Isotropic rectangular clamped and simply supported square plates are analysed using shear deformable plate theory. The equations are discretised using graded finite differences and the procedures for determining the mesh grading are explained. The Dynamic Relaxation (DR) algorithm is used to solve the governing system of plate equations. The algorithm did not give correct solutions at first and the modifications introduced to the out-of-plane equilibrium equation, which led to the resolution of this problem, are explained. Brief details are given of two tests, carried out on square patch loaded steel plates, in order to provide data for checking the DR analysis. A number of theoretical and experimental results comparisons are presented for clamped and simply supported plates subjected to uniform central square and rectangular patch loads. These comparisons confirm that the DR analysis is able to provide good predictions of the elastic small and large deflection response of shear deformable plates subjected to patch pressure loading.

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