• Smart Structures and Systems
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• 제19권4호
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• pp.441-448
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• 2017

This paper uses the four-variable refined plate theory for the free vibration analysis of functionally graded material (FGM) rectangular plates. The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Equations of motion are derived from the Hamilton's principle. The closed-form solutions of functionally graded plates are obtained using Navier solution. Numerical results of the refined plate theory are presented to show the effect of the material distribution, the aspect and side-to-thickness ratio on the fundamental frequencies. It can be concluded that the proposed theory is accurate and simple in solving the free vibration behavior of functionally graded plates.

• Coupled systems mechanics
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• 제13권2호
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• pp.115-132
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• 2024

This paper introduces an improved shear deformation theory for analyzing the buckling behavior of functionally graded plates subjected to varying temperatures. The transverse shear strain functions employed satisfy the stress-free condition on the plate surfaces without requiring shear correction factors. The material properties and thermal expansion coefficient of the porous functionally graded plate are assumed temperature-dependent and exhibit continuous variation throughout the thickness, following a modified power-law distribution based on the volume fractions of the constituents. Moreover, the study considers the influence of porosity distribution on the buckling of the functionally graded plates. Thermal loads are assumed to have uniform, linear, and nonlinear distributions through the thickness. The obtained results, considering the effect of porosity distribution, are compared with alternative solutions available in the existing literature. Additionally, this study provides comprehensive discussions on the influence of various parameters, emphasizing the importance of accounting for the porosity distribution in the buckling analysis of functionally graded plates.

• Steel and Composite Structures
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• 제14권4호
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• pp.335-347
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• 2013

In this paper, the nonlinear cylindrical bending behavior of functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) is studied using an efficient and simple refined theory. This theory is based on assumption that the in-plane and transverse displacements consist of bending and shear components in which the bending components do not contribute toward shear forces and, likewise, the shear components do not contribute toward bending moments. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTCRs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The fundamental equations for functionally graded nanocomposite plates are obtained using the Von-Karman theory for large deflections and the solution is obtained by minimization of the total potential energy. The numerical illustrations concern the nonlinear bending response of FG-CNTRC plates under different sets of thermal environmental conditions, from which results for uniformly distributed CNTRC plates are obtained as comparators.

• Steel and Composite Structures
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• 제30권1호
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• pp.57-67
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• 2019

This paper deals with the static analysis of axially functionally graded rectangular plates. It is assumed that the flexural rigidity of the plate varies exponentially along one of the plate's in-plane dimensions. Both an analytical approach and a numerical method are utilized to solve the problem. The analytical solution is obtained by using the Green's function method. To employ this approach, the adjoint boundary value problem is established. Then, exact solutions for deflection of the plate for different boundary conditions are found. In another way, a finite element formulation for the problem is developed. In order to demonstrate the validity of the Authors' formulation, the results obtained via both mentioned schemes are compared with each other for functionally graded plates and with results of previously published works for homogeneous plates. The effect of plate parameters on the response of the plate is also investigated. To remind the research background, a brief review on the application of Green's function method in plates' analysis and functionally graded plates is also presented.

• Structural Engineering and Mechanics
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• 제62권3호
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• pp.311-324
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• 2017

In this paper a new eight-unknown higher order shear deformation theory is proposed for functionally graded (FG) material plates. The theory based on full twelve-unknown higher order shear deformation theory, simultaneously satisfy zeros transverse stresses at top and bottom surface of FG plates. Equations of motion are derived from principle of virtual displacement. Exact closed-form solutions are obtained for simply supported rectangular FG plates under uniform loading. The accuracy of present numerical results has been verified by comparing it with generalized shear deformation theory. The effect of power law index of functionally graded material, side-to-thickness ratio, and aspect ratio on static behavior of FG plates is investigated.

• Smart Structures and Systems
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• 제15권5호
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• pp.1345-1362
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• 2015

The present paper deals with the free vibration analysis of the functionally graded solid and annular circular plates with two functionally graded piezoelectric layers at top and bottom subjected to an electric field. Classical plate theory (CPT) is used for description of the all deformation components based on a symmetric distribution. All the mechanical and electrical properties except Poisson's ratio can vary continuously along the thickness direction of the plate. The properties of plate core can vary from metal at bottom to ceramic at top. The effect of non homogeneous index of functionally graded and functionally graded piezoelectric sections can be considered on the results of the system. $1^{st}$ and $2^{nd}$ modes of natural frequencies of the system have been evaluated for both solid and annular circular plates, individually.

• Structural Engineering and Mechanics
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• 제52권4호
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• pp.663-686
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• 2014

This paper deals with free vibration analysis of bidirectional functionally graded annular plates resting on a two-parameter elastic foundation. The formulations are based on the three-dimensional elasticity theory. This study presents a novel 2-D six-parameter power-law distribution for ceramic volume fraction of 2-D functionally graded materials that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. Various material profiles along the thickness and in the in-plane directions are illustrated by using the 2-D power-law distribution. The effective material properties at a point are determined in terms of the local volume fractions and the material properties by the Mori-Tanaka scheme. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The fast rate of convergence of the method is shown and the results are compared against existing results in literature. Some new results for natural frequencies of the plates are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded ceramic volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded materials.

• Structural Engineering and Mechanics
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• 제30권4호
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• pp.501-512
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• 2008

The axisymmetric problem of a functionally graded annular plate is considered by extending the theory of functionally graded materials plates suggested by Mian and Spencer (1998). In particular, their expansion formula for displacements is adopted and the hypothesis that the material parameters can vary along the thickness direction in an arbitrary continuous fashion is retained. However, their analysis is extended here in two aspects. First, the material is assumed to be transversely isotropic, rather than isotropic. Second, the plate is no longer tractions-free on the top and bottom surfaces, but subject to uniform loads applied on the surfaces. The elasticity solutions are given for a uniformly loaded annular plate of functionally graded materials for a total of six different boundary conditions. Numerical results are given for a simply supported functionally graded annular plate, and good agreement with those by the classical plate theory is obtained.

• Steel and Composite Structures
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• 제18권1호
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• pp.91-120
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• 2015

A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates is presented in this paper. It contains only four unknowns, accounts for a hyperbolic distribution of transverse shear stress and satisfies the traction free boundary conditions. Equations of motion are derived from Hamilton's principle. The Navier-type and finite element solutions are derived for plate with simply-supported and various boundary conditions, respectively. Numerical examples are presented for functionally graded sandwich plates with homogeneous hardcore and softcore to verify the validity of the developed theory. It is observed that the present theory with four unknowns predicts the response accurately and efficiently.

• Structural Engineering and Mechanics
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• 제53권2호
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• pp.337-354
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• 2015

In this article, free vibration of functionally graded (FG) elliptic plates subjected to various classical boundary conditions has been investigated. Literature review reveals no study has been performed based on functionally graded elliptic plates till date. The mechanical kinematic relations are considered based on classical plate theory. Rayleigh-Ritz technique is used to obtain the generalized eigenvalue problem. The material properties of the FG plate are assumed to vary along thickness direction of the constituents according to power-law form. Trial functions denoting the displacement components are expressed in simple algebraic polynomial forms which can handle any edge support. The objective is to study the effect of geometric configurations and gradation of constituent volume fractions on the natural frequencies. New results for frequency parameters are incorporated after performing a test of convergence. A comparison study is carried out with existing literature for validation in special cases. Three-dimensional mode shapes for circular and elliptic FG plates are also presented with various boundary conditions at the edges.