Analytical solutions of heterogeneous rectangular plates with transverse small periodicity

2012 ◽  
Vol 43 (3) ◽  
pp. 1056-1062 ◽  
Author(s):  
Wen-ming He ◽  
Hua Qiao ◽  
Wei-qiu Chen
Keyword(s):  
Analytical Solutions ◽  
Rectangular Plates

On the buckling of advanced composite sandwich rectangular plates

2020 ◽  
pp. 109963622092508 ◽  
Author(s):  
Atteshamuddin S Sayyad ◽  
Yuwaraj M Ghugal
Keyword(s):  
Shear Deformation ◽  
Power Law ◽  
Analytical Solutions ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Skin Thickness ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Aspect Ratios

In this paper, higher order closed-formed analytical solutions for the buckling analysis of functionally graded sandwich rectangular plates are obtained using a unified shear deformation theory. Three-layered sandwich plates with functionally graded skins on top and bottom; and isotropic core in the middle are considered for the study. The material properties of skins are varied through the thickness according to the power-law distribution. Two types of sandwich plates (hardcore and softcore) are considered for the detail numerical study. A unified shear deformation theory developed in the present study uses polynomial and non-polynomial-type shape functions in terms of thickness coordinate to account for the effect of shear deformation. In the present theory, the in-plane displacements consider the combined effect of bending rotation and shear rotation. The parabolic shear deformation theory of Reddy and the first-order shear deformation theory of Mindlin are the particular cases of the present unified formulation. The governing differential equations are evaluated from the principle of virtual work. Closed-formed analytical solutions are obtained by using the Navier’s technique. The non-dimensional critical buckling load factors are obtained for various power-law coefficients, aspect ratios and skin-core-skin thickness ratios.

Analytical Solutions of Loaded Multifunctional Multilayered Plates

2013 ◽  
Vol 682 ◽  
pp. 127-134 ◽  
Author(s):  
M. Ajdour ◽  
L. Azrar
Keyword(s):  
Mechanical Loading ◽  
Analytical Solutions ◽  
Electric Potential ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Multilayered Plate ◽  
Linear Elastic ◽  
Propagator Matrix ◽  
Arbitrary Thickness ◽  
Multilayered Plates

Analytical solutions are derived for multifunctional N-layered rectangular plates. The multilayered plate may consist of linear elastic or piezoelectric laminates of arbitrary thickness. The related equations and formulae are developed based on the Stroh like formalism. Solutions for multilayered plates are expressed in terms of the propagator matrix and satisfy the continuity conditions of material layers. Various types of electrical and mechanical loading may be considered. Numerical results of stresses, electric potential and displacement for some multifunctional multilayered plates are analyzed

Bending of Thick Rectangular Plates with Different Boundaries under Concentrated Load

2010 ◽  
Vol 163-167 ◽  
pp. 1440-1444
Author(s):  
Ying Jie Chen ◽  
Gang Li ◽  
Zhen Xian Zhang ◽  
Bao Lian Fu
Keyword(s):  
Analytical Solutions ◽  
Thick Plate ◽  
Engineering Application ◽  
Reciprocal Theorem ◽  
Rectangular Plates ◽  
Concentrated Load ◽  
Simply Supported ◽  
The Third ◽  
Thick Rectangular Plate ◽  
Reissner’S Theory

Reciprocal theorem method (RTM) is generalized to solve the problem of bending of thick rectangular plate under concentrated load with four edges fixed and with two opposite edges fixed, the third edge simply supported, and the fourth edge free based on Reissner’s theory. The analytical solutions of the thick plate are given, and the relevant date and diagram are given to guidance engineering application.

Squeeze Films between Two Rough Rectangular Plates

1978 ◽  
Vol 20 (4) ◽  
pp. 183-188 ◽  
Author(s):  
J. Prakash ◽  
H. Christensen
Keyword(s):  
Surface Roughness ◽  
Theoretical Analysis ◽  
Analytical Solutions ◽  
Squeeze Film ◽  
Parameter Study ◽  
Rectangular Plates

The paper describes a theoretical analysis of the effects of various types of surface roughness on the response of a squeeze film between two rectangular plates of finite dimensions. Unlike other finite bearing geometries, it is possible to obtain analytical solutions for various bearing characteristics, thus facilitating a more comprehensive parameter study than has hitherto been feasible. It is shown that the nominal geometry has a profound effect on the system.

Effect of Shear Deformation on Free Flexural Vibration of Clamped Rectangular Plates

1991 ◽  
Author(s):  
W. L. Cleghorn ◽  
S. D. Yu
Keyword(s):  
Shear Deformation ◽  
Analytical Solutions ◽  
Flexural Vibration ◽  
Rectangular Plates ◽  
Aspect Ratios ◽  
Reissner’S Theory ◽  
Shear Deformable ◽  
Shear Deformable Plates

Abstract Reissner’s theory on shear-deformable plates is applied to analyze free flexural vibration of clamped rectangular plates. Accurate analytical solutions are obtained using the method of supeiposition. The first six eigenvalues with four digits of accuracy are presented for plates with three thickness ratios and six plate aspect ratios.

On wave propagation and free vibration of piezoelectric sandwich plates with perfect and porous functionally graded substrates

2022 ◽  
pp. 1045389X2110721
Author(s):  
Mahmoud Askari ◽  
Eugenio Brusa ◽  
Cristiana Delprete
Keyword(s):  
Wave Propagation ◽  
Free Vibration ◽  
Analytical Solutions ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Numerical Results ◽  
Rectangular Plates ◽  
Fg Plates ◽  
Higher Order Theory

This paper aims to develop analytical solutions for wave propagation and free vibration of perfect and porous functionally graded (FG) plate structures integrated with piezoelectric layers. The effect of porosities, which occur in FG materials, is rarely reported in the literature of smart FG plates but included in the present modeling. The modified rule of mixture is therefore considered for variation of effective material properties within the FG substrate. Based on a four-variable higher-order theory, the electromechanical model of the system is established through the use of Hamilton’s principle, and Maxwell’s equation. This theory drops the need of any shear correction factor, and results in less governing equations compared to the conventional higher-order theories. Analytical solutions are applied to the obtained equations to extract the results for two investigations: (I) the plane wave propagation of infinite smart plates and (II) the free vibration of smart rectangular plates with different boundary conditions. After verifying the model, extensive numerical results are presented. Numerical results demonstrate that the wave characteristics of the system, including wave frequency and phase velocity along with the natural frequencies of its bounded counterpart, are highly influenced by the plate parameters such as power-law index, porosity, and piezoelectric characteristics.

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