Strain–Displacement Expressions and their Effect on the Deflection and Strength of Plate

Abstract

This paper studied the bending analysis of an isotropic rectangular plate for the effects of aspect ratio, shear and deflection on the critical lateral load of the plates using the polynomial shear deformation theory (PSDT). One of the plate is clamped at opposite edge clamped and the other opposite edge simply supported (CSCS). The other of the plate is simply supported at the first and fourth edge, clamped at second edge and free of support at the third edge (SCFS). Direct variational method of analysis was adopted using straindisplacement expressions to obtain the direct governing equations for the determination of the coefficient of deflection and shear deformation along the direction of x and y coordinate. From the established equation, a new model for determination of the critical lateral imposed load of the plate is developed. The study revealed that: (i) as the specified thickness of the plate increases, the value of critical lateral imposed load increase (ii) the critical lateral imposed load decrease as the plates span increases. Numerical comparison was conducted to verify and demonstrate the efficiency of the present theory. The result obtained are in good agreement with those in the literature.

Analytical Solution of Thick Rectangular Plate with Clamped and Free Support Boundary Condition using Polynomial Shear Deformation Theory

“…Thus, the in-plane displacements, u and v, are differentiable in x, y, and z coordinates, while the deflection, w, is only differentiable in x and y coordinates. Figure 1 shown the two in-plane displacements: in-plane displacement in the direction of x coordinates (u) and in-plane displacement in the direction of y coordinates (v) are represented in Equations (1) and (2) (see the author in [1]): The shear deformation profile of plate section S( ) is given (see the author in [5]) as:…”

“…Plates have been classified based on thickness as: thick, moderately thick, and thin plates [4], based on material composition as: isotropic and anisotropic plates, based on shape as: circular, rectangular, triangular, elliptical, and skew plates, [5]. The edges of plates can be of different kinds of supports such as: simply supported support, point and fixed supports, etc.…”

Static Elastic Bending Analysis of a Three-Dimensional Clamped Thick Rectangular Plate using Energy Method

“…Also, their analysis did not cover for thick plates with all-round clamped boundary conditions. Onyeka et al (2020) [30] analyzed the bending behavior of rectangular thick CSCS and SCFS plates based on fourth-order polynomial shear deformation function. The authors developed a new approach to achieve the critical load of the plate from the established equation.…”

“…It can be deduced that, the difference with past works in consideration percentagewise at a/t of 10 and 20 gives a constant value of 0.15% and 0.13% respectively, a value which could be the same difference when compared with the value of the CPT. From Table 3, it is found that the average the difference with 3-D elasticity trigonometric theory percentagewise and those of the 2-D HSDT with assumed polynomial shape function [30] and 2-HSDT with exact shape function [34] is 0.36% and 0.29% respectively. The average the difference percentagewise with 2-D Mindlin FSDT [37,39] is about 2.41% and 3.62%, while the average difference percentagewise with the 2-D thick plate numeric analysis [35] and moderately thick [38] is 53% and 61% respectively.…”

Exact Three-Dimensional Stability Analysis of Plate Using an Direct Variational Energy Method

“…Plate structures are used in structural engineering, mechanical engineering, and aerospace engineering etc., in making retaining walls, floor slabs, bridges, railways, ships etc. [2,3]. The plates are usually under the action of axially compressive or tensile loads acting in the mid-plane of the plate.…”