Influence of Axisymmetric Initial Imperfections of a Spherical Shell on its Critical Load

Abstract

The work examines pre- and postbuckling behavior of a thin, elastic and shallow dome, which is clamped at own boundary and is under uniform external pressure. It is supposed, that before pressure application the dome has small axisymmetric initial imperfections. Solving of this boundary problem is based on Marguerre's equations and obtained by means Rayleigh-Ritz method and arch-length incremental method. Search of different forms of initial imperfections of a dome from spherical at the maximal deviation up to 30% of its thickness enables receiving of a range of its critical loadings which completely comprised all experimental values.