<DOC>
<DOCNO>
732
</DOCNO>
<TITLE>
on the analogues relating flexure and extension of
flat plates .
</TITLE>
<AUTHOR>
southwell,r.v.
</AUTHOR>
<BIBLIO>
q. j. mech. app. math. 3, 1950, 257.
</BIBLIO>
<TEXT>
  the displacement of a flat plate bent
by transverse loading, and the extensional
or in 'plane stress', are governed by equations
of identical form ,. and the boundary
conditions have identical form when edgedisplacements
are specified in the flexural,
edge-tractions in the extensional problem,
so mathematically, in these circumstances,
only a single problem is presented .  this,
the 'first analogue' relating flexure and
extension, is well known .
  a 'second analogue', relating the flexural
problem when edge-tractions with the
extensional problem when edge-displacements
are specified, is believed to have been
first propounded in 1941 .  by introducing
two quantities u and v, analogous with
the components u and v of extensional
displacement, it permits a treatment of the
flexural problem by any method--e.g.
which yields extensional solutions of this
second type .
  in this paper both analogues are combined
in an inclusive statement covering the
perforated (multiply connected) plates which
were discussed in 1948 .  reasons are
stated for believing that 'two-diagram technique'
is preferable in problems governed
by 'mixed' boundary conditions .
</TEXT>
</DOC>
