Bending of an Elastically Restrained Elliptical Plate under the Combined Action of Lateral Load and In-Plane Force

The study on the bending of an elliptical plate clamped rigidly against deflection and restrained elastically against rotation along its periphery, subjected to the uniform lateral load and in-plane force simultaneously, is performed by introducing the elliptical coordinates. The analytical solution satisfying perfectly the differential equation of deflection and the boundary conditions is exactly derived in the form of Mathieu function series. The expressions for the bending moments are also derived rigorously. The deflection and bending moments obtained here coincide with those for a simply supported elliptical plate and the perfectly clamped elliptical plate when the rotational spring stiffness is zero and infinity, respectively. A limiting case of a circular plate is discussed in detail. The effects of the in-plane force and the rotational spring stiffness on the deflection and the bending moments are calculated numerically and are presented in tables and figures.