| This dissertation provides a detailed examination of the theories of elastic stability for cylindrical shells. A particular emphasis is placed on identifying the assumptions which were made to achieve a solution and the effect that these assumptions have on the result.; The linear stability theory for shells is well known to be dramatically unconservative in predicting critical buckling loads. One explanation of the difference between experiment and theory is the effect of imperfections in the cylinders tested. Studies and analyses of the effect of imperfections in cylinders on the buckling strength show that this can be a major factor, but the commercial quality cylinders used in experiments do not have a level of imperfections that would be significant, thus suggesting that the theory has intrinsic flaws.; By re-creating a complete derivation of the linear shell theory, the required simplifying assumptions are identified and evaluated. In this investigation it is found that one of the major assumptions, which produces a linear theory, is one that neglects the effect of the bending moments. The resulting simplified equilibrium equations reduce to the same closed form solution for any differentiable function used for the displacements. This explains why the non-linear solutions, which account for geometric non-linearities, are able to produce far more accurate theoretical results at the expense of not having a concise closed-form relationship. |
