This paper presents a numerically exact cable finite element model for static nonlinear analysis of cable structures. The model derives the exact expression of the tension field using the geometrically exact beam theory coupled with the fundamental mechanical characteristics of cables. The equations for the cable element are formulated by addressing the equilibrium conditions at the element boundaries and ensuring compatibility within the element. Unlike previous studies that typically provide explicit expressions for cable models, this study develops a formulation that emphasizes numerical precision and broad applicability. It achieves this by deriving linearized equations with implicit expressions incorporating integrals. The proposed model accurately computes internal forces and deformation states, and determines the unstrained length of the cable. Additionally, it accounts for the variability in cross-sectional stiffness along the cable's length. The paper discusses solution implementations using the complete tangent matrix and element internal iterations. The effectiveness of the proposed cable element is demonstrated through numerical examples.

翻译：本文提出了一种用于索结构静力非线性分析的数值精确索有限元模型。该模型结合几何精确梁理论与索的基本力学特性，导出了张力场的精确表达式。通过处理单元边界处的平衡条件并确保单元内部的协调性，建立了索单元的方程。与以往通常为索模型提供显式表达式的研究不同，本研究开发了一种强调数值精度和广泛适用性的公式。它通过推导包含积分的隐式表达式线性化方程来实现这一点。所提出的模型能够精确计算内力和变形状态，并确定索的无应变长度。此外，它还考虑了沿索长度方向截面刚度的可变性。本文讨论了使用完全切线矩阵和单元内部迭代的求解实现。通过数值算例验证了所提索单元的有效性。