Integral Equation Method for a Corner Plate

An integral equation method is developed for the analysis of thin elastic plates. The integral equations are based on a Green's formula and are adapted for the solution of the biharmonic problem of plate analysis. By means of this method, a numerical solution is obtained for a simply-supported, uniformly loaded corner plate. Deflections and bending moments along the diagonal and shear forces along the edges are found. Values of these quantities previously calculated by means of a finite difference technique for a right-angled plate are confirmed by this new method and the analysis is extended to corner plates with different angles at the corner. Furthermore, for a right-angled corner plate, detailed contour plots of bending and twisting moments inside the plate are presented. With a digital computer these results are obtained without undue difficulty, and it appears that the integral equation method is well suited to this type of problem.