By a method, related somewhat to a technique used in the theory of he multiple scattering of light, integral equations are derived for the mean and mean-square solution of systems undergoing random changes. These equations are in essential agreement with similar equations derived elsewhere in the literature by completely different methods. The theory developed herein is applied to the analysis of a circular cylindrical shell under random end thrusts. It is found that the shell buckles when the mean-square value of the fluctuation of the end thrusts exceeds a certain critical level determined by damping.

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