<DOC>
<DOCNO>
830
</DOCNO>
<TITLE>
nonlinear deflections of shallow spherical shells .
</TITLE>
<AUTHOR>
reiss,e.l., greenberg,h.j. and keller,h.b.
</AUTHOR>
<BIBLIO>
j. ae. scs. 24, 1957, 533.
</BIBLIO>
<TEXT>
  the equations obtained by chien for the nonlinear deflection
of shallow spherical shells under uniform external pressure are
solved by means of power series expansions, following procedures
introduced by friedrichs and stoker in their treatment of buckling
of circular plates .  these equations depend upon two parameters
.  one of these parameters is related to the external pressure,
while the other depends upon the dimensions of the shell .
the equations are solved for several ranges of the parameters
under boundary conditions corresponding to a fixed edge .
  the solution, carried out numerically on the aec univac
at new york university, yields a complete description of the
stresses and deflections as functions of the polar angle over a
wide range of values of the loading parameter and the dimensional
parameter .  prediction of the upper buckling load is then
made by means of a numerical criterion based on the load vs.
deflection curve .  for some cases, the postbuckling behavior
is investigated .  the results agree well with existing experimental
and theoretical studies and cover a wide range of cases
not previously treated .
</TEXT>
</DOC>
