Static Bending Solutions for an Isotropic Rectangular Clamped/Simply Supported Plates Using 3-D Plate Theory

A polynomial displacement function was applied with three-dimensional (3-D) elasticity theory to solve the bending problem of isotropic rectangular thick plate that is simply-supported at the first and fourth edges, clamped and free on the second-third edges (SCFS). In the analysis, the model addressed the effect of shear deformation as well as the transverse normal strain-stress, obviating the coefficients of shear correction. The 3-D kinematic and constitutive relations were used to formulate the total potential energy expression, thereafter, the equilibrium equation developed from the energy functional transformation was used to get the relationship for slope and deflection. The solution of the equilibrium equation birthed the exact polynomial deflection function while the coefficient of deflection of the plate was produced from the governing equation using direct variation approach. These solutions were employed to analyze the bending characteristics of the SCFS rectangular plate by establishing the expression for calculating the displacement and stresses of the plate. The outcome of this study certifies that solutions from 3D model is exact and safe compared to refined plate theories applied by previous authors. Compared with the 3-D plate analysis, the percentage differences presented are as close as 2.9% and 3.7% for all span-to-thickness ratios. The comprehensive average percentage variation of the center deflection values obtained by Onyeka et al., (2020) and Gwarah (2019), is 0.39%. This revealed that at the 99.7 % confidence level, the 3-D plate theory is most suitable and reliable for studying the bending characteristics of thick plates.