University of Minnesota
Aerospace Engineering and Mechanics
Fall 1999 Seminar Series



Buckling of Thin Cylindrical Shells: An Attempt to Resolve a Paradox


Prof. Chris Calladine

Department of Engineering, University of Cambridge


Abstract


The classical theory of buckling of axially loaded thin cylindrical shells predicts that the buckling stress is directly proportional to the thickness, t, other things being equal. But empirical data show clearly that the buckling stress is actually proportional to t 1.5, other things being equal. As is well known, there is wide scatter in the buckling-stress data, going from one half to twice the mean value. Current theories of shell buckling attribute the scatter and the low buckling stress - in comparison with the classical - to "imperfection-sensitive", non-linear behaviour. But those theories always take the classical analysis of an ideal, perfect shell as their point of reference. My aim in this talk is to explain the observed t 1.5 law, including the scatter, without the need to invoke the classical theory. Experiments on self-weight buckling of open-topped cylindrical shells agree well with the mean experimental data mentioned above; and those results may be associated with a well-defined post-buckling "plateau" in load/deflection space, that is revealed by finite-element studies. This plateau is linked with the appearance of a characteristic "dimple" of a mainly inextensional character in the deformed shell wall. A somewhat similar post-buckling dimple is also found by finite-element studies when a thin cylindrical shell is loaded axially at an edge by a localised force; and it turns out that such a dimple grows under a more-or-less constant force that is proportional to t 2.5, other things being equal. That 2.5-power law can be explained in broad terms by analogy with the inversion of a thin spherical shell by an inward-directed force. The deformation of the shell is generally inextensional except for a narrow "knuckle" or boundary layer in which the combined elastic energy of bending and stretching is proportional to t 2.5, other things being equal. The modes of deformation in the post-buckling dimples of cylindrical shell are likewise practically independent of thickness, except in the highly-deformed boundary-layer regions which separate the inextensionally-distorted portions of the shell. These ideas lead in turn to an explanation of the t 1.5 law for the post-buckling stress of open-topped cylindrical shells loaded by their own weight. The absence of experimental scatter in the self-weight buckling of open-topped cylindrical shells may be attributed to the statical determinacy of the situation, which allows a post-buckling dimple to grow at a well-defined load. Conversely, the large experimental scatter in tests on cylinders with closed ends may be attributed to the lack of statical determinacy there.

Friday, April 5, 1999
209 Akerman Hall
2:30-3:30 p.m.


Refreshments served after the seminar in 227 Akerman Hall.
Disability accomodations provided upon request.
Contact Kristal Belisle, Senior Secretary, 625-8000.