Effects of Number of Terms on Solution of Simply Supported Thin Isotropic Rectangular Plate

Abstract

This paper investigates the effects of number of terms of characteristic coordinate polynomial functions in approximating the deformation characteristics- deflections and moments- of a uniformly-loaded thin isotropic rectangular plate with all edges simply supported. Polynomial deflection function series satisfying the prescribed boundary conditions of the plate were developed. First, second, truncated third and third approximations of the polynomial series were used in the Galerkin method to work out maximum deflection and maximum span moment coefficient values for each approximation corresponding to different aspect ratios (p = b/a) ranging from 1.0 to 2.0. The results were compared with the results from previous works in literature and their accuracy and pattern of convergence observed. Inferences were drawn based on the observed response patterns. The results of the short span moment coefficient values for instance, showed average percentage differences of 6.83, 5.04, 25.17 and 279.89 for the first, second, truncated third and third approximations respectively when compared with the results of the classical solution. Hence, it is concluded that beyond the second approximation, the present formulation showed a notable divergence with the results of the classical solution for the mid-span coefficient values.