低张力缆索有限元模型及其应用  

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

作　　者：方子帆[1] 贺青松[1] 向兵飞[1] 肖华攀[1] 何孔德[1] 杜义贤[1] 

机构地区：[1]三峡大学机械与材料学院,湖北宜昌443002

出　　处：《工程力学》2013年第3期445-450,共6页Engineering Mechanics

基　　金：湖北省自然科学基金项目(2010CDB10804)

摘　　要：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。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.

关 键 词：低张力缆索 有限元模型 弯曲刚度 扭转刚度 三次样条插值 Galerkin加权残值法 

分 类 号：O313[理学—一般力学与力学基础] TB122[理学—力学]