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.

翻译：本文提出一种基于精确张力场描述的索有限元模型，用于索结构的静力非线性分析。所提出的索单元基于几何精确梁模型建立，充分考虑了大变形的效应。通过忽略抗弯刚度和剪切变形，分别给出了给定无应力长度和未确定无应力长度工况下的索有限元列式。此外，还介绍了基于完全切向矩阵和单元内部迭代的求解实现方法。通过数值算例验证了所提列式在不同条件下进行索分析的准确性，并展示了所提单元及求解方法的计算效率。结果表明，所提出的索有限元不仅具有极高的精度，而且能有效解决未知无应力长度下的索状态确定问题，体现了该单元的广泛适用性。通过采用弧长控制迭代算法并引入附加控制条件，该索有限元可进一步用于解决复杂的实际工程问题。