Vibration and elastic instability of thin-walled domes under uniform external pressure

Abstract

Two thin-walled varying meridional curvature axisymmetric shell elements are presented for the vibration and elastic instability of thin-walled hemi-ellipsoidal domes under uniform external pressure. The theoretical analysis is an extension of previous work carried out by the author, where for the two elements presented in the present report, a cubic and a quadratic variation was assumed for the meridional and the circumferential displacements along the meridian of these elements. In the previous study, only linear variations were assumed for the meridional and circumferential displacements along the meridian of these elements. Comparisons were made between experiment and theory for both buckling and vibration of hemi-ellipsoidal shell domes, which varied from very flat oblate vessels to very long prolate vessels. In general, agreement between experiment and theory was good for the hemi-spherical dome and the prolate vessels, but not very good for the fat oblate vessels. Additionally, the two new elements gave poorer results than the original simpler element for the cantilever mode of vibration, but better results for the lobar modes of vibration.