This paper presents the formulation of a finite element enclosing a specific internal mechanical equilibrium in order to model cable-based structures in dynamics conditions. It is based on the concept of macro finite element which allows embedding complex mechanical systems solved inside the element boundaries. A significant advantage is to allow an easy implementation within classical commercial codes. The proposed macro finite element describes a cable interacting with a sliding object assimilated to a punctual mass where friction can be accounted for. The dynamic response is described by a model developed within the framework of the DEM (Discrete Element Method) where geometrical nonlinearity (large displacements) is considered. A model combining the proposed macro finite element and a classical linear truss finite element is presented in order to validate its implementation. Finally, illustrative examples are presented. First, a cable yarning system is considered. The effect of friction and of the bending stiffness of the posts on the overall kinematics and force within the system are explored. Then the vulnerability of a cable-stayed bridge to earthquake is explored accounting for guy ropes failure.

本文提出了包含特定内部机械平衡的有限元的公式化，以便在动力学条件下对基于电缆的结构进行建模。它基于宏有限元的概念，该概念允许将复杂的机械系统嵌入到单元边界内。一个显着的优点是允许在经典商业代码中轻松实现。拟议的宏有限元描述了一种电缆，该电缆与滑动物体相互作用，该滑动物体与点状质量（可计入摩擦）相结合。动态响应由在DEM（离散元素方法）框架内开发的模型描述，该模型考虑了几何非线性（大位移）。提出了将所提出的宏有限元与经典线性桁架有限元相结合的模型，以验证其实现。最后，给出了说明性示例。首先，考虑电缆光缆系统。探讨了摩擦力和柱子的弯曲刚度对系统整体运动学和力的影响。然后，研究了斜拉桥在地震中的脆弱性，以解释拉索的失效。