<DOC>
<DOCNO>
734
</DOCNO>
<TITLE>
the bending of uniformly loaded clamped plate in the
form of a circular sector .
</TITLE>
<AUTHOR>
hasse,h.r.
</AUTHOR>
<BIBLIO>
q. j. mech. app. math. 3, 1950, 271.
</BIBLIO>
<TEXT>
  the deflexion of a uniformly loaded
plate in the form of a semicircle clamped
along its boundary is obtained by a
method due to weinstein .  this problem
requires the solution of the biharmonic
equation where z is given,
subject to the conditions that w = 0 and
on the boundary, n being the
direction of the outward normal .  the solution
is expressed in the form
where, writing is found
by solving (in succession) two harmonic
equations of the forms where z may
be zero, and where f and
have to satisfy certain boundary conditions .
the constants are then determined
to satisfy the boundary condition .
  numerical calculations show that five or six
terms of the series give a
good approximation to the accurate value as
judged by the closeness with which
the approximate solution satisfies the boundary
condition .  the procedure
to be adopted in the case of the general
circular sector and for non-uniform
loading is indicated briefly .
  the connexion between the deflexion problem
and that of plane strain in which
the stress function satisfies the equation,
where and have given
values on the boundary, is discussed as a preliminary
to the further consideration
of the latter problem by a method of the same type .
</TEXT>
</DOC>
