<DOC>
<DOCNO>
1053
</DOCNO>
<TITLE>
spherical cap snapping .
</TITLE>
<AUTHOR>
keller,h.b. and reiss,e.l.
</AUTHOR>
<BIBLIO>
j. ae. scs. 26, 1959, 643.
</BIBLIO>
<TEXT>
  a nonlinear boundary value problem for the determination of
the rotationally symmetric deformations of a clamped spherical
cap under external pressure is solved by finite differences .  the
numerical solutions are obtained by employing a previously developed
iteration procedure .  a special case of the difference
equations is solved explicitly and yields a justification of the
iteration method as well as insight into the properties of the more
accurate numerical solutions .
  buckled and unbuckled equilibrium states are obtained and
the shape of the pressure-deflection curve which is usually assumed
for these states is verified for a large class of caps .  close estimates
are given for the upper and lower buckling loads and an
intermediate buckling load--i.e., the /dead-weight/ load .  the
stresses and deflections in the buckled and unbuckled states are
examined and compared with an asymptotic solution valid in the
interior of very thin shells .  boundary layers are found to develop
in the buckled states both as the loading increases and as
the thickness of the shell decreases .
</TEXT>
</DOC>
