The Green’s Function Method for the Supported Plate Boundary Value Problem

  • Steven H. Schot

    American University Library, Washington, USA

Abstract

The deflection uu of a thin elastic plate is governed by the biharmonic equation Δ2u=0\Delta^2u = 0, where Δ\Delta is the two-dimensional Laplace operator. The problem of solving this equation in the domain DD occupied by the plate when uu and Δu\Delta u are assigned on the boundary δD\delta D is often called the supported plate boundaly value problem. Strictly speaking this terminology is not correct since Δu\Delta u should be replaced by the more complicated expression for the plate’s moment M(u)M(u) on δD\delta D; however, when δD\delta D consists only of rectilinear segments (or when the Poisson ratio is unity) M(u)M(u) reduces to Δu\Delta u. Here, the supported plate problem is solved by a Green’s function method, closed form solutions are obtained for the disk and the half-plane, and the supported plate Green’s functions for these domains are computed explicitly. As a check, the solutions of these boundary value problems are also derived using a modification of the Goursat-Almansi method.

Cite this article

Steven H. Schot, The Green’s Function Method for the Supported Plate Boundary Value Problem. Z. Anal. Anwend. 11 (1992), no. 3, pp. 359–370

DOI 10.4171/ZAA/601