<DOC>
<DOCNO>
730
</DOCNO>
<TITLE>
on the bending of a clamped plate .
</TITLE>
<AUTHOR>
weinstein,a., rock,d.h.
</AUTHOR>
<BIBLIO>
q. app. math. 2, 1944, 262.
</BIBLIO>
<TEXT>
  the present paper contains an application
of a recently developed variational
method to the boundary value problem of the
bending of a clamped plate of arbitrary
shape .  it will be shown that this problem
can be linked to the simpler problem
of the equilibrium of a membrane by a chain
of intermediate problems, which can be
solved explicitly and in finite form in terms
of the membrane problem .  in the intermediate
problems, the deflection converges
uniformly in the domain of the plate
of the clamped plate, and the derivatives
of all orders of the deflection converge
uniformly in every domain completely interior
to the plate .  (in the ritz method, not even
the convergence of the slopes can be
guaranteed .)  the method yields numerical
results for plates of all shapes for which
the membrane problem (which we shall call
the base problem) admits an explicit solution
.  as an example we shall consider a
clamped square plate under a uniform load .
this problem has been the object of
numerous investigations, some of which are
theoretical, while others are purely numerical,
use infinite simple and double series,
and operate with an infinite number of
linear equations and an infinite number of
unknowns .  an inspection of the general
formulae derived in the present paper, formulae
which become simple in numerical
applications, would show how some of the
numerical methods might be rendered
rigorous .  the convergence of higher derivatives
is of great practical interest for
the approximate computation of the stresses .
</TEXT>
</DOC>
