Analytical Solution and Buckling of Hemi-Ellipsoidal Shell Structures of Revolution
under Uniformly Distributed Load

This paper focuses on the analytical procedure for determining novel exact
expressions for internal forces and displacements of hemi-ellipsoidal shells formed as
an axisymmetric shell of revolution under uniformly distributed load such as imposed
loads. The simplest form of expressions for solutions are derived based on the linear
membrane theory under symmetrical loading that is formed as a shell of revolution.
The results have been validated and have a good consistency with numerical solutions
from the finite-element method (FEM) which are derived based on the principle of
virtual work and differential geometry. The obtained analytical exact solution is only
valid for small displacements or if the response does not exceed the linearity limit. In
cases of large displacements, geometrical nonlinear finite-element analysis is
recommended to determine the solution. The linearity limit determination is
demonstrated, and the effects of shells’ geometry, thickness, and magnitude of applied
loads are presented. Additionally, the linear buckling analysis has been performed. The
study found that the size ratio and support condition have a significant effect on the
critical load of the first mode, and the hemispherical shells have the highest buckling
resistance due to the geometry.