Bending of a Simply Supported Elliptical Plate under the Combined Action of Uniform Lateral Load and In-Plane Force

Abstract

The bending of an elliptical plate undergoing the combined action of uniform lateral load over its entire surface and uniform in-plane force distributed in its middle plane is treated in the present paper. The analysis is based on the small-deflection theory of the plate and performed in the elliptical coordinate system. The general solution, which satisfies perfectly the basic equation of deflection and the boundary condition, is presented in the form of an infinite series of Mathieu functions. In addition, the intensities of bending moments, twisting moment, shearing forces and effective shear force are rigorously formulated in the form of infinite series. A special case of a circular plate under the combined action of uniform lateral load and in-plane force is discussed in detail. Numerical calculation is also performed and the calculated results will be given in tables and figures.