中文摘要：

基于能量法推导了外压作用下椭圆截面柱壳弹性屈曲临界荷载的理论解，推导中考虑了椭圆截面连续变化的曲率，引入带有衰减系数的位移函数以反映外压作用下椭圆柱壳的变形特点，并利用里兹法求解外压椭圆柱壳的能量方程。由椭圆柱壳理论解退化求得的圆柱壳外压屈曲荷载与已有文献的经典解吻合良好，与有限元分析结果的比较进一步验证了该文理论解的准确性。基于理论解的参数分析表明：在外压作用下，椭圆柱壳具备比圆柱壳更优越的力学性能；椭圆柱壳的外压屈曲荷载随椭圆截面比的增大而增大，随壳体名义径厚比的减小而增大；椭圆柱壳的外压屈曲荷载随壳体长度的增大而降低，但当名义长径比大于1左右后，屈曲荷载基本保持不变。

英文摘要：

An analytical solution based on the energy method is derived for the elastic buckling of elliptical cylindrical shells under external pressure. During the theoretical derivation, the effect of continuous curvature variation around the elliptical circumference is accounted for, and a damped exponential is introduced into the displacement function to reflect the deformation behavior of elliptical shells under external pressure. The Ritz method is employed to solve the established energy equation, leading to the analytical solution for the critical buckling load of externally-pressurized elliptical shells. The elastic buckling loads of circular cylindrical shells under external pressure, which are obtained by degeneration of the current analytical solution for elliptical shells, are found to be in good agreement with the classical solutions in the existing literature. The accuracy of the analytical solution is further verified by comparing its predictions with results obtained from finite element analysis. Results from parametric analysis based on the proposed analytical solution indicate that the structural behavior of cylindrical shells subjected to external pressure with elliptical sections is superior to those with circular sections. Specifically, the elastic buckling pressure of elliptical cylindrical shells is on the rise as the aspect ratio increases and the nominal radius-thickness ratio decreases. With the longer shell length, the elastic buckling pressure of elliptical cylindrical shells undergoes a decreasing trend, however the buckling pressure basically maintains a constant level after the length-nominal radius ratio reaches about 1.