Achieving stable configurations in tensegrity structures requires efficient and robust form-finding algorithms. Conventional methods often suffer from stiffness matrix singularity and limited control over structural stability. This paper proposes a novel and efficient form-finding method specifically aimed at generating super-stable tensegrity structures while overcoming these limitations.
A multi-constraint optimization framework is established based on the eigenvalue decomposition of the force density matrix. The form-finding problem is reformulated as a nonlinear least-squares optimization model with internal force constraints. By minimizing the sum of the squares of the smallest eigenvalues, the rank deficiency of the force density matrix is precisely controlled. Force density coefficients are treated as design variables, and a sequential quadratic programming (SQP) algorithm is employed to enhance numerical robustness and effectively avoid ill-conditioning and singularity issues.
Numerical examples demonstrate that the proposed method can reliably generate super-stable tensegrity configurations with high accuracy. The results show effective control of matrix rank deficiency and improved stability compared to conventional analytical and numerical approaches. Validation through a physical model further confirms the feasibility and effectiveness of the method. Comparative studies indicate that the proposed approach achieves superior computational accuracy and efficiency.
This study introduces an eigenvalue-based, optimization-driven form-finding strategy for super-stable tensegrity structures. By integrating strict constraint control with a robust SQP solution scheme, the proposed method provides a reliable and efficient alternative to existing techniques and shows strong potential for practical engineering applications.
