A stochastic approach to the problem of stability of a spherical shell with initial imperfections

A probabilistic method is applied to the problem of stability of a spherical shell with initial imperfections, subjected to uniform external pressure. The distribution law of the normal deflections of the shell is obtained following the Smoluchovsky equation, at a given density of the initial deflections. On this basis the probability for the deflections to be in a given interval is found. A relation for the probability for a jump transition to a new stability form is obtained for a spherical shell with a given probability distribution of the initial imperfections. The relations obtained can be used for solving different kinds of reliability problems, as well as problems for prediction of the shell stability forms together with the probability for their realization.