• Structural Engineering and Mechanics
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• v.62 no.3
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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.

• Structural Engineering and Mechanics
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• v.53 no.2
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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.

• Steel and Composite Structures
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• v.26 no.4
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• pp.387-405
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• 2018

A novel higher shear deformation theory (HSDT) is proposed for the bending, buckling and free vibration investigations of isotropic and functionally graded (FG) sandwich plates. It contains only four variables, which is even less than the first shear deformation theory (FSDT) and the conventional HSDTs. The model accounts for a parabolic variation of transverse shear stress, respects the traction free boundary conditions and contrary to the conventional HSDTs, the present one presents a novel displacement field which incorporates undetermined integral terms. Equations of motion determined in this work are applied for three types of FG structures: FG plates, sandwich plates with FG core and sandwich plates with FG faces. Analytical solutions are given to predict the transverse displacements, stresses, critical buckling forces and natural frequencies of simply supported plates and a comparison study is carried out to demonstrate the accuracy of the proposed model.

• Structural Engineering and Mechanics
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• v.77 no.6
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• pp.797-807
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• 2021

A new simple solution for critical buckling of FG sandwich plates under axial and biaxial loads is presented using new modified power-law formulations. Both even and uneven distributions of porosity are taken into account in this study. Material properties of the sandwich plate faces are assumed to be graded in the thickness direction according to a modified power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FG sandwich plate with various boundary conditions are derived using the higher-order shear deformation plate theory. The results reveal that the distribution shape of the porosity, the gradient index, loading type and functionally graded layers thickness have significant influence on the buckling response of functionally graded sandwich plates.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.04a
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• pp.279-283
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• 2004

Thermal postbuckling and vibration analyses of functionally graded plates (FG plates) are performed. The nonlinear finite element equation based on the first-order shear deformation plate theory is formulated for the FG plate. The von Karman strain-displacement relation is used to account for the thermal large deflection. The incremental method considering the effect of the initial deflection and the initial stress is adopted for temperature-dependent material properties of functionally graded materials. The numerical result shows characteristics of the thermal postbuckling and vibration of FG plates in the pre- and post- buckled regions.

• Steel and Composite Structures
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• v.14 no.4
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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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• v.11 no.4
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• pp.341-358
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• 2011

This paper presents the effects of thermal environment and temperature-dependence of the material properties on axisymmetric bending of functionally graded (FG) circular and annular plates. The material properties are assumed to be temperature-dependent and graded in the thickness direction. In order to accurately evaluate the effect of thermal environment, the initial thermal stresses are obtained by solving the thermoelastic equilibrium equations. Governing equations and the related boundary conditions, which include the effects of initial thermal stresses, are derived using the virtual work principle based on the elasticity theory. The differential quadrature method (DQM) as an efficient and robust numerical tool is used to obtain the initial thermal stresses and response of the plate. Comparison studies with some available results for FG plates are performed. The influences of temperature rise, temperature-dependence of material properties, material graded index and different geometrical parameters are carried out.

• Steel and Composite Structures
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• v.16 no.4
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• pp.339-356
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• 2014

This paper presents a study of the nonlinear cylindrical bending of an exponential functionally graded plate (simply called E-FG) with variable thickness. The plate is subjected to uniform pressure loading and his geometric nonlinearity is introduced in the strain-displacement equations based on Von-Karman assumptions. The material properties of functionally graded plates, except the Poisson's ratio, are assumed to vary continuously through the thickness of the plate in accordance with the exponential law distribution; and the solution is obtained using Hamilton's principle for constant plate thickness. In order to analyze functionally graded plate with variable thickness, a numerical solution using finite difference method is used, where parabolic variation of the plate thickness is studied. The results for E-FG plates are given in dimensionless graphical forms; and the effects of material and geometric properties on displacements and normal stresses through the thickness are determined.

• Structural Engineering and Mechanics
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• v.84 no.6
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• pp.723-731
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• 2022

Functionally graded materials (FGMs) have been spotlighted as an advanced composite material, accordingly the intensive studies have focused on FGMs to examine their mechanical behaviors. Among them is thermal buckling which has been a challenging subject, because its behavior is connected directly to the safety of structural system. In this context, this paper presents the numerical analysis of thermal buckling of metal-ceramic functionally graded (FG) plates. For an accurate and effective buckling analysis, a new numerical method is developed by making use of (1,1,0) hierarchical model and 2-D natural element method (NEM). Based on 3-D elasticity theory, the displacement field is expressed by a product of 1-D assumed thickness monomials and 2-D in-plane functions which are approximated by NEM. The numerical method is compared with the reference solutions through the benchmark test, from which its numerical accuracy has been verified. Using the developed numerical method, the critical buckling temperatures of metal-ceramic FG plates are parametrically investigated with respect to the major design parameters.

• Steel and Composite Structures
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• v.50 no.2
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• pp.135-148
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• 2024

This paper analytically investigates the free vibration analysis of functionally graded-carbon nanotube reinforced composite (FG-CNTRC) plates by dynamic stiffness method (DSM). The properties of CNTRC are determined with the extended rule of mixture. The governing differential equations of motion based on the first-order shear deformation theory of CNTRC plate are derived using Hamilton's principle. The FG-CNTRC plates are studied for a uniform and two different distributions of carbon nanotubes (CNTs). The accuracy and performance of the DSM are compared with the results obtained from closed closed-form and semi-analytical solution methods in previous studies. In this study, the effects of boundary condition, distribution type of CNTs, plate aspect ratio, plate length to thickness ratio, and different values of CNTs volume fraction on the natural frequencies of the FG-CNTRC plates are investigated. Finally, various natural frequencies of the plates in different conditions are provided as a benchmark for comparing the accuracy and precision of the other analytical and numerical methods.