Analytical Study of Bending Characteristics of an Elastic Rectangular Plate using Direct Variational Energy Approach with Trigonometric Function

F C Onyeka,B O Mama

doi:10.28991/esj-2021-01320

F C Onyeka, B O Mama

Open Access

https://doi.org/10.28991/esj-2021-01320

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Abstract

In this paper, an analytical three-dimensional (3D) bending characteristic of an isotropic rectangular thick plate with all edges simply supported (SSSS) and carrying uniformly distributed transverse load using the energy technique is presented. The three-dimensional constitutive relations which involves six stress components were used in the established, refined shear deformation theory to obtain a total potential energy functional. This theory obviates application of the shear correction factors for the solution to the problem. The governing equation of a thick plate was obtained by minimizing the total potential energy functional with respect to the out of plane displacement. The deflection functions which are in form of trigonometric were obtained as the solution of the governing equation. These deflection functions which are the product of the coefficient of deflection and shape function of the plate were substituted back into the energy functional, thereafter a realistic formula for calculating the deflection and stresses were obtained through minimizations with respect to the rotations and deflection coefficients. The values of the deflections and stresses obtained herein were tabulated and compared with those of previous 3D plate theory, refined plate theories and, classical plate theory (CPT) accordingly. It was observed that the result obtained herein varied more with those of CPT and RPT by 25.39% and 21.09% for all span-to-thickness ratios respectively. Meanwhile, the recorded percentage differences are as close as 7.17% for all span-to-thickness ratios, when compared with three dimensional plate analysis. This showed that exact 3D plate theory is more reliable than the shear deformation theory which are quite coarse for thick plate analysis. Doi: 10.28991/esj-2021-01320 Full Text: PDF

Highlights

The applications of thick plate in engineering are numerous due to its flexible characteristics such as light weight and economy [1, 2]
The strain energy and external work done on the plate, the total potential energy equation of a thick rectangular plate using energy expression was developed from the 3-D constitutive relations and kinematic deformation
Thereafter, the total potential energy equation was minimized using the function of rotation and deflection to obtain their coefficient and stresses in the plate

Summary

Introduction

The applications of thick plate in engineering are numerous due to its flexible characteristics such as light weight and economy [1, 2]. Classifications of plate can be based on the thickness (t) as; thin and thick plates [3]. The plates are mostly subjected to transverse and uniformly distributed loads acting in the middle plane of the plate. When a plate is subjected to such applied load at the boundary perpendicular to the mid-surface and distributed through the plate’s thickness, the state of loading is called uniformly distributed lateral load [4]. Lateral loading causes a plate to bend or become elastically deformed. The bending and deformation of the plate caused by applying load can lead to failure of structure if not properly managed. To avoid failure of the plate, relatively more accurate and practical studies on bending analysis of plate are required

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