A simple nonlinear analysis of a spherical pressure vessel with axi-symmetric band of geometric imperfection

Abstract

A simple nonlinear analysis is presented to evaluate the displacements and stresses which arise from an axi-symmetric band of geometric imperfection in a pressurised sphere. The displacements and stresses solutions are derived in terms of Fourier series. Different shapes of initial geometric imperfections can be readily analysed by representing the shapes by Fourier series. It is concluded that the peak meridional stress is greater than the peak circumferential stress. Furthermore, the magnitude of the peak stress is scarcely influenced by the location of the imperfection shape. Generally, the stress distribution at the distorted region of the sphere can be characterised by the shape of imperfection and the membrane stress value; it is not so much affected by the different ‘radius to thickness’ ratio. The simple analysis highlights some important results which are not apparent in the other solution approaches.