A cable finite element formulation based on exact tension field for static nonlinear analysis of cable structures

This paper introduces a cable finite element model based on an accurate description of the tension field for the static nonlinear analysis of cable structures. The proposed cable element is developed using the geometrically exact beam model that adequately considers the effects of large displacements. By neglecting flexural stiffness and shear deformation, the formulation of the cable finite element for scenarios involving given unstrained length and undetermined unstrained length is respectively presented. Additionally, the implementations of solutions based on complete tangent matrix and element internal iteration are introduced. Numerical examples are conducted to validate the accuracy of the presented formulation for cable analysis under various conditions and to demonstrate the computational efficiency of the proposed element and solution method. The results indicate that the proposed cable finite element not only exhibits extremely high accuracy but also effectively addresses the problem of determining the cable state with an unknown unstrained length, demonstrating the wide applicability of the proposed element. Through the utilization of an iteration algorithm with arc-length control and the introduction of additional control conditions, the proposed cable finite element can be further utilized to solve complex practical engineering problems.