# Non-linear bending and stress analysis of a transversely loaded isotropic plates material using 3-D plate theory

### Abstract

This paper presents the bending stress analysis of anisotropic plate material under transverse loading using a three-dimensional (3-D) plate theory. The static elastic theory was used to formulate the total energy expression of the plate thereafter, transformed into a compatibility equation through general variation to get the slope and deflection relationship. The solution of equations of the equilibrium gave rise to the exact polynomial deflection function while the coefficient of deflection and shear deformation of the plate was gotten 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 the rectangular plate. This formula was used for the solution of the bending problem of the rectangular plate that is clamped at the first-two edge and the other edges simply supported (CCSS). The result of the deflection and stresses decrease 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 from that refined plate theory (RPT) of assumed deflection by 5.5% whereas exact 2-D RPT by 5.3%. This shows the efficacy of the exact 3-D plate theory for flexural characteristics of CCSS isotropic rectangular thick plate.

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*Journal of Advances in Science and Engineering*,

*7*(1), 1-8. https://doi.org/10.37121/jase.v7i1.190

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