基于非线性有限元法的二维水下拖缆研究

Research of Two Dimensional Underwater Towed Cable Based on Nonlinear Finite Element

水下拖缆研究是拖曳系统设计和使用的基础。由于受到水流力的作用,水下缆索呈现复杂的特性。本文首先推导了水下拖曳缆索的静力悬链线方程,将其结果作为非线性有限元方法的初始值;接着采用二节点等参索单元建立基于完全拉格朗日表述的增量平衡方程并使用牛顿-拉谱逊迭代法求解该方程;最后,采用Matlab编程,研究了该方法的收敛性及拖缆在重力、浮力和水流力作用下的形态与张力分布,得到了不同航速条件下缆索的形态及缆索张力的一些分布规律。

The research of the underwater towed cables is the foundation of design and application of the towed system. Due to the effect of water flow force, the towed cables present complex features. Firstly, the static catenary equation of the underwater towed cable is derived and the result is applied as the initial value of the nonlinear finite element method. Then, the equation of nonlinear finite element method using isoparametric cable element with two nodes is briefly presented on the basis of the total Lagrangian formulation and Newton-Raphson iterative method for solving this equation. Finally, utilizing Matlab code, the convergence of the method, the geometries of towing cable with cable weight, cable buoyancy, fluid drag, and the forces exerted on the cable by the submersible are studied. The conclusions about the relationship between geometry and distribution of tension of the cable with different currents are presented.