Buckling of thin cylindrical shells: theory and what actually happens
Professor C.R. Calladine
CUED
It is well known that the buckling strength of axially loaded thin cylindrical shells falls below the predictions of classical, linearised theory; and that there is much scatter in experimentally determined buckling loads. For example shells having radius/thickness values of 1800 are found, according to the trend of collected data from the literature, to buckle at loads ranging from 0.1 to 0.4 of classical. A widely-held explanation for such observations is that the buckling is "imperfection sensitive" : according to non-linear theory, the peak buckling load is extremely sensitive to the presence of small but unavoidable geometric imperfections.
In this talk I shall present two sets of experimental data - obtained by E.R. Lancaster and P. Mandal, respectively - that do not fit within that widely-accepted conceptual scheme.
First, we found in many tests on a "melinex" cylinder 0.9 m diameter and 0.25 mm thick (radius/thickness = 1800) that the mean buckling load was about 0.35 of classical and that the presence of large geometric imperfections - e.g. dimples having a central radial deflection of some 10 thicknesses - made little difference to the buckling load. The end-conditions of the shell were somewhat unusual : the shell was secured to its end-discs by means of friction, achieved through a tensioned belt. In the second set of tests, we did some self-weight buckling experiments on small-scale open-topped silicone rubber shells having radius/thickness values in the range 80 to 400. The observed self-weight buckling stress fitted the trend of collected data from the literature; but there was very little scatter.
These experimental observations are puzzling. We are inclined to attribute the lack of scatter in both sets of tests to an overall actual, or near, static determinacy. In computer studies of the self-weight buckling experiments we have found a well-defined flat "post buckling plateau" in the plot of gravity load against radial deflection - extending up to about six shell thicknesses - which corresponds to the measured buckling loads.
We cannot claim to have got to the bottom of this paradox; but our work sheds some fresh light on the situation and suggests some practical strategies for design.
