Coupled Integral Equations for Uniformly Loaded Rectangular Plates Resting on Unilateral Supports

Abstract

The present paper deals with the integral equations formulation through the method of finite Hankel integral transform techniques for solving the mixed boundary value problem of unilaterally supported rectangular plates loaded by uniformly distributed load. Due to the absent concentrated corner forces at all plate corners, the occurrence of mixed boundary conditions between a plate and the supports can be reduced from the coupled dual-series equations that resulted in using the Levy’s approach for the plate deflection function to a set of two coupled integral equations of Fredholm-type. The highlight of problem is that the analyticalformulation explicitly considers the nature of the inverse-square-root shear singularities at the ends of unilateral supports in the plate loaded state.