Self-equilibrium and super-stability of rhombic truncated regular tetrahedral and cubic tensegrities using symmetry-adapted force-density matrix method

[摘要] 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 blockdiagonalized 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.

[发布日期] 2021-12-15

[关键词] Tensegrity;Form-finding;Group representation theory;Force-density matrix