Buckling of thick orthotropic spherical shells

Abstract

This paper is concerned with the semi-analytical solution for the axisymmetric buckling for perfect complete thick orthotropic spherical shells and hemispherical shells under various edge conditions, subjected to uniform full external pressures. The meridional and radial mid-surface displacements and the circumferential cross-sectional rotation are expressed as an expansion in Legendre polynomials respectively in the meridional coordinate. Transverse shear strain effects are included in the energy formulation of small strains. The solutions are achieved directly by use of the Ritz method without considering the force and moment equilibrium and solving the complicated governing equations. Critical buckling loads and the various modes are found from the equations by use of orthogonality and some integral relations.