Self-equilibrium and super-stability of rhombic truncated regular tetrahedral and cubic tensegrities using symmetry-adapted force-density matrix method. (15th December 2021) - Zhang, Li-Yuan; Jiang, Jin-Hong; Wei, Kai; Yin, Xu; Xu, Guang-Kui; Zhang, Jingyao
Graphical abstract: Highlights: Form-finding of rhombic truncated regular tetrahedral and cubic tensegrities are studied. Their force-density matrices are block-diagonalized using group representation theory. Conditions for their self-equilibrium and super-stability are analytically established. These tensegrities help to develop biomechanical models, metamaterials, and robotics. Abstract: Tensegrities consisting of axially loaded strings and bars have various technologically important applications, for which symmetric configurations are preferred as prototypes. In this study, we investigate the self-equilibrated states of rhombic truncated regular tetrahedral and cubic tensegrities by combining group representation theory and force-density matrix method. The force-density matrices of these tensegrities are analytically block-diagonalized using the irreducible representation matrices of tetrahedral and cubic groups. By making the symmetry-adapted force-density matrix satisfy the necessary number of nullity and positive semi-definiteness, we derive the analytical expressions for self-equilibrium and super-stability of rhombic truncated regular tetrahedral and cubic tensegrities. This work helps to design highly symmetric tensegrities for developing biomechanical models, mechanical metamaterials, and flexible robotics.