Integral transform solutions to the bending problems of moderately thick rectangular plates with all edges free resting on elastic foundations

Double finite integral transform method is proposed in this paper to obtain the analytical bending solutions of moderately thick rectangular plates with all edges free resting on elastic foundations, which was difficult to be acquired due to the complexity of the mathematical model. The accuracy of the method is validated by the literature as well as the finite element method (FEM). The solution approach presented here can be used to solve the problems of plates with different boundary conditions in an elegant, step-by-step way without predetermining any trial solutions. The results obtained in this paper can serve as benchmarks for future reference.