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给出了描述弯曲井眼中管柱屈曲及后屈曲行为的解析结果。通过求解由平衡法得到的管柱屈曲平衡方程，得到了管柱的正弦屈曲的构型和螺旋屈曲构型的解析解。解析结果与相应的数值结果有良好的一致性。在此基础上，确定了管柱的初始屈曲临界载荷、保持正弦屈曲构型的最大载荷和螺旋屈曲临界载荷。由此，进一步得到了管柱在后屈曲进程中载荷与变形受力的关系。
The analytical results describing the buckling and post-buckling behavior of the cased borehole are given. By solving the buckling equilibrium equation of the pipe string obtained by the equilibrium method, the sinusoidal buckling configuration and the analytical solution of the helical buckling configuration are obtained. The analytical results are in good agreement with the corresponding numerical results. On this basis, the initial buckling critical load of the string is determined, and the maximum load of the sinusoidal buckling configuration and the critical load of helical buckling are maintained. Thus, the relationship between load and deformation stress in the post-buckling process is further obtained.