Modeling the Buckling of Axially Compressed Elastic Cylindrical Shells

Abstract

This exercise is intended to provide a direct correlation between the axial compressive buckling of elastic thin-walled cylinders and the response of a mechanical model that exhibits a peak load at large deformation. The model is similar, but more general, to those used by Budiansky and Hutchinson and by Kounadis and associates to illustrate dynamic buckling behavior of imperfection sensitive nonlinear systems. Here, an empirical relation between observed static shell buckling loads and the shell geometry is used to characterize the restraining spring parameter of the model. The resulting model indicates realistic imperfection sensitivity of the load-deflection relation and, as a good physical analogy, provides insight into the shell buckling mechanism. Specifically, from the perspective of the model, shell buckling is viewed as a local event governed by shallow arch-like behavior where the extent of the arch depends on the shell geometry. This implies that the specific geometry of local axial imperfections of the shell (out of straightness) might be more important than that of circumferential imperfections (out of roundness) for shell buckling under axial loading. Moreover, use of an imperfection slope factor rather than an imperfection displacement term might be more suitable for actual shells in some cases. In addition, the model analogy indicates that the buckling (peak) load also depends on the shell geometry and that the bifurcation load serves only as a reference value. A comparison is made to Koiter's approximate formula for axially compressed isotropic shells.