scholarly journals Quasi 3-D trigonometric plate theory for bending analysis of EG plates resting on Pasternak foundations

2018 ◽  
Vol 5 (1) ◽  
pp. 146-155
Author(s):  
Ahmed F. Radwan ◽  
Ashraf M. Zenkour
Keyword(s):  
Thick Plate ◽  
Plate Theory ◽  
Equilibrium Equations ◽  
Bending Analysis ◽  
Elastic Foundations ◽  
Good Comparison ◽  
Graded Material ◽  
Inhomogeneity Parameter ◽  
Two Parameter ◽  
Exponentially Graded

AbstractThis paper deals with the bending analysis of exponentially graded material (EGM) plates resting on two-parameter elastic foundations according to a trigonometric shear deformation plate theory (TPT) using Navier’s technique. The normal and shear deformations are both includes. The present TPT does not need a shear correction factors. The material properties of plate like, Lamé’s coefficients convert exponentially in a given constant orientation. The equilibrium equations according to the EG plate resting on Pasternak foundations are presented. Numerical results for the EG thick plate on elastic foundations are presented. A good comparison of results with those being in the literature. The influences played by Winkler and Pasternak parameters, side-to-thickness ratio, inhomogeneity parameter and aspect ratio on the bending responses of EG plates are debated.

Elastic Foundation Analysis of Uniformly Loaded Functionally Graded Viscoelastic Sandwich Plates

2012 ◽  
Vol 28 (3) ◽  
pp. 439-452 ◽  
Author(s):  
A. M. Zenkour ◽  
M. Sobhy
Keyword(s):  
Power Law ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Equilibrium Equations ◽  
Graded Material ◽  
Plate Aspect Ratio ◽  
Type V ◽  
Power Law Index

AbstractThis paper deals with the static response of simply supported functionally graded material (FGM) viscoelastic sandwich plates subjected to transverse uniform loads. The FG sandwich plates are considered to be resting on Pasternak's elastic foundations. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic-viscoelastic FGM layers. Material properties are graded according to a power-law variation from the interfaces to the faces of the plate. The equilibrium equations of the FG sandwich plate are given based on a trigonometric shear deformation plate theory. Using Illyushin's method, the governing equations of the viscoelastic sandwich plate can be solved. Parametric study on the bending analysis of FG sandwich plates is being investigated. These parameters include (i) power-law index, (ii) plate aspect ratio, (iii) side-to-thickness ratio, (iv) loading type, (v) foundation stiffnesses, and (vi) time parameter.

scholarly journals Free Vibration and Static Bending Analysis of Piezoelectric Functionally Graded Material Plates Resting on One Area of Two-Parameter Elastic Foundation

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Hong Nguyen Thi
Keyword(s):  
Free Vibration ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Engineering Practice ◽  
Parameter Study ◽  
Bending Analysis ◽  
Wide Range ◽  
Graded Material ◽  
Two Parameter

Free vibration and static bending analysis of piezoelectric functionally graded material plates resting on one area of the two-parameter elastic foundation is firstly investigated in this paper. The third-order shear deformation theory of Reddy and 8-node plate elements are employed to derive the finite element formulations of the structures; this theory does not need any shear correction factors; however, the mechanical response of the structure is described exactly. Verification problems are performed to evaluate the accuracy of the proposed theory and mathematical model. A wide range of parameter study is investigated to figure out the effect of geometrical, physical, and material properties such as the plate dimension, volume fraction index, piezoelectric effect, elastic foundation coefficients, and the square size of the area of the foundation on the free vibration and static bending of piezoelectric functionally graded material plates. These numerical results of this work aim to contribute to scientific knowledge of these smart structures in engineering practice.

Analysis of Stress Singularities at Bi-Material Corners in Reddy's Theory of Plate Bending

2006 ◽  
Vol 22 (1) ◽  
pp. 67-75 ◽  
Author(s):  
C. S. Huang
Keyword(s):  
Thick Plate ◽  
Isotropic Plate ◽  
Plate Theory ◽  
Stress Singularity ◽  
Numerical Approach ◽  
Sharp Corner ◽  
Equilibrium Equations ◽  
Third Order ◽  
Isotropic Plates ◽  
Expansion Technique

AbstractThe order of stress singularity at a sharp corner of a plate needs to be known before a numerical approach can be taken to determine accurately the stress distribution of a plate with irregular geometry (such as a V-notch) under loading. This work analyzes the order of the stress singularity at a bi-material corner of a thick plate under bending, based on Reddy's third-order shear deformation plate theory. An eigenfunction expansion technique is used to derive the asymptotic displacement field in the vicinity of the sharp corner by solving the equilibrium equations in terms of displacement functions. This paper explicitly shows the first known characteristic equations for determining the order of the stress singularity at the interface corner of a bonded dissimilar isotropic plate. Moreover, the numerical results are given in graphic form for the order of stress singularity at the interface corner in bonded dissimilar isotropic plates and at the vertex of a bi-material wedge with free radial edges. The results presented herein fill some of the gaps in the literature

