An asymptotic expansion procedure proposed by E. Reissner is applied to the simple Donnell equations for circular cylindrical shells, and a simple explicit solution is obtained for the interaction problem of an infinite cylinder reinforced by a central ring subjected to a nonuniform radial load. It is shown that the sign of the dominant stresses depends entirely upon whether the shell is reinforced by inside or outside rings. In addition, even when only the lower harmonic contributions are retained, good agreement with an exact solution for the case of concentrated loads is achieved.

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