Deflection of an Isotropic All-Round Simply Supported Rectangular Plates Incorporating Shear Effect Using Characteristic Orthogonal Polynomial Function

Abstract

The breadth and dexterity with which plates are used in the vast majority of engineering structures necessitates an ever-increasing and deeper study focus on plate strength and stiffness at the ultimate and serviceability limit states of response. From Kirchhoff’s hypothesis, thin plates when subjected to transverse loading, bend and experience transverse deflections that are typically minor in comparison to the plate thickness. However, for thicker plates there is an observed limitation in the application of Kirchhoff’s hypothesis, as this theory ignore the effect of transverse shear on the deformation of plates. This study therefore analytically examines the effect of induced shear on the deflection indices of plates with varying aspect ratios, using the characteristic orthogonal polynomial function. Result obtained shows a close agreement between present study and Kirchhoff’s hypothesis for membrane and thin plates. However, a significant difference was observed for moderately thick plates and thick plates, which clearly shows the effect of transverse shear as the plate thickness increases, which further validates the limitations of Kirchhoff’s hypothesis for moderately thick as well as thick plates. For an aspect ratio of 1.0 – 2.0 at 0.1 interval, results obtained indicated a percentage difference in deflection between the Present study and Kirchhoff’s hypothesis to range between -0.040 – 3.508%, 0.527 – 3.552%, 4.266 – 5.858%, and 13.980 – 17.011% for membrane, stiffened, moderately thick, and thick plates respectively. The validation of the Kirchhoff’s hypothesis for membrane as well as stiffened plates by the present study, indicates the suitability of the application of the characteristic orthogonal polynomial function in the evaluation of the deflection of plates regardless of thickness.