فهرست مطالب festus onyeka

The bending attributes of a uniformly-loaded thick plate was modelled with three-dimensional (3-D) elasticity plate theory using exact polynomial displacement function. Plates with free support at its third edge and simply supported at other edges (SSFS), were covered in this study. The effect of shear deformation along with the transverse normal strain stress was considered in this model obviating the coefficients of shear correction. The total potential energy expression was formulated from 3-D kinematic and constitutive relations. The slope and deflection relationship was obtained from the equilibrium equation developed from the energy functional transformation. The solution of the equilibrium equation produced an exact polynomial deflection function while the coefficient of deflection of the plate was formed from the governing equation employing a direct variation approach. The formular for computing the displacement-stress components of the plate was established from these solutions in order to evaluate the bending properties of the plate. The solutions realized herein certifies that the 3D model is exact and consistent compared to refined plate theories applied by previous authors in the available literature. The total average percentage variation of the center deflection values obtained by Onyeka and Okeke, (2020) and Gwarah (2019), is 3.28%. This showed that at 97% confidence level, 3D model is most suitable and safe for analyzing the bending characteristics of thick plates unlike the 2-D RPTs.

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.

In this study, an exact solution for the bending analysis of a three-dimensional (3-D) rectangular plate under transverse loading is presented using fundamentals of elasticity theory. The theoretical model whose formulation is based on static elastic principle considered transverse shear deformation and still obviate the need for shear correction factor effect which is associated to refined plate theory (RPT). As an improvement to RPT, the equations of equilibrium are obtained from elastic principle using 3-D kinematic and constitutive relations which is later converted to energy equation using general variation to get the deflection and rotation relationship. The solution of the equilibrium equation produced an exact trigonometric displacement function which is a product of the coefficient of deflection and shape function of the plate. By minimizing the general energy equation with respect to the coefficients of deflection and shear deformation rotation, a theoretical model for calculating the deflection, moment and stresses of thick rectangular plate are obtained. The comparative analysis between the present results and other theories shows that this 3-D predicts the vertical displacement, moments and the stresses more accurately than previous studies considered in this paper. It was observed that the present theory varied more with those of those of 2-D numeric analysis and 2-D HSDT with about 7.83% and 6.01%. Meanwhile, the recorded percentage differences showed that a derived 2-D HSDT predicted accurately the bending characteristics of the plate with 2.55%, proving that assumed deflection is coarser for the thick plate analysis. It is concluded that unlike an assumed function, a derived 2-D theory can give a close form solution, but a typical 3-D theory of elasticity is required for an exact solution of rectangular plate and can be recommended for the analysis of any type of rectangular plate with such loading and boundary condition.