<DOC>
<DOCNO>
825
</DOCNO>
<TITLE>
inelastic instability and incremental theories of plasticity .
</TITLE>
<AUTHOR>
onat,e.t. and drucker,d.c.
</AUTHOR>
<BIBLIO>
j. ae. scs. 20, 1953, 181.
</BIBLIO>
<TEXT>
  a most troublesome paradox has existed for a number of years
with respect to buckling in the plastic range .  theoretical considerations
and all direct experimental evidence show conclusively
that an incremental or flow type of mathematical theory
of plasticity is valid .  however, the results of plastic buckling
tests are well correlated by a simple total or deformation theory
and bear no resemblance to published predictions of incremental
theory .
  the suggestion was made that initial imperfections of shape
or loading might well explain this most peculiar result .  however,
subsequent investigations by several authors seem to have
given the impression that excessively large imperfections would
be needed and that the answer would be overly sensitive to the
magnitude of such imperfections .
  it is the purpose of this paper to demonstrate that extremely
small, and therefore unavoidable, imperfections of shape do account
for the paradox in a simple manner .  the buckling load is
shown to be extremely insensitive to the amount of imperfection .
the example chosen is a simplified version of the long rectangular
plate hinged along one edge and free on the other under uniform
compressive stress at the ends .  this is the equivalent of
the case of the cruciform column, which has been so disturbing
in the past because incremental theory applied to a perfect cruciform
column did lead to an entirely incorrect result .
</TEXT>
</DOC>
