Abstract
On the basic of the classical small-deflection theory, the purely analytical solution for the deflection due to the bending of a clamped elliptical plate subjected to the combined action of uniform lateral load distributed over its entire surface and uniform in-plane force distributed in its middle plane is derived in the elliptical cylinder coordinate system. The general solution of the differential equation for the deflection surface is expressed in the form of an infinite series of Mathieu functions and the final solution satisfying the boundary conditions is derived by using the orthogonality of Mathieu functions. In additon, the bending moment distributions are formulated rigorously in the form of infinite series. Special cases of an elliptical plate without the action of in-plane force and a circular plate under the combined action of uniform lateral load and in-plane force are also discussed in detail. It will be shown that the deflection and the bending moments are directly proportional to the uniform lateral load whether or not the in-plane force acts along the periphery. Numerical calculation results will be given in tables and figures.
