Stresses in Circular Plates on Elastic Foundations

The von Karmen equations with the Winkler foundation terms added are solved for a uniform load by assuming an infinite series expansion for the plate deflections. The spatial functions chosen include both regular and modified Bessel functions and are chosen to be the eigenfunctions for the linear biharmonic operator. A coupled set of nonlinear algebraic equations governing the plate deflections are derived using the Galerkin averageing techniques. Dimensionless plots of plate deflections and stresses are shown for both fixed and simply supported plates with both radially movable and immovable edges for various values of the dimensionless stiffness. The limitations of the approximate stress equations commonly used for large amplitude plate deflections are presented.