Research on the Buckling Load of Clamped Spherical Caps Under External Pressure: Analyzed by the Fourier Series Model With Initial Geometric Imperfections

The knockdown factor (KDF), which characterizes the difference between the actual buckling pressure and the classical theoretical pressure of clamped spherical caps under external pressure, is highly discrete. The mechanism that causes this discreteness is still not understood and has not been reproduced in numerical simulation. By scanning six clamped spherical caps, the geometric characteristics of the shells were analyzed, and a geometric model was established based on the Fourier series. The geometric model was simulated by the geometric and material double nonlinear buckling analysis method. The results were compared with the experimental data from this study and other references. 720 sets of clamped spherical caps under external pressure were simulated using the proposed Fourier series model and simulation method. The influence of the yield strength, geometrical parameter λ, dimensionless parameters radius-thickness ratio R/t, and the imperfection-thickness ratio e/t on KDF were studied, and the highly discrete characteristics of KDF were reproduced. The results showed that the proposed method has a better predictive effect on KDF, which is significantly improved over the “Eigemode imperfections” method. KDF is not only related to λ and e/t, but is also affected by the yield strength and R/t. The lower envelopes of KDF were obtained when e/t was less than 1.0 and 2.0. The NASA SP-8032 curve corresponds to the lower envelope of KDF when e/t is less than 8.0, and the curve is below the lower envelope of KDF when e/t is less than 1.0 and 2.0. As stipulated in the pressure vessel standard, the KDF obtained by NASA SP-8032 will be conservative for design conditions with e/t less than 1.0 or 2.0, and appropriate adjustment should be considered.