The Interaction between a Uniformly Loaded Circular Plate and an Isotropic Elastic Halfspace: A Variational Approach

ABSTRACT

The axially symmetric flexural interaction of a uniformly loaded circular plate resting in smooth contact with an isotropic elastic halfspace is examined by using an energy method. In this development the deflected shape of the plate is represented in the form of a power series expansion which satisfies the kinematic constraints of the plate deformation. The flexural behavior of the plate is described by the classical Poisson-Kirchhoff thin plate theory. Using the energy formulation, analytical solutions are obtained for the maximum deflection, the relative deflection, and the maximum flexural moment in the circular plate. The results derived from the energy method are compared with equivalent results derived from numerical techniques. The solution based on the energy method yields accurate results for a wide range of relative rigidities of practical interest.