A unified approach for analysis of cable and tensegrity structures using memoryless quasi-newton minimization of total strain energy

Abstract

A unifying approach is presented for the nonlinear static analysis of cable structures and for the form-finding of tensegrity structures. The novelty lies in the possibility of static analyses of structures where the stiffness matrix is singular throughout the path to equilibrium. The unification of static analyzes and form-finding procedures allows the understanding and treatment of tensegrity and cable structures as a single type of structure. A total potential energy function is derived in terms of nodal displacements which are the unknowns of a nonlinear programming problem. The proposed approach uses a Quasi-Newton method overcoming a limitation of the Newton Raphson Method employed by widel-used commercial Finite Element software packages. Example analyses are presented and compared with experimental results reported in the literature to demonstrate the feasibility of the proposed approach which is particularly useful for under-constrained structures that contain pre-tensioned elements.