海洋工程大变形柔性结构非线性力学分析模型

Nonlinear analysis model for the flexible structures with large deformation in ocean engineering

为精确考虑海洋工程柔性结构物的大变形几何非线性问题,本文基于绝对节点坐标法(ANCF)、连续介质力学及有限元法的相关理论,建立了适用于大变形柔性构件的精确力学分析模型。通过在总体坐标下用斜率坐标代替传统的转角坐标,建立当前构形与参考构形下的参量映射关系,提出了以当前构形描述微元非线性几何关系的方法;由能量变分原理推导建立绝对节点坐标法梁单元的刚度矩阵、质量矩阵及外载荷矩阵,利用有限元法进行单元组装,形成静力和动力的平衡方程。利用FORTRAN语言编写计算程序,选取具有解析解的梁模型进行静力与动力程序验证,最后以缓波形钢悬链立管为例进行静力与动力计算,分析对比了立管的静态与动态特性。结果表明:本文绝对节点坐标法模型可以模拟出缓波形钢悬链立管的构型、张力及弯矩等基本特征,并且能够保持很好的精度。

To solve large deformation of thin,long,and flexible structures in ocean engineering,a precise mechanical analysis model,suitable for structures with large deformation,was established on the basis of absolute nodal coordinate formulation(ANCF)and several theories of continuum mechanics and the finite element method.By replacing traditional angle coordinates with the slope coordinate in the overall coordinate system,mapping relations of parameters in the current and reference configurations were defined.A method is proposed for describing nonlinear geometrical relations with current configurations.Based on the energy variational principle,a generalized elastic force and stiffness matrix of the element were derived,and the static and dynamic equilibrium equations were then obtained by introducing the mass matrix and the external load matrix,and by conducting the element assembly process using the finite element method.The calculation programs were compiled using FORTRAN,whose reliability and accuracy were then checked by the case of the beam model with analytical solution.Finally,a type of steel-lazy wave catenary riser was taken as an example to compare and analyze their static and dynamic characteristics.Results showed that the ANCF model proposed in this paper can simulate the features of a steel-lazy wave catenary riser,including configurations,extension,and bending moment,with good precision.