Static/Dynamic Buckling of Axially Compressed Thin-Walled Cylindrical Shells Using Simple Models

The postbuckling response of elastic thin-walled circular cylindrical shells under axial compression is discussed using equivalent 1 and 2 degrees-of-freedom imperfect models characterized by a nonlinear spring component simulating the analogous restraining membrane force in the shell. The initial geometric shell imperfections are related to the out of straightness of shell generators. Very recently, Bodner and Rubin ("Modeling the Buckling of Axially Compressed Elastic Cylindrical Shells," AIAA Journal, Vol. 43, No. 1, 2005, pp. 103-110) proposed a 1 degree-of-freedom mechanical model, whose buckling mechanism can be viewed as a local event governed by a shallow archlike behavior depending on the shell geometry, which they related to an empirical formula based on experimentally measured shell buckling loads. This formula, relating the critical load to the ratio thickness-to-radius of the shell, was used for determining the aforementioned nonlinear spring component, necessary for the subsequent analysis of the model. In the present analysis, a new, more reliable 2 degree-of-freedom model for both axisymmetric and asymmetric buckling mechanisms of axially compressed circular cylindrical shells is proposed which can include antisymmetric imperfections and mode coupling. Another advantage of the proposed models is their ready extension to the dynamic buckling. Moreover, a semi-empirical formula is proposed which generalizes Koiter's formula to include the effect of the ratio thickness-to-the shell radius. Numerical examples illustrate the simplicity and efficiency of the analysis for establishing static and dynamic buckling estimates, quite satisfactory for structural design purposes.