scholarly journals Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported

2012 ◽  
Vol 36 (1) ◽  
pp. 488-503 ◽  
Author(s):  
B. Yang ◽  
H.J. Ding ◽  
W.Q. Chen
Keyword(s):  
Functionally Graded ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Elasticity Solutions

scholarly journals An Elasticity Solution for Vibration Analysis of Laminated Plates with Functionally Graded Core Reinforced by Multi-walled Carbon Nanotubes

2017 ◽  
Vol 61 (4) ◽  
pp. 309 ◽  
Author(s):  
Vahid Tahouneh
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Mass Density ◽  
Functionally Graded ◽  
Laminated Plates ◽  
Rectangular Plates ◽  
Multiwalled Carbon ◽  
Simply Supported ◽  
Pasternak Model ◽  
Multi Walled Carbon Nanotubes

In the present work, vibration characteristics of functionally graded (FG) sandwich rectangular plates reinforced by multiwalled carbon nanotubes (MWCNTs) resting on Pasternak foundation are presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. Modified Halpin-Tsai equation is used to evaluate the Young’s modulus of the MWCNT/epoxy composite samples by the incorporation of an orientation as well as an exponential shape factor in the equation. The mass density and Poisson’s ratio of the MWCNT/phenolic composite are considered based on the rule of mixtures. The proposed sandwich rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the sandwich plates are investigated.

Three-dimensional elasticity solution of simply supported functionally graded rectangular plates with internal elastic line supports

2009 ◽  
Vol 44 (4) ◽  
pp. 249-261 ◽  
Author(s):  
Y P Xu ◽  
D Zhou
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Lower Surface ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Elastic Line ◽  
Simply Supported ◽  
Three Dimensional Elasticity

This paper studies the stress and displacement distributions of simply supported functionally graded rectangular plates with internal elastic line supports. The Young's modulus is graded through the thickness following the exponential law and the Poisson's ratio is kept constant. On the basis of three-dimensional elasticity theory, the solutions of displacements and stresses of the plate under static loads, which exactly satisfy the governing differential equations and the simply supported boundary conditions at four edges of the plate, are analytically derived. The reaction forces of the internal elastic line supports are regarded as the unknown external forces acting on the lower surface of the plate. The unknown coefficients in the solutions are then determined by the boundary conditions on the upper and lower surfaces of the plate. Convergence and comparison studies demonstrate the correctness and effectiveness of the proposed method. The effect of variations in Young's modulus on the displacements and stresses of rectangular plates and the effect of internal elastic line supports on the mechanical properties of plates are investigated.

On the thermal buckling of simply supported rectangular plates made of a sigmoid functionally graded Al/Al2O3 based material

2016 ◽  
Vol 51 (2) ◽  
pp. 177-187 ◽  
Author(s):  
H. A. Atmane ◽  
E. A. A. Bedia ◽  
M. Bouazza ◽  
A. Tounsi ◽  
A. Fekrar
Keyword(s):  
Thermal Buckling ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Simply Supported

scholarly journals On the Development of Refined Plate Theory for Static Bending Behavior of Functionally Graded Plates

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Van Thom Do ◽  
Van Vinh Pham ◽  
Hoang Nam Nguyen
Keyword(s):  
Plate Theory ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Rectangular Plates ◽  
Refined Plate Theory ◽  
Bending Performance ◽  
Unknown Variable ◽  
Simply Supported ◽  
Plane Normal ◽  
Bending Behavior

This work gives information about the development of refined plate theory to study the static bending behavior of functionally graded material (FGM) plates. The significant advantage of our proposed theory is that only one unknown variable exists in its displacement formula and governing equation. To illustrate the accuracy and effectiveness of this theory, an analytical approach based on the Navier solution is employed to obtain the solution for static bending of simply supported FGM plates. A good agreement for static bending of FGM plates with other literature results has been instituted. This work also investigates the deflection, in-plane normal, and shear stresses of sinusoidally loaded FGM rectangular plates with four simply supported edges. The influence of some parameters on the bending performance of FGM plates is also carefully considered.

On the analytical approach for the bending/stretching of linearly elastic functionally graded rectangular plates with two opposite edges simply supported

2009 ◽  
Vol 223 (9) ◽  
pp. 2009-2016 ◽  
Author(s):  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Rectangular Plate ◽  
Plate Theory ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Rectangular Plates ◽  
Partial Differential ◽  
Simply Supported

In this article, a new analytical method for bending—stretching analysis of thick functionally graded (FG) rectangular plates is presented. Using this method, the governing equations of FG rectangular plates based on the first-order shear deformation or Mindlin plate theory are decoupled. Five coupled partial differential equations of the Mindlin FG plate are converted into two uncoupled partial differential equations in terms of transverse displacement and a new function. It is analytically shown that by introducing an equivalent flexural rigidity, the equations of FG rectangular plate become similar to those of the homogeneous isotropic plate. Solving these equations, the solutions are obtained for the FG rectangular plate with two opposite edges simply supported. A comparison of the present results with available solutions from previous studies is made and a good agreement can be seen. Also, the numerical results for stress and deflection of the FG rectangular plate with various boundary conditions are obtained.

A novel analytical approach for the buckling analysis of moderately thick functionally graded rectangular plates with two simply-supported opposite edges

2010 ◽  
Vol 224 (9) ◽  
pp. 1831-1841 ◽  
Author(s):  
M Mohammadi ◽  
A R Saidi ◽  
E Jomehzadeh
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Mindlin Plate ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Fg Plates

In this article, a novel analytical method for decoupling the coupled stability equations of functionally graded (FG) rectangular plates is introduced. Based on the Mindlin plate theory, the governing stability equations that are coupled in terms of displacement components are derived. Introducing four new functions, the coupled stability equations are converted into two independent equations. The obtained equations have been solved for buckling analysis of rectangular plates with simply-supported two edges and arbitrary boundary conditions along the other edges (Levy boundary conditions). The critical buckling loads are presented for different loading conditions, various thickness to side and aspect ratios, some powers of FG materials, and various boundary conditions. The presented results for buckling of moderately thick FG plates with two simply-supported edges are reported for the first time.

A Study on Free Vibrational Response of Functionally Graded Nanocomposite Sandwich Plates Reinforced by Randomly Oriented Straight Carbon Nanotubes

2016 ◽  
Vol 880 ◽  
pp. 77-82
Author(s):  
Vahid Tahouneh
Keyword(s):  
Carbon Nanotube ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Rectangular Plates ◽  
Reinforced Composites ◽  
Technical Literature ◽  
Simply Supported ◽  
Vibrational Response ◽  
Three Dimensional Elasticity

This paper is motivated by the lack of studies in the technical literature concerning to the three dimensional vibration analysis of thick laminated rectangular plates with continuously graded carbon nanotube-reinforced (CGCNTR) sheets. The formulations are based on the three-dimensional elasticity theory. The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The structure is supported by an elastic foundation with Winkler’s (normal) and Pasternak’s (shear) coefficients. The material properties of the functionally graded carbon nanotube reinforced composites are graded along the thickness and estimated through Mori-Tanaka method.

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