Nonlinear programming approach to form-finding and folding analysis of tensegrity structures using fictitious material properties

An optimization approach is presented for form-finding of tensegrity structures. It is shown that various equilibrium shapes can be easily found by solving a forced-deformation analysis problem formulated as a minimization problem considering the nodal coordinates as design variables. The objective function is defined in terms of the member lengths, and it can be regarded as the total strain energy corresponding to fictitious elastic material properties. The self-equilibrium forces can be found from the optimality conditions of the nonlinear programming problem. Stability of the self-equilibrium shape is investigated based on the local convexity of the objective function. Similarity between form-finding problem of a structure with zero-unstressed-length cables and the problem of minimum square-length network is also discussed. Furthermore, folding of a structure with small unstressed-length cables is approximately simulated using affine transformation of equilibrium shape.