A novel scheme for large deflection analysis of suspended cables made of linear or nonlinear elastic materials

This paper presents a new approach to investigate the static response of horizontal and inclined suspended cables with deformable cross-section, made of general linear or nonlinear elastic materials, and subjected to vertical concentrated and distributed loads. The proposed technique also includes large sag and extensibility effects, and is based on an original finite difference scheme combined to a nonlinear least squares numerical solution. The mathematical formulation is developed for various loading cases, and an innovative computational strategy is used to transform the resulting nonlinear system of equations into a scaled nonlinear least squares problem. The numerical scheme is programmed and its application illustrated through examples highlighting the effects of coupling between the tension in a cable and the deformation of its cross-section as well as the use of cables made of neo-Hookean materials. The results obtained are in excellent agreement with analytical solutions when available. The proposed technique can be easily programmed and constitutes a valuable tool for large deflection analysis of suspended cables made of nonlinear elastic materials.