Abstract
Abstract 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.
Highlights
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 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
For each of the three tensegrity structures, the analysis was conducted by considering five different conditions: 1) the case in which the flexibility matrix is equal to the identity matrix, that is, F = I; in this case, the Distributed Static Indeterminacy (DSI) vector coincides with ωm and the corresponding internal force vector is denoted by tnm; 2) a possible assignment of the axial stiffness of the elements which lead to the results reported by the literature; in such case, the vector named ω and the vector termed t were calculated
Summary
Abstract: The form-finding analysis is a crucial step for determining the stable self-equilibrated states for tensegrity structures, in the absence of external loads. Tran and Lee [67] presented a numerical method for form-finding of tensegrity structures in which the topology and the types of members are the only required information; the eigenvalue decomposition of the Force Density matrix and the single value decomposition of the equilibrium matrix are performed iteratively The approach here proposed effectively allows for determining the Force Density matrix and its properties with a low computational cost It reveals to be useful for all the analysis for the tensegrity structures above recalled: the form-finding analysis, the investigation of the superstability conditions, and the study of the relations between elements and of the self-stress level according to the actual axial stiffness of the elements.
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