Form-finding and stability analysis of tensegrity with interconnected rigid bodies

Tensegrity structures with arbitrarily shaped rigid bodies have found broad applications in various fields. Current studies on this topic are typically limited to the cases where the rigid bodies are isolated or connected by simple pin-jointed nodes, which may restrict the design flexibility and applications of these structures. This paper extends the concept of tensegrity to more generalized cases, incorporating interconnected rigid bodies with various connection modes. A unified energy-based framework is proposed for form-finding and stability analysis of such structures. The potential energy of various element types and constraint equations of different connection modes are derived. Equilibrium equations for form-finding and static analysis are established using the Lagrange principle, and the Levenberg-Marquardt algorithm is adopted to solve these equations. The constraint space of the generalized degrees of freedom is determined through the singular value decomposition (SVD) of the Jacobian matrix of the constraint equations. Structural stability is assessed through the positive definiteness of the Hessian matrix of the potential energy within the constraint DOF space. The proposed method is validated by typical numerical examples, showing potential applicability in improving the structural stability of deployable mechanisms and designing structures with tunable stiffness.