Bending Analysis of Thin Plates with Variable Thickness Resting on Elastic Foundation by Element Free Galerkin Method

Abstract

Element Free Galerkin method was used to analyze bending of thin plates with variable thickness resting on one parameter elastic foundation. Thickness of plate is considered as linearly varying in one direction. Formulation could be applied to plates of any shape with general boundary conditions and loadings. Convergence of solution was examined for different number of nodes, thickness variation and foundation parameters. It was found that for deflection good results were achieved even with small number of nodes regardless of boundary condition, thickness variation and foundation parameters. Accuracy of method is checked against available results and good agreements were found. Applicability of method is demonstrated by solving numerical examples with different boundary conditions, thickness and foundation parameters, and loadings.

Bending of variable thickness rectangular thin plates resting on a double-parameter foundation: integral transform solution

“…As no previous study on bending of rectangular thin plates with linearly varying thicknesses resting on a two-parameter foundation was encountered in the literature, we verify our hybrid analytical-numerical solution by comparing separately with available solutions for uniform and linearly varying thickness plates without foundation (Zenkour, 2003), uniform plate resting on a two-parameter foundation (Chen and Cheng, 2018) and linearly varying thickness plates resting on a Winkler foundation (Rahbar-Ranji and Bahmyari, 2012).…”

“…Table 4 shows the comparisons of square isotropic thin plates with linearly variable thickness under uniformly distributed load and resting on Winkler foundation, w ( a /2, b /2) D 0 /(0.01 a 4 q 0 ), between the present hybrid solution by GITT, the reference finite difference solution, and results by Rahbar-Ranji and Bahmyari (2012) for boundary conditions of fully clamped edges (CCCC), opposite edges clamped and two simply supported edges (CSCS), all-edges simply supported edges (SSSS), two opposite edges clamped and the other two edges free (CFCF) and two opposite edges simply-supported and the other two edges free (SFSF). The varying thickness coefficient λ is taken as 0.05, with K 2 = 0.…”

“…The governing equation is integral transformed along the uniformthickness direction of the plate, resulting in a linear system of ordinary differential equations along the variable-thickness direction, which is solved by using a fourth-order finite difference method. The integral transform solution is validated against a reference fourth-order finite difference solution of the original partial differential equation, and available results from the literature (Zenkour, 2003;Rahbar-Ranji and Bahmyari, 2012;Chen and Cheng, 2018), showing excellent agreement. Parametric studies are carried out to investigate the effects of the coefficients of the double-parameter foundation, the variablethickness coefficients and the aspect ratio of the rectangular plate for six combinations of clamped, simply-supported and free boundary conditions, and uniform and linearly varying loads.…”

“…Katsikadelis and Yiotis (2003) discussed the problem of plates on nonlinear biparametric elastic foundation using a BEM-based meshless method. Rahbar-Ranji and Bahmyari (2012) applied the element-free Galerkin method to study the bending of rectangular plates with linearly varying thickness on a Winkler foundation and carried out parametric analysis to investigate the effect of different node numbers, thickness changes and foundation parameters on the bending of the plate. Ghomshei (2020) proposed a numerical study to investigate the thermal buckling of variable thickness Mindlin circular FGM plate on a two-parameter foundation based on differential quadrature method.…”

Pure Bending Analysis of Isotropic Thin Rectangular Plates Using Third-Order Energy Functional

“…Similarly, solving out equation (9) gave: v = −z ∂w ∂y (11) Substituting equations (10) and (11) into equations (4) and (5) respectively gave:…”