A novel finite element for nonlinear static and dynamic analyses of helical cables

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Cables and wire ropes are structural components designed for high axial strength and relatively low torsion and flexure stiffness. Given the complex geometry of helical cables, analytical models for predicting their mechanical behavior include many assumptions and limitations. Three-dimensional finite elements can be used, but its practical use in Engineering applications with hundreds or thousands of meters long is hampered. On the other hand, beam finite elements do not consider the complexity of the cable construction, leading to wrong results, and therefore they are not an option neither, in general. To circumvent this problem, a new finite element is designed and implemented, aiming to incorporate the behavior of a 3D cable modeled using solid elements into a 1D beam element. The designed element is able to combine the accuracy of solid models with the practical implementation of line elements in nonlinear regime. In comparison with the cable modelled with solid elements, the proposed equivalent element yielded deviations of about 4% in the strain energy, when submitted to a variety of load conditions. High accuracy was also obtained in comparing axial, torsional, and bending stiffness of the equivalent element as function of the cable helix angle. Stiffness coupling terms, however, showed lower accuracy. Regarding the dynamic behavior, modal analysis yielded errors below 10% when comparing natural frequencies. Cable’s response under harmonic loading was also accurately reproduced by the introduced element.