A Refinement of the Theory of Buckling of Rings Under Uniform Pressure

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Abstract
A general variational theory of elastic stability that was originated by E. Trefftz (1) is applied to the problem of buckling of rings of rectangular cross section subjected to uniform external pressure. The theory is believed to be more rigorous than previous treatments of the problem, since it avoids conventional assumptions of curved-beam theory, such as the assumptions that plane sections remain plane and that radial stresses vanish. The classical result of Levy (2) is confirmed for a ring of infinitesimal thickness. New results are obtained which show the effect of the finite thickness of a ring on the coefficients in the buckling formula.

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