Loss of stability of thin, elastic, strongly convex shells of revolution with initial imperfections, subjected to uniform pressure. A probabilistic approach

Abstract

This paper presents an attempt to evaluate theoretically the influence of initial geometric imperfections in the shell surface on the value of the upper critical load of a strictly convex shell of revolution which is subjected to uniform pressure. Pogorelov's geometric method for nonlinear stability problems of thin shells is applied to obtain an analytical formula for the upper critical load, dependent on the initial imperfections. A probabilistic solution of the problem is presented. As a result, the stochastic influence of the initial deviations in the shell surface on the probability density function of the critical load and on the shell reliability are estimated and presented graphically. An example is given for an ellipsoidal shell of revolution.