Form-finding of tensegrity structures using an optimization method

• An efficient form-finding method was proposed for regular and non-regular tensegrity structures.
• The force densities of a tensegrity were obtained by minimizing a special objective function.
• The sufficient condition to guarantee a non-degenerate state was used to obtain the geometry.
• Two tensegrity structures were studied to demonstrate the capability of the proposed method.

The process of finding an equilibrium configuration, called form-finding, is a key step in the design of a tensegrity structure. An efficient form-finding method based on the optimization method is proposed for regular and non-regular tensegrity structures. The force densities of a tensegrity are obtained by minimizing a special objective function, which satisfies the non-degeneracy necessary condition. Two examples, planar and spatial tensegrity structures, are used to prove the efficiency of the proposed method. It can be found that the results of regular tensegrity are the same as those given by the analytical method in the literatures.