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SUMMARY:Understanding The Buckling of Cylindrical Shells - Emeritus Prof C
 hris Calladine (CUED)
DTSTART:20070119T150000Z
DTEND:20070119T160000Z
UID:TALK6391@talks.cam.ac.uk
CONTACT:Nami Norman
DESCRIPTION:The classical theory of buckling of axially-loaded thin cylind
 rical shells predicts that the buckling stress is directly proportional to
  the thickness t\, other things being equal.  But empirical data show clea
 rly that the buckling stress is actually proportional to t1.5\, other thin
 gs 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 th
 eories of shell buckling attribute both the scatter and the low buckling s
 tress – in comparison with the classical – to "imperfection-sensitive"
 \, non-linear structural behaviour.  But those theories always take the cl
 assical analysis of an ideal\, perfect shell as their point of reference.\
 n\nMy aim in this talk is to explain directly the observed t1.5 law\, incl
 uding the scatter\, without the need to invoke the misleading classical th
 eory.\n\nExperiments on self-weight buckling of open-topped cylindrical sh
 ells agree well with the mean experimental data mentioned above\; and thos
 e 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 m
 ainly inextensional character in the deformed shell-wall.\n               
                                                                           
                                                A somewhat similar post-buc
 kling dimple is also found by finite-element studies when a thin cylindric
 al 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 b
 e explained in broad terms by analogy with the inversion of a thin spheric
 al shell by an inward-directed force.  The deformation of the shell is gen
 erally inextensional except for a narrow boundary-layer\, in which the com
 bined elastic energy of bending and stretching is proportional to t2.5\, o
 ther things being equal.  The modes of deformation in the post-buckling di
 mples of a cylindrical shell are likewise practically independent of thick
 ness\, 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 op
 en-topped cylindrical shells loaded by their own weight.\n\nThe absence of
  experimental scatter in the self-weight buckling of open-topped cylindric
 al shells may be attributed to the static determinacy of the situation\, w
 hich allows a post-buckling dimple to grow at a well-defined load.  Conver
 sely\, the large experimental scatter in tests on cylinders with closed en
 ds may be attributed to the lack of static determinacy there.\n
LOCATION:Engineering Department - LR6
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