Abstract Sliding cables are widespread in engineering applications. The friction between the cable and the sliding components results in the existence of diversified motion states of the contact points, which leads to many difficult problems for traditional analysis methods. This paper proposes an effective and robust nonlinear complementarity function based framework for static and dynamic analyses of sliding cable problems. The core idea is that the involved sliding criterion is expressed by complementarity relationships which can be further reformulated as a set of equation by using the modified Fischer-Burmeister complementarity function. By considering the instrumental sliding lengths as additional degrees of freedom in the finite element model, the sliding nodes searching and the geometric configuration searching in the analysis can be handed in a unified framework. The solution can be obtained by using classical Newton-Raphson scheme with a closed-form expression of tangent matrix. Cumbersome trial and error iterations for sliding node searching in traditional analysis methods are rigorously avoided, and always the same equation is used regardless of whether a particular contact point would be sticking or sliding. This framework is developed mainly for implicit static and dynamic analyses, but can also be integrated into explicit analyses. Some typical examples are presented to illustrate the robustness and versatility of the proposed approach. The result highlight its ability to capture the complex and diverse motion states of the contact points in a rather direct way.

中文翻译：

---

滑索建模：基于非线性互补函数的框架

摘要 滑动电缆在工程应用中广泛应用。缆索与滑动部件之间的摩擦导致接触点存在多种运动状态，这给传统分析方法带来了许多难题。本文提出了一种有效且稳健的基于非线性互补函数的框架，用于滑索问题的静态和动态分析。其核心思想是将所涉及的滑动准则用互补关系表示，利用修正的Fischer-Burmeister互补函数可以进一步将其重新表述为一组方程。通过将仪器滑动长度视为有限元模型中的附加自由度，分析中的滑动节点搜索和几何构型搜索可以交到一个统一的框架中。该解可以通过使用经典的 Newton-Raphson 格式和切线矩阵的闭式表达式来获得。严格避免了传统分析方法中用于滑动节点搜索的繁琐反复试验，并且无论特定接触点是粘着还是滑动，始终使用相同的方程。该框架主要用于隐式静态和动态分析，但也可以集成到显式分析中。提供了一些典型的例子来说明所提出的方法的鲁棒性和通用性。结果突出了它以相当直接的方式捕捉接触点复杂多样的运动状态的能力。