<DOC>
<DOCNO>
1119
</DOCNO>
<TITLE>
plastic stability theory of thin shells .
</TITLE>
<AUTHOR>
gerard,g.
</AUTHOR>
<BIBLIO>
j. ae. scs. 24, 1957.
</BIBLIO>
<TEXT>
  considerable interest is currently centered on the
role of deformation and flow types of plasticity
theories in the solution of stability problems .  for
thin flat plates, deformation theory combined with
classical stability theory appears to yield results which
are in substantially good agreement with test data .
on the other hand, flow or incremental theories appear
to require the introduction of initial imperfections in
order to obtain a satisfactory degree of correlation with
tests .
  thus, in view of the current state of development of
plastic stability theory, it appears fruitful to exploit
the mathematical simplicity inherent in deformation
theory in the investigation of the plastic stability of
thin shells .  although there may be theoretical objections
to deformation theories as a class, test data on
flat plates do suggest the predictive value of the results
obtained from this theory .
  in this paper, a set of equilibrium differential equations
for the plastic buckling of thin shells of constant
unequal radii is derived .  this set of three equations
applies to flat plates, cylinders, and spheres under any
loading system leading to buckling .  for particular
problems such as buckling of cylinders under axial
compression, torsion or lateral pressure, and spheres
under external pressure, the set of equations can be
reduced to a single eighth-order partial differential
equation of the donnell type in terms of the radial displacement
only .  these donnell-type equations are
used to obtain solutions for plastic buckling of spheres
under external pressure and long and moderate length
cylinders under lateral pressure or torsion loads .  the
limiting cases of a simply supported flat plate under
compression or shear, represent the solutions for short
cylinders under lateral pressure or torsion, respectively .
</TEXT>
</DOC>
