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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。
In order to accurately calculate the cable movement at low tension, a three-dimensional finite element model suitable for low tension cables was established in consideration of the tensile stiffness, flexural rigidity and torsional stiffness of the cable under low tension. Firstly, the dynamic differential equation of the cable is derived based on the slender rod theory. Then, the cubic spline curve is used as the trial function, the element stiffness matrix is deduced by using the Galerkin weighted residual method, and finally the integral matrix equation of the cable is established. And use Matlab to solve the program. Applying it to the example, the results are consistent with the experimental results. The research results provide theoretical basis for the motion analysis and design of towed cables, mooring cables, umbilicals and other marine cables.