低张力缆索有限元模型及其应用

为准确计算缆索在低张力时的运动状态，该文考虑缆索低张力状态时的拉伸刚度、弯曲刚度和扭转刚度，建立了一种适用于低张力缆索的三维有限元模型。首先基于细长杆理论推导了缆索的动力学微分方程，接着以三次样条曲线为试函数，运用Galerkin加权残值法导出了单元刚度矩阵，最后对其进行组合建立了缆索的整体矩阵方程，并采用Matlab编写了求解程序。将其应用于实例中，所得结果与实验结果相一致。研究成果为拖曳缆、系泊缆、潜行器脐带缆等海洋缆索的运动分析与设计提供了理论依据。

RESEARCH AND APPLICATIONS OF FE MODEL ON CABLES IN LOW-TENSION

To accurately calculate the motion of cable in low tension, a new three-dimensional finite element model is established in this paper, with tension stiffness, bending stiffness and torsional stiffness being considered. Based on the rod theory, the dynamical differential equation is first derived. Subsequently, by taking the cubic spline interpolation as trial function, the element stiffness matrix is obtained using the Galerkin method. Finally, the element stiffness matrixes are combined to obtain the global stiffness matrix. The model is applied to several examples using Matlab programming. The numerical result is coincident with the experimental results. The results of the present study are expected to be useful for kinematics analysis and design of ocean cable, such as mooring cables, towing rope and ROV umbilical cables.