Bending of an Elliptical Plate on Elastic Foundation and under the Combined Action of Lateral Load and In-Plane Force

Abstract

The plane plates resting on elastic foundations are of practical importance in many engineering fields as seen in plate-subgrade structure, floating plate structure, composite material and so on. In some cases, the plates are subjected to large temperature differences from which considerable in-plane forces in the plates result. As structural elements in the wide fields of engineering, various types of elliptical plates may be used in order to avoid the high stress concentration and improve the usability of the instrument and the beauty of the architecture. In recent years, the author has been studied the vibration, buckling and bending problems of elliptical plates subjected to the combined action of lateral load and in-plane force [1]–[5]. In the reference [2] has been discussed also the influence of elastic foundation on the vibration and buckling of a clamped elliptical plate.

From the viewpoint of the usefulness of an elliptical plate as structural element and the importance of the analytical solution in the mathematical theory of elasticity, it is the aim of this report to develop the exact theoretical analysis on the bending of an elliptical plate resting on a Winkler-type elastic foundation and subjected to the combined action of uniform lateral load and in-plane force. Here is considered the case that the plate-edge conditions are clamped and simply supported. Based on the classical small-deflection theory, the theoretical analysis is rigorously made in the elliptical coordinate system and the deflection surface due to bending of the plate is obtained in the form of an infinite Mathieu function series. The influences of elastic foundation and in-plane force on the bending of the elliptical plate are calculated by digital computer, and the new results obtained here will be presented in tables and figures.