Elastic Buckling of Oblate Hemi-Ellipsoidal Shells Subjected to Hydrostatic Pressure

This study investigates the elastic buckling behavior of oblate hemi-ellipsoidal shells
(OHES) subjected to non-uniform external hydrostatic pressure. The virtual workenergy
of OHES consists of virtual strain energy due to membrane, bending, in-plane
stress resultants, and virtual work of hydrostatic pressure. For buckling analysis, the
geometric stiffness matrix is obtained from the strain energy due to in-plane stress
resultants. A finite element procedure via a C1 continuity axisymmetric element is
applied to solve the critical hydrostatic pressure from the eigenvalue buckling problem.
The buckling pressure of the hemi-ellipsoidal dome subjected to uniform external
pressure is verified with the previous research and FEM commercial software. Present
results also indicate that the maximum in-plane stress of the hemi-ellipsoidal shell
shapes are near the apex point as the axisymmetric buckling shape. In the case of
hydrostatic pressure, the critical hydrostatic pressure of OHES is determined and are in
good agreement when compared with the experimental results in published research.
Furthermore, the shape ratio influences the difference in critical load results between
uniform pressure and hydrostatic pressure, especially when the shape ratio is higher
than 0.5 and the a/t ratio is less than or equal to 100. Seawater depth limitations in
subsea engineering are also presented and found that the shell thickness and shape
ratio are the major factors affecting critical seawater depth.