Buckling of a Clamped Elliptical Plate on the Elastic Foundation under Uniform Compression.

Abstract

This paper presents the study on the stability of a clamped elliptical plate on the elastic foundation subjected to uniform compression in the middle plane of the plate according to the ordinary thin plate theory. The analysis is rigorously made by the use of Mathieu functions and modified Mathieu functions which are the solutions of the equibrium equation of the buckled plate. The stability condition equations are derived by applying the orthogonality of the Mathieu function. The calculated eigenvalues of buckling are given in tables for various aspect ratios and dimensionless foundation moduli.