Simplified form-finding for tensegrity structures through reference joints of symmetry orbits

Tensegrity structures are a class of free-standing and prestressed cable-strut structures. Different from traditional elastic structures, both geometric shapes and initial prestress distributions of tensegrity systems are indetermi-nate. Thus, it is of great significance to develop a robust and effective form-finding method for tensegrity sys-tems. Based on reference joints of symmetry orbits and force density theory, this study proposes a simplified form-finding method for tensegrity structures. This method makes full use of the inherent symmetry of struc-tural systems. It introduces a series of orthogonal transformation matrices for certain reference joints to represent independent force equilibriums of similar joints from the same symmetry orbit. Then, the original form-finding problem is simplified into finding null spaces for several small-sized force density matrices about the reference joints. Thus, the force density of each type of components and the nodal coordinate of each joint can be effec-tively obtained. Illustrative examples show that the proposed method can significantly simplify the computa-tional complexity of form-finding for tensegrity systems with symmetry orbits.

Automated summary

This study proposes a simplified form-finding method for tensegrity structures based on reference joints of symmetry orbits and force density theory. The method utilizes the inherent symmetry of structural systems by introducing a series of orthogonal transformation matrices for certain reference joints. The original form-finding problem is simplified into finding null spaces for several small-sized force density matrices about the reference joints. The proposed method can significantly simplify the computational complexity of form-finding for tensegrity systems with symmetry orbits.