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管柱在水平井眼中的屈曲方程是一个含有小参数的四阶非线性常微分方程。屈曲方程有两个临界点，一个对应于正弦屈曲，另一个对应于螺旋屈曲。本文利用线性化分析方法和小参数摄动分析方法，求得了两个相应的临界屈曲载荷。其结果与他人用能量法导出的结果和用实际数据拟合的结果非常吻合。本文还对管柱屈曲后与井壁之间的法向接触力、弯矩及应力等进行了分析。
The buckling equation of a string in horizontal wellbore is a fourth-order nonlinear ordinary differential equation with small parameters. Buckling equations have two critical points, one corresponding to sinusoidal buckling and the other to helical buckling. In this paper, two corresponding critical buckling loads are obtained by linear analysis method and small parameter perturbation analysis method. The results are in good agreement with the results obtained by others using the energy method and those obtained with the actual data. The paper also analyzes the normal contact force, bending moment and stress between the column and the wellbore after buckling.