Non-linear bending of shear deformable laminated plates under lateral pressure and thermal loading and resting on elastic foundations

2000 ◽  
Vol 35 (2) ◽  
pp. 93-103 ◽  
Author(s):  
Hui-Shen Shen
Keyword(s):  
Thermal Loading ◽  
Lateral Pressure ◽  
Plate Theory ◽  
Perturbation Technique ◽  
Laminated Plates ◽  
Graphical Form ◽  
Elastic Foundations ◽  
Non Linear ◽  
Shear Deformable ◽  
Two Parameter

A non-linear bending analysis is presented for a simply supported shear deformable composite laminated plate subjected to a combined uniform lateral pressure and thermal loading and resting on a two-parameter (Pasternak-type) elastic foundation. The formulations are based on Reddy's higher-order shear deformation plate theory, including the plate-foundation interaction and thermal effects. The analysis uses a mixed Galerkin-perturbation technique to determine the load-deflection curves and load-bending moment curves. Numerical examples are presented that relate to the performances of antisymmetric angleply and symmetric cross-ply laminated plates subjected to thermomechanical loading and resting on two-parameter elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The influences due to a number of effects e.g. foundation stiffness, plate aspect ratio, total number of plies, fibre orientation and initial thermal bending stress, are studied. Typical results are presented in a dimensionless graphical form.

Auxetic Plates on Auxetic Foundation

2014 ◽  
Vol 974 ◽  
pp. 398-401 ◽  
Author(s):  
Teik Cheng Lim
Keyword(s):  
Elastic Foundation ◽  
Thick Plate ◽  
Plate Theory ◽  
Materials Selection ◽  
Selection Technique ◽  
Elastic Foundations ◽  
Design Considerations ◽  
Negative Poisson's Ratio ◽  
Plates On Elastic Foundation ◽  
Maximum Stresses

Auxetic solids are materials that exhibit negative Poisson’s ratio. This paper evaluates the maximum stresses in point-loaded (a) auxetic plates on conventional elastic foundation, (b) conventional plates on auxetic elastic foundation, and (c) auxetic plates on auxetic elastic foundation vis-à-vis conventional plates on conventional elastic foundation. Using thick plate theory for infinite plates on elastic foundation, it was found that in most cases the auxetic plates and auxetic foundation play the primary and secondary roles, respectively, in reducing the plate’s maximum stresses. It is herein suggested that, in addition to materials selection technique and other design considerations, the use of auxetic plates and/or auxetic foundation be introduced for reducing stresses in plates on elastic foundations.

Thermo-Mechanical Bending Response of Exponentially Graded Thick Plates Resting on Elastic Foundations

2015 ◽  
Vol 07 (04) ◽  
pp. 1550062 ◽  
Author(s):  
A. M. Zenkour ◽  
M. N. M. Allam ◽  
A. F. Radwan ◽  
H. F. El-Mekawy
Keyword(s):  
Thermal Loading ◽  
Plate Theory ◽  
Rectangular Plates ◽  
Elastic Foundations ◽  
Mechanical Responses ◽  
Mechanical Bending ◽  
Lamé Coefficients ◽  
Bending Response ◽  
Exponentially Graded ◽  
Principle Of Virtual Displacements

The trigonometric shear and normal deformations plate theory is used to study the thermo-mechanical bending analysis of exponentially graded (EG) thick rectangular plates resting on Pasternak elastic foundations. Material properties of the plate are assumed to be graded in the thickness direction according to an exponential law distribution, meaning that Lamé coefficients vary exponentially in a given fixed z-direction. The governing equations are derived from the principle of virtual displacements. The analytical solutions are obtained by using Navier technique and the effects of stiffness of the foundations, thermal loading, and gradient index on thermo-mechanical responses of the plates are discussed. Numerical results for the bending response for EG rectangular plates are investigated and some of them are compared with those available in the literature.

Thick plate bending analysis using a single variable simple plate theory

2021 ◽  
Author(s):  
Rajesh A Shetty ◽  
Deepak S.A. ◽  
Sudheer Kini K ◽  
Dushyanthkumar G.L.
Keyword(s):  
Thick Plate ◽  
Plate Theory ◽  
Plate Bending ◽  
Single Variable ◽  
Bending Analysis
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