An uncoupled eighth-order equation for the buckling of axially compressed cylinders, within the framework of the Koiter-Budiansky shell equations, is derived for the first time herein. A solution of this equation is then used to generate some different types of approximations for the buckling stresses of a circular cylinder. Comparisons to previous solutions are given, as are some remarks on the nature of the approximations and their relationships to the limiting cases of infinitely short and infinitely long shells. Also given is a summary of the uncoupled system of equations of Sanders’ linear shell theory.

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