Collapse by ponding of shells

Abstract

The problem of stability of shells of positive Gaussian curvature subjected to a concentrated load, internal or external pressure and an accumulating ponding fluid in the depression caused by the load is the subject of this paper. Critical values of the load are calculated by a so called “geometrical method”, using variational Lagrangian principles. The shape of the shell is assumed to be nearly isometrical to the initial shape and its bending rigidity is taken into account. Simple relations for the critical load are obtained and the results presented in graphical form. The expressions and diagrams presented facilitate calculation of critical loads and describe the behaviour of the shell undergoing very large deflections.