<DOC>
<DOCNO>
828
</DOCNO>
<TITLE>
stresses and small displacements of shallow spherical
shells .
</TITLE>
<AUTHOR>
reissner,e.
</AUTHOR>
<BIBLIO>
j. math. phys. 25, 1946, 80.
</BIBLIO>
<TEXT>
  the purpose of the present paper is to derive a system of
equations which can be used for the analysis of shallow segments of
thin, elastic, spherical shells .  a segment will be called shallow if
the ratio of its height to base diameter is less than, say .  the
results obtained on the basis of this assumption will often also be
applicable to shells which are not shallow, namely then, when the loads
are such that the stresses are effectively restricted to shallow zones .
  the problem of the spherical elastic shell has been the subject of
numerous researches .  for the rotationally symmetric case the
fundamental results were obtained in 1912 (1) and have been the starting
point of many applications .  while it is possible to deduce from these
results approximate equations equivalent to part of what follows, it is
believed that the present approach to the problem of the shallow shell
may be of some interest even for rotationally symmetric cases .
  a number of investigations have been concerned with the shell loaded
in a non-rotationally symmetric manner (2,3,4) .  in its general form
this problem is quite difficult and the results so far obtained are not
easy to apply .  restricting attention to the shallow shell in the
manner of the present paper brings with it a very considerable
simplification of the analysis .
</TEXT>
</DOC>
