Form-finding method for multi-mode tensegrity structures using extended force density method by grouping elements

Multistable tensegrity structures are an intriguing form of compliant prestressed structures. Due to their attractive properties, these structures are attractive for a wide range applications. This papers aims the form-finding problem of tensegrity structures with multiple equilibrium modes. An optimization method for form-finding of multi-mode tensegrity structures is applied and then an equivalent optimization problem of energy-based objective function with Lagrange multiplier, regarded as an extension of the original force density method, is established. After the structural elements are grouped according to the property of symmetry, the objective function is minimized by the gradient descent algorithm, and as a result, the lengths of cable as well as the nodal coordinates are obtained and different structural modes corresponding to different grouping conditions can be achieved. Finally, several different modes in different grouping conditions of a planar and a spatial tensegrity structure have been obtained to verify the efficiency of proposed method.