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 shallow spherical shells under external pressure. By scanning six shallow spherical shells, the geometric characteristics of the shells were analyzed, and a geometric model was established based on the Fourier series. 720 sets of shallow spherical shells 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 is 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.