On Axially Symmetric Bending of Nearly Cylindrical Shells of Revolution

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Abstract
The words “nearly cylindrical” are used in this paper to describe a thin elastic shell of revolution which is such that (a) the maximum variation of the radial dimension is small compared to the average radial dimension, and (b) the rate of change of the radial dimension with respect to the axial dimension is small compared to unity. For any particular type of loading a nearly cylindrical shell may or may not exhibit a behavior similar to that of a shell which is exactly cylindrical. The purpose of this paper is to demonstrate this fact and to present a method for obtaining approximate solutions for the stresses and deflections in either event. The method involves a perturbation procedure based on the assumption that all desired quantities can be represented as expansions in powers of two small parameters. The procedure leads to a set of linear differential equations with constant coefficients, which may be solved successively.

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