Bending of an Elliptical Plate by Edge Loading

Publisher Website
Google Scholar
Abstract
A series solution is presented for the problem of the small deflections of a thin elliptical plate with the following boundary conditions: (a) The edge of the plate is supported and is given a small prescribed deflection in a direction perpendicular to the middle plane of the plate. (b) The external load applied to the plate consists of a general distribution of bending moments acting around the edge of the plate. Since the loading consists of moments distributed around the edge of the plate, the general Lagrange differential equation for the middle surface of the plate reduces to the biharmonic equation. Elliptic co-ordinates are used and the problem reduces to finding a solution of the biharmonic equation, in elliptic co-ordinates, which satisfies the boundary conditions. Solutions to this equation are of two types: (a) harmonic functions, and (b) biharmonic functions which are not harmonic. Functions of type (a) are found by the method of separation of variables in Laplace’s equation expressed in elliptic co-ordinates. Functions of type (b) are found by the use of complex variable theory.

This publication has 0 references indexed in Scilit: