An analytical solution for evaluating the critical pressure of pipes under hydrostatic pressure was proposed. The stability equations and the correct boundary conditions for 3D problem in cylindrical coordinates were established by using energy method. The stability equations were solved together with the derived correct boundary conditions and the solution of the critical pressure for elastic buckling of the pipes was expressed in closed form. By adopting the three-layers model for elastic-plastic buckling analysis, the solution was available for the critical pressure prediction of the pipes in elastic-plastic collapse. The effect of the initial ovality was incorporated in formulation. It shows that the increase in the magnitude of the axial compressive stress results in the further reduction in the critical pressure for fully elastic buckling while the pressures for elastic-plastic collapse are always higher than those of the 2D solutions based on the plane strain deformation. The influence of the initial ovality on the pressure capacity of the elastic-plastic buckling of the pipes was discussed and the results from the present approach were compared with the other solutions and experiments.

提出了一种在静水压力下评估管道临界压力的解析解决方案。利用能量法建立了圆柱坐标系中3D问题的稳定性方程和正确的边界条件。将稳定性方程与导出的正确边界条件一起求解，并以闭合形式表示管道弹性屈曲的临界压力的解。通过采用三层模型进行弹塑性屈曲分析，该解决方案可用于弹塑性塌陷中管道的临界压力预测。初始椭圆度的影响被并入配方中。它表明，轴向压缩应力的大小增加导致完全弹性屈曲的临界压力进一步减小，而弹塑性崩溃的压力始终高于基于平面应变变形的2D解的压力。讨论了初始椭圆度对管道弹塑性屈曲压力能力的影响，并将本方法的结果与其他解决方案和实验进行了比较。