Non-Axisymmetric Buckling Stress of Axially Compressed Circular Cylindrical Shells: Closed-Form and Simplified Formulae

Due to their thin-walled characteristics, axially loaded circular cylindrical shells (CCSs) commonly undergo buckling failure. The limiting buckling stress of such shells has not yet been fully developed due to a wide range of influencing parameters such as sensitivity to imperfections, nonlinearity, and buckling mode. It has been proved early, and in this study, that the non-axisymmetric buckling stress can be one of the remedies that casts into eliminating the overestimation caused by the classical axisymmetric buckling formula. However, the complex non-linear constrained optimization required to obtain the non-axisymmetric buckling stress and mode remains to be the main obstacle for practicing engineers to approach the non-axisymmetric buckling. In this study, the non-axisymmetric buckling formula has been cast in a compact form and possible approaches to utilize it have been discussed considering the degree of user knowledge and availability of computational tools. Moreover, it has been used to derive a closed-form buckling stress formula that considers the effect of all geometric and material properties. The proposed closed-form formula predicts buckling stress that is always less than that of the classical formula for L/R greater than 0.91 and the amount of reduction increases with the increase of L/R ratio. In comparison with the exact non-axisymmetric buckling formula, the proposed closed-form formula yields buckling stress within ± 4%. Thus, it shares the simplicity of the classical axisymmetric buckling formula and the accuracy of the non-axisymmetric buckling formula.