Establishment of iterative modeling method for spherical tensegrity structure using rotational symmetry and regular polyhedron configuration

Tensegrity structures are attractive light-weight structures. In particular, spherical tensegrity structures are expected to be applied in various fields. This article proposes a simple method for modeling spherical tensegrities. Firstly, the nodal coordinates of the spherical tensegrity are systematically determined based on rotational symmetry and regular polyhedral configuration. This approach enables the systematic acquisition of the nodal coordinates of spherical tensegrities of all sizes by introducing a three-dimensional rotation matrix and the dihedral angle of the regular polyhedron. Secondly, the prestress ratio is determined iteratively. For the stability analysis of the spherical tensegrity, nonlinear analysis with prestress is required. For the analysis considering the prestress, a tangent stiffness matrix is applied in this study. The simple determination method enables the modeling of spherical tensegrities. The natural frequencies and mode shapes of the spherical tensegrity are identified by frequency analysis. A vibration experiment is conducted as a verification experiment. The natural frequencies from the analysis are compared to the resonance frequencies from the experiment. This comparison confirms the validity of the frequency analysis results, based on the two proposed methods.