弯曲井眼中受压管柱的屈曲分析

Buckling Analysis for Pipe String Constrained in Curved Boreholes

本文通过微元体的变形和受力分析，导出了弯曲井眼中受压管柱的屈曲方程──一个合参数。的四阶非线性常微分方程。ε是一个综合考虑轴压（Ｆ０）、管柱截面抗弯刚度（ＥＪ）、井眼轴线轨迹曲车半径（Ｒ）以及共眼有效半径（ｒ）的无因次参数。本文利用线性化方法及小参数摄动法求得了屈曲方程的一次分叉点ε１及二次分叉点ε２。当ε＞ε１时，管柱处于稳定状态，对应于屈曲方程的零解；当ε２＜ε≤ε１时，管柱处于正弦屈曲状态，对应于屈曲方程的周期解；当ε≤ε２时，管柱处于螺旋屈曲状态，对应于屈曲方程的螺线解。本文给出的弯曲井眼中受压管柱的两个临界屈曲载荷（与两个分叉声、对应），发生螺旋屈曲时的螺距等理论结果与他人发表的实验结果吻合较好。

Buckling equation is derived by this paper based on analyzing the geometric deformation and equilibrium equations of elastic beam in curved boreholes,which is a four order non-linear ordinary differential equation with a parameter ε,ε is a nondimensional parameter, which represents the combinedeffects of axial force(F0), Curvature radius of borehole (R), radial clearance between pipe and borehole (r) et al. Two critical points (bifurcation points)ε1 and ε2 are given by this paper using linearization and small parameter perturbation analysis methods. The pipe in a borehole keeps stable state(which relates to the zero solution to the buckling equation) when ε>ε1,, then changes its configuration into a sinusoidal wave form as ε2<<ε≤ε1, (relates to the periodic solution), and then into a helixform as ε≤ε2(relates to the belieal solution). The theoretical results of critical forces, helix pitch et algiven by this paper are well coincided with the experimental data pubulished by others.