Exact solution of bending problem of clamped orthotropic rectangular thin plates

An, Chen; Gu, Jijun; Su, Jian

doi:10.1007/s40430-015-0329-1

Cited by 16 publications

(10 citation statements)

References 22 publications

(29 reference statements)

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“…The numerical results of bending problem of clamped rectangular thin plates presented in [77] are in excellent agreement between the exact numerical-analytical solution obtained by the generalized integral transform technique (GITT) and FEM obtained by the commercial program ABAQUS, but during the analysis, the plates were discretized using sufficiently refined S4R elements − 200 elements in the x direction and 200 × c elements in the y direction. This means that sufficient accuracy was obtained for 40,000 elements, while in the examples presented in this article, the model consists of 512 elements.…”

Section: Rectangular Plate Clamped At the Contoursupporting

confidence: 60%

The New Approach to Analysis of Thin Isotropic Symmetrical Plates

Delyavskyy

Rosiński

2020

Applied Sciences

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A new approach to solve plate constructions using combined analytical and numerical methods has been developed in this paper. It is based on an exact solution of an equilibrium equation. The proposed mathematical model is implemented as a computer program in which known analytical formulae are rewritten as wrapper functions of two arguments. Partial derivatives are calculated using automatic differentiation. A solution of a system of linear equations is substituted to these functions and evaluated using the Einstein summation convention. The calculated results are presented and compared to other analytical and numerical ones. The boundary conditions are satisfied with high accuracy. The effectiveness of the present method is illustrated by examples of rectangular plates. The model can be extended with the ability to solve plates of any shape.

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Section: Rectangular Plate Clamped At the Contoursupporting

confidence: 60%

The New Approach to Analysis of Thin Isotropic Symmetrical Plates

Delyavskyy

Rosiński

2020

Applied Sciences

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“…The boundary conditions at free edges of the rectangular plate were treated exactly by carrying out integral transform of the boundary conditions along the free edge direction. Generalized integral transform technique is a hybrid analytical-numerical method that has been applied successfully in a wide range of flow and heat transfer problems [17][18][19][20], as well as in static and dynamic structural analyses [21][22][23][24][25][26][27][28][29][30][31][32][33][34]. In this work, the free vibration of orthotropic thin rectangular plates with a pair of opposite edges clamped and one or two free edges (CSCF, CCCF, CFCF) is studied analytically by using generalized integral transform technique.…”

Section: Introductionmentioning

confidence: 99%

Generalized integral transform solution for free vibration of orthotropic rectangular plates with free edges

2020

J Braz. Soc. Mech. Sci. Eng.

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Free vibration of orthotropic rectangular thin plates of constant thickness with two opposite edges clamped and one or two edges free is analyzed by generalized integral transform technique. Numerically stable eigenfunctions in exponential function forms of Euler-Bernoulli beams with appropriate boundary conditions are adopted for each direction of the plate. The governing fourth-order partial differential equation for the mode function of free vibration is transformed into a system of linear equations, by integral transform in both directions of the rectangular plate. The boundary conditions at free edges are satisfied exactly by considering the terms generated in the transformed equations by integration by parts, which are absent in the equations by traditional Rayleigh-Ritz method. The natural frequencies of free vibration of orthotropic rectangular thin plates obtained by the proposed integral transform solution are compared with available results in the literature and numerical solutions by finite element analysis, showing excellent agreement and high convergence rate.

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“…used the general integral transform technique (GITT) in the bending analysis of fully clamped orthotropic rectangular plates, by transforming only in one spatial coordinate. 28 GITT is mathematically more general, which has been successfully applied in heat, fluid flow, and structural problems. 28–32 Similar semi-analytical method has bee proposed before by Mukhopadhyay.…”

Section: Introductionmentioning

confidence: 99%

“…28 GITT is mathematically more general, which has been successfully applied in heat, fluid flow, and structural problems. 28–32 Similar semi-analytical method has bee proposed before by Mukhopadhyay. 33…”

Section: Introductionmentioning

confidence: 99%

Bending of orthotropic rectangular thin plates with two opposite edges clamped

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

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This work presents integral transform solutions of the bending problem of orthotropic rectangular thin plates with constant thickness, subject to five sets of boundary conditions: (a) fully clamped; (b) three edges clamped and one edge simply supported; (c) three edges clamped and one edge free; (d) two opposite edges clamped, one edge simply supported, and one edge free; and (e) two opposite edges clamped and two edges free. By adopting eigenfunctions of Euler–Bernoulli beams with corresponding boundary conditions for each direction of the plate, the governing fourth-order partial differential equation is integral transformed into a system of linear algebraic equations. Boundary conditions at the free edges are treated exactly by carrying out integral transform in the boundary formulations, which are incorporated in the transformed governing equations by integration by parts. The numerical difficulties with the high-order beam functions are overcome by using modified exponential forms, thus limiting the eigenfunctions to the range between −2 and 2. Analytical integration forms are used for the integrals of the coefficients of the transformed equations, further avoiding numerical difficulties with large high-order eigenvalues. The accuracy and convergence of the solutions are shown through numerical examples in comparison with available solutions in the literature and with finite element solutions obtained by using Abaqus program.

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Exact solution of bending problem of clamped orthotropic rectangular thin plates

Cited by 16 publications

References 22 publications

The New Approach to Analysis of Thin Isotropic Symmetrical Plates

The New Approach to Analysis of Thin Isotropic Symmetrical Plates

Generalized integral transform solution for free vibration of orthotropic rectangular plates with free edges

Bending of orthotropic rectangular thin plates with two opposite edges clamped

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