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

Abstract

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 indeterminate. Thus, it is of great significance to develop a robust and effective form-finding method for tensegrity systems. 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 structural 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 effectively obtained. Illustrative examples show that the proposed method can significantly simplify the computational complexity of form-finding for tensegrity systems with symmetry orbits.