### Analytical Solution for the Static Bending Elastic Analysis of Thick Rectangular Plate Structures Using 3-D Plate Theory

#### Abstract

In the current work, an analytical solution for static bending analysis of the thick rectangular plate structure was obtained using three-dimensional plate theory. First, the energy equation was formulated from the static elastic principles and transformed into a compatibility equation through general variation to get the slope and deflection relationship. The solution of the compatibility equation gave rise to the exact polynomial deflection function. In contrast, the coefficient of deflection and shear deformation of the plate was obtained from the governing equation through the direct variation method. These solutions were used to obtain the characteristic expression for analyzing the displacement and stresses of a rectangular plate. This formula was used for the solution of the bending problem of rectangular plate support conditions of two clamped edges, one free edge, and a simply-supported edge (CCFS). The result of the deflection and stresses decreases as the span-thickness ratio increases. More so, the aspect ratio effect of the shear stress of isotropic plates is investigated and discussed after a comparative analysis between the present work and previous studies. The result shows that the present study differs with RPT) of assumed deflection by 2.7%, whereas exact 2-D RPT by 1.9%. This shows the efficacy of the exact 3-D plate theory for rectangular plate analysis under CCFS support and loading condition.

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