斜直井中钻柱非线性屈曲分析的有限元增量加权迭代法

建立了直井中有重钻柱非线性屈曲平衡方程及相应的泛函表达式，构造了一种能避免发散并加速收敛的有限元增量加权迭代法求解斜直井中钻柱屈曲问题，首次采用直接求解非线性特征值的方法来分析钻柱屈曲问题。计算结果表明，井斜角和屈曲位移幅值中任意一项增大，钻柱的非线性屈曲临界载荷也随之增大，且呈非线性；重力线密度对屈曲载荷的影响与屈曲状态有关；井壁约束力和特征向量的幅值随屈曲位移幅值增大而增大；扭矩对屈曲的影响很小，可以略去。研究结果为实际钻井作业中屈曲载荷的确定提供了参考。

Finite Element Incremental Weighted Iteration Method for Nonlinear Buckling Analyses of Tubing in Deviated Wells

The equilibrium equations and the potential energy function of tubing nonlinear buckling in arbitrary straight wells were derived. A finite element incremental weighted iteration method, which can avoid divergency and speed up the convergence process,was proposed to solve the problems of tubing buckling in deviated wells. It is for the first time to obtain the buckling load of the tubing by directly solving the nonlinear eigen-value problems. It is shown that the critical buckling load of tubing increases with the increase of the amplitude of buckling displacement and the deviation angle. The effects of weight per unit length on critical buckling load are related to the buckling state. The amplitudes of eigen-vector and the restrain forces of the well increase with the increase of the amplitudes of the buckling displacements. The influence of torque on buckling is small enough to be neglected. The analyses give powerful support to determine the buckling load of tubing in real drilling engineering.