tensegrity structures, in the absence of external loads. This form-finding problem leads to the evaluation of both the self-stress in the elements and the shape of the tensegrity structure. This paper presents a novel method for determining feasible integral self-stress states for tensegrity structures, that is self-equilibrated states consistent with the unilateral behaviour of the elements, struts in compression and cables in tension, and with the symmetry properties of the structure. In particular, once defined the connectivity between the elements and the nodal coordinates, the feasible self-stress states are determined by suitably investigating the Distributed Static Indeterminacy (DSI). The proposed method allows for obtaining feasible integral self-stress solutions by a unique Singular Value Decomposition (SVD) of the equilibrium matrix, whereas other approaches in the literature require two SVD. Moreover, the proposed approach allows for effectively determining the Force Denstiy matrix, whose properties are strictly related to the super-stability of the tensegrity structures. Three tensegrity structures were studied in order to assess and discuss the efficiency and accuracy of the proposed innovative method.

The quality of being adaptable/deployable of tensegrity structures provides intriguing challenges for researchers and designers. In this work, the shape-change capabilities of a V-Expander tensegrity column are analyzed: a numerical investigation is carried out for the study of the cable-actuation process for a column composed of elementary V-Expander tensegrity cells sharing horizontal cables. The actuation is performed by considering suitable sets of active and passive cables among the whole set of cables of the column. The attention is focused on the following kinds of shape-changes: stretching/shrinking, flexure, shear and torsion. Moreover, a strategy for predicting the nonlinear response of the tensegrity column in the cable-actuation process is proposed. This strategy allows for estimating quickly, among all the possible choices of active and passive cable sets, those leading to maximum displacements or rotations and to the minimum ratio between the normalized work of active cables and the deformation of the column. Further numerical analyses are performed by varying the aspect ratio of the V-Expander cell, to evaluate the effects of changes in the geometrical parameters on the nonlinear actuation process of the column. Tensegrity structures have inspired artists, biologists, engineers, and architects. Many studies have been conducted in recent years, especially related to geometry, form finding, static analysis, and dynamic response. Their use is very encouraging in projects requiring adaptable and/or deployable structures. Indeed, a tensegrity system can provide the minimal mass structure required to sustain a given external load, an intriguing feature for uses as lightweight deployable systems, such as satellites, antennas, or robots. Tensegrity systems are reticulated structures composed of bars in compression maintained in equilibrium by a network of cables in tension. This work focuses on the shape-change capabilities of V-Expander tensegrity columns, a promising type of tensegrity system in this context. Shape change can be obtained by shortening some cables using actuators, while other cables lengthen elastically keeping the system in equilibrium during the process. A fast linear prediction strategy is proposed for evaluating the efficiency of any choice of actuated elements. This strategy allows to prefigure the choices of lengthening and shortening cables which lead to the most efficient shape-change processes of V-Expander columns, here presented for the first time. Such a strategy can be applied with minor adjustments to the other types of tensegrity systems. [ABSTRACT FROM AUTHOR]