University of Cambridge > > Engineering Department Structures Research Seminars > Understanding The Buckling of Cylindrical Shells

Understanding The Buckling of Cylindrical Shells

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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 t1.5, other things being equal. As is well known, there is wide scatter in the buckling-stress data, ranging from one half to twice the mean value. Current theories of shell buckling attribute both the scatter and the low buckling stress – in comparison with the classical – to “imperfection-sensitive”, non-linear structural 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 directly the observed t1.5 law, including the scatter, without the need to invoke the misleading 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 t2.5, 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 boundary-layer, in which the combined elastic energy of bending and stretching is proportional to t2.5, other things being equal. The modes of deformation in the post-buckling dimples of a 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 t1.5 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 static 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 static determinacy there.

This talk is part of the Engineering Department Structures Research Seminars series.

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