微分求积单元法分析变曲率井内受径向约束管柱的非线性屈曲

Nonlinear Tubular Buckling Analysis Under Radial Constrains in Variable Curvature Wells by DQEM

基于Love的空间弯扭杆平衡方程,通过引入井壁约束条件导出了平面变曲率井内受径向约束管柱的平衡方程。采用微分求积单元和增量迭代法求解了曲率线性变化的井内管柱的非线性屈曲问题,通过与有限元计算结果的对比验证了所构建方法和编写程序的正确性,而且还表明微分求积单元法有方法简单、易于实施,计算量少、精度较高等优点。计算结果表明,等曲率井内管柱屈曲的临界载荷明显大于曲率线性变化井内管柱屈曲的临界载荷,另外,变曲率井眼的曲率变化对管柱弯矩、井壁约束力有显著的影响。

Based on Love equilibrium equations for a curved and twisted bar in space, the 2-D equilibrium equations of the tubular restrained by the radial wall of a variable curvature well are obtained by introducing of the radial constraint. The nonlinear tubular buckling within 2-D wellbore with a linear varying curvature is solved by the differential quadrature element （DQE） method together with the incremental iteration scheme. The established method and the developed program are verified compared numerical results with data obtained by the finite element method. The result shows that the DQE method has advantages of simple, easy to use, less computation effort, and higher accuracy. Numerical results indicate that the load tubular buckling in a constant-curvature well is larger than that in linear varying curvature wells. The curvatures change of variable-curvature wells has an appreciated effect on the bending moment and tubular constraint force.