An improved dog-leg method for form-finding of tensegrity structures

This paper presents a novel and highly efficient form-finding method for tensegrity structures. The method is based on converting the nonlinear equilibrium equations with the nodal coordinates vector as the variables into nonlinear least-squares problems. Subsequently, the Dog-Leg method is applied to solve these transformed problems. Furthermore, the Dog-Leg method is combined with the MBFGS (Modified Broyden-Fletcher-GoldfarbShanno) method to overcome the singularity problem of the stiffness matrix. The resulting improved Dog-Leg method, i.e., DL-MBFGS method, can effectively address form-finding problems not only in self-stressed and non-self-stressed tensegrity structures, but also for tensegrities subjected to external loads and other scenarios including mechanisms and large displacements problems, which shows its great versatility and robustness. Several numerical examples are presented to validate the accuracy and effectiveness of the proposed method.