Energy-Based Solution for Bending Analysis of Thin Plates on Nonhomogeneous Elastic Foundation

In this paper, the application of Ritz method to the bending of thin plates having mixed boundary conditions and resting on nonhomogeneous foundation with varied subgrade reaction is presented. A typical application of the considered problem is in the analysis and design of foundations resting on a varying soil bed. The proposed model can tackle different kinds of changes in the subgrade reaction including zero subgrade reaction at some locations (cavity zones) as well as rigid zones. The variation of the subgrade reaction modulus is represented by an appropriate mathematical expression that accounts for its possible discontinuous variation. A systematic approach for deriving Ritz trial functions that satisfy the geometric boundary conditions is illustrated for different plate supporting conditions. Three numerical examples are solved to verify the accuracy of the proposed method.