BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//NA-M-87-06
       ENTRY:: January 28, 1996
ORGANIZATION:: Stanford University, Department of Computer Science, Numerical
               Analysis Project
       TITLE:: Numerical assessment of the validity of two-dimensional plate
               models
        TYPE:: Manuscript
      AUTHOR:: Miara, Bernadette
        DATE:: June 1987
       PAGES:: 26
    ABSTRACT:: The objective of this paper is to verify numerically the
               convergence of the solution to the three-dimensional problem
               of a clamped plate towards the solution to the corresponding
               "limit" two-dimensional problem when the thickness of the
               plate goes to zero.

               Standard finite elements discretization of the
               three-dimensional problem fails to show this convergence [M.
               Vidrascu, 1978] as they lead to ill-conditioned linear
               systems when the discretization parameter is of the order of
               the thickness. We will therefore use a spectral approximation
               of the solution of the three-dimensional problem.

               First, we shall review the three-dimensional and
               two-dimensional linear models of a clamped plate and give the
               convergence results obtained by P.-G. Ciarlet and P.
               Destuynder [1979], [1981]. Then we will discuss two kinds of
               spectral approximations: the Galerkin and Tau approximations.
               Finally we give the numerical results obtained by Tau
               approximation.
       NOTES:: [Adminitrivia V1/Prg/19960128]
         END:: STAN//NA-M-87-06