Nodal flexibility and kinematic indeterminacy analyses of symmetric tensegrity structures using orbits of nodes

Abstract

A tensegrity structure may undergo large deformations under external loads, resulting in significant impact on its mechanical properties. Therefore, the nodal flexibility analysis of tensegrity structures, that is, analyzing the sensitivity of nodal displacements to external loads and the evaluation of critical nodes, is important in the structural design of tensegrities. Here, we present a numerical method for the symmetry-adapted flexibility analysis and kinematic indeterminacy of tensegrity structures using orbits of nodes and the Moore–Penrose inverse of involved matrices. To evaluate the contribution of each node to the total kinematic indeterminacy of a tensegrity structure, the distributed kinematic indeterminacies associated with the nodes of different orbits are independently computed. A flexibility ellipsoid is introduced to visually characterize the nodal flexibility of tensegrity structures. Several examples of tensegrities with different symmetries are presented to demonstrate the efficiency of the presented method. This method can be applied to the design and analysis of tensegrity structures under external loads, where flexibility ellipsoids are expected to be full and similar and each node is expected to have proper sensitivity to the external loads along different directions.