The Green’s Function Method for the Supported Plate Boundary Value Problem
Steven H. Schot
American University Library, Washington, USA
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Abstract
The deflection of a thin elastic plate is governed by the biharmonic equation , where is the two-dimensional Laplace operator. The problem of solving this equation in the domain occupied by the plate when and are assigned on the boundary is often called the supported plate boundaly value problem. Strictly speaking this terminology is not correct since should be replaced by the more complicated expression for the plate’s moment on ; however, when consists only of rectilinear segments (or when the Poisson ratio is unity) reduces to . 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