Buckling of elastic cylindrical shells under symmetric but non-uniform bending moment distributions

The behaviour of cylindrical shells and circular hollow sections under uniform bending has long received significant research attention. This is mainly due to the phenomenon of Brazier cross-sectional ovalisation which is known to lead to an almost 50% reduction in the buckling moment relative to the classical analytical prediction. However, very little research appears to have been carried out to investigate the ovalisation behaviour under non-uniform bending moment distributions (BMDs). This appears to be because until only relatively recently, most studies on the topic were analytical in nature which made the buckling analysis of anything but a uniform BMD difficult. With the rise of modern computing it is now possible to undertake extensive parametric studies to investigate any desired load condition.

This paper employs the finite element method to explore the elastic stability of perfect simply-supported cylinders or tubes under load cases that represent symmetric parabolic and triangular BMDs, and to compare them with the behaviour under the hitherto most-commonly studied uniform BMD. Each non-uniform BMD is investigated by four different three-dimensional shell loading arrangements. While these all share the same resultant BMD, they exhibit very different buckling behaviours illustrating the ambiguity inherent in realistically modelling such systems. This is a consequence of the loss of uniqueness when projecting a 1D construct onto a 3D space.

In addition to linear bifurcation analyses, nonlinear elastic buckling analyses are presented to explore the effect of ovalisation at long lengths under the proposed loading arrangements. It is found that ovalisation becomes fully developed at approximately the same dimensionless length and leads to a similar ∼50% reduction in the buckling strength of asymptotically long cylinders for almost any representation of the three considered symmetric BMDs.