基于总体坐标法的大变形锚泊线的静力分析

Static analysis of the mooring line under large deformation by utilizing the global coordinate method

为解决锚泊线轴向大拉伸问题,提出了一种联合应用总体坐标、能量变分原理和有限元法的解决方法。通过总体坐标使用节点斜率取代转角,直接在总体坐标系下以当前构形形成微元非线性应变位移关系的描述方法,同时建立当前构形与参考构形下的参量映射关系;利用能量变分原理建立应变能和外力功的平衡方程,进而形成锚泊线的单元刚度矩阵;按照有限元法完成单元组装和数值求解。这种方法在三维空间内较为准确地刻画了锚泊线的大转动和大拉伸变形,并且在单元组装时,不必进行局部坐标与总体坐标之间的转换,节省了计算时间。与具有解析解的可拉伸悬链线理论的对比显示,该方法具有较快的收敛速度和较高的计算精度。

To solve the defect of large axial stretching of the mooring line, a new solution jointly applying the global coordiantes, the energy variational principle and the finite element method have been proposed. The rotation angles were replaced by the slope of the node in the global coordinate, in order to make the description of the nonlinear relationship of the strain and the displacement. At the same time, mapping relationships of the parameters of the current and the reference configurations were set up. Then the equilibrium equations of the strain energy and external-force work were created on the basis of the energy variational principle so as to form the element stiffness matrix of the mooring line. Finally, all the elements were assembled and solved by use of the numerical method. This new method shows a precise presentation of the deformation of the large rotation and the large stretch in the 3D, and no translation is needed between the element coordinates and the global coordinates when the assembling is performed. One comparison was executed with the extensible catenary theory which has the analytical resolution. The compari-son results show that this new method has rapid convergency and good accuracy.