Symmetry representations and elastic redundancy for members of tensegrity structures

Unexpectable damage of a member may cause a significant change in the load-bearing capacity or collapse of a tensegrity structure, thus redundancy analysis is important. Nevertheless, conventional approaches generally neglect the inherent symmetry and material properties. Here, we propose a method for symmetry representations and elastic redundancy for members of tensegrity structures. The symmetry and member stiffness are taken into account. To evaluate the contribution of each member to the total static indeterminacy, irreducible representation and full symmetry subspace of every type of members are computed. Then, distributed static indeterminacy of the members can be independently obtained by a simplified process. The accuracy and efficiency of the presented method are demonstrated through examples of some well-known tensegrity structures with different symmetries. This method can offer reasonable design on tensegrity structures, which are assembled by many cables and struts with identical sensitivity to initial elongations and equal importance to load-bearing capacity.