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Showing papers on "Functionally graded material published in 2011"


Journal ArticleDOI
J. N. Reddy1
TL;DR: In this article, a microstructure-dependent nonlinear Euler-Bernoulli and Timoshenko beam theory was proposed to account for through-thickness power-law variation of a two-constituent material.
Abstract: A microstructure-dependent nonlinear Euler–Bernoulli and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material are developed using the principle of virtual displacements. The formulation is based on a modified couple stress theory, power-law variation of the material, and the von Karman geometric nonlinearity. The model contains a material length scale parameter that can capture the size effect in a functionally graded material, unlike the classical Euler–Bernoulli and Timoshenko beam theories. The influence of the parameter on static bending, vibration and buckling is investigated. The theoretical developments presented herein also serve to develop finite element models and determine the effect of the geometric nonlinearity and microstructure-dependent constitutive relations on post-buckling response.

574 citations


Journal ArticleDOI
TL;DR: In this paper, the in-plane dynamic crushing of two-dimensional honeycombs with both regular hexagonal and irregular arrangements was investigated using detailed finite element models, and three distinct crushing modes for honeycomb with a constant relative density: quasi-static, transition and dynamic.

315 citations


Journal ArticleDOI
TL;DR: In this article, a modified couple stress theory is proposed to capture the small-scale size effects in the mechanical behavior of structures, where the beam properties are assumed to vary through the thickness of the beam.

277 citations


Journal ArticleDOI
TL;DR: In this article, an improved third order shear deformation theory is employed to investigate thermal buckling and vibration of the functionally graded beams, and a power law distribution is used to describe the variation of volume fraction of material compositions.

166 citations


Journal ArticleDOI
TL;DR: Functionally graded carbon nanotube (CNT)-reinforced aluminum (Al) matrix composites have been successfully fabricated by a powder metallurgy route as mentioned in this paper, which offers a feasible approach to fabricating Al-CNT nanocomposites.
Abstract: Functionally graded carbon nanotube (CNT)-reinforced aluminum (Al) matrix composites have been successfully fabricated by a powder metallurgy route. The gradient layers containing different amounts of CNT additions showed different microstructures and hardness. Each layer demonstrated good adhesion, with no serious pores or microcracks. We controlled the characteristics of the bulk composite by the efficient design of each CNT gradient layer. The functionally graded material concept offers a feasible approach to fabricating Al-CNT nanocomposites.

166 citations


Journal ArticleDOI
TL;DR: In this article, a closed-form solution for the critical mechanical buckling loads of the FGM cylindrical shells surrounded by an elastic medium is presented. But the authors do not consider the effects of shell geometry, the volume fraction exponent, and the foundation parameters on the critical buckling load.

162 citations


Journal ArticleDOI
TL;DR: An edge-based smoothed finite element method (ES-FEM) with stabilized discrete shear gap (DSG) technique using triangular meshes was proposed to enhance the accuracy of the existing FEM with the DSG for analysis of isotropic Reissner/Mindlin plates.

148 citations


Journal ArticleDOI
TL;DR: In this paper, the linear free flexural vibration of cracked material plates is studied using the extended finite element method using a 4-noded quadrilateral plate bending element based on field and edge consistency requirement with 20 degrees of freedom per element.

141 citations


Journal ArticleDOI
TL;DR: In this article, the nonlinear behaviors of functionally graded material (FGM) plates under transverse distributed load are investigated using a high precision plate bending finite element. And the effective material properties are then evaluated based on the rule of mixture.

129 citations


Journal ArticleDOI
TL;DR: In this article, different samples with different layers of aluminum/steel functionally graded materials were compacted using steel die and punch at the same compacted pressure and sintered temperature.
Abstract: Aluminum/steel electric transition joints (ETJs) are used in aluminum reduction cell for the purpose of welding aluminum rod and steel bracket components. Solid state welding process used for joining aluminum and steel at the electric transition joints have the drawbacks of cracking and separation at the interface surfaces. Cracking and separation at the electric transition joints are caused by the stress singularities that developed due to the mismatch in thermal and mechanical properties of each material. To overcome the drawback of electric transition joints, aluminum/steel functionally graded may be used as electric transition joints or proposed. Therefore manufacturing and investigation of aluminum/steel functionally graded materials fabricated by powder metallurgy process were carried out through the current work. Different samples with different layers of aluminum/steel functionally graded materials were compacted using steel die and punch at the same compacted pressure and sintered temperature. After investigating the different samples of aluminum/steel functionally graded materials under different fabrication conditions, the suitable fabrication regime was determined with the aid of microscopic observations.

118 citations


Journal ArticleDOI
TL;DR: In this article, a free vibration analysis of functionally graded beams via several axiomatic refined theories is presented, where material properties of the beam are assumed to vary continuously on the cross-section according to a power law distribution in terms of the volume fraction of the material constituents Young's modulus, Poisson ratio and density can vary along one or two dimensions all together or independently.

Journal ArticleDOI
TL;DR: In this article, the pull-in instability of micro-switches was investigated under the combined electrostatic and intermolecular forces and axial residual stress, accounting for the force nonlinearity and geometric non-linearity which stems from midplane stretching.
Abstract: This paper investigates the pull-in instability of micro-switches under the combined electrostatic and intermolecular forces and axial residual stress, accounting for the force nonlinearity and geometric nonlinearity which stems from mid-plane stretching. The micro-switch considered in the present study is made of either homogeneous material or non-homogeneous functionally graded material with two material phases. Theoretical formulations are based on Euler–Bernoulli beam theory and von Karman type nonlinear kinematics. The principle of virtual work is used to derive the nonlinear governing differential equation which is then solved using the differential quadrature method (DQM). Pull-in voltage and pull-in deflection are obtained for micro-switches with four different boundary conditions (i.e. clamped–clamped, clamped-simply supported, simply supported and clamped-free). The present solutions are validated through direct comparisons with experimental and other existing results reported in previous studies. A parametric study is conducted, focusing on the combined effects of geometric nonlinearity, gap ratio, slenderness ratio, Casimir force, axial residual stress and material composition on the pull-in instability.

Journal ArticleDOI
TL;DR: In this paper, a beam element is proposed which takes advantage of the shape functions of homogeneous uniform beam elements, and the effects of varying cross-sectional dimensions and mechanical properties of the functionally graded material are included in the evaluation of structural matrices.
Abstract: Structural analysis of axially functionally graded tapered Euler-Bernoulli beams is studied using finiteelement method. A beam element is proposed which takes advantage of the shape functions of homogeneous uniform beam elements. The effects of varying cross-sectional dimensions and mechanical properties of the functionally graded material are included in the evaluation of structural matrices. This method could be used for beam elements with any distributions of mass density and modulus of elasticity with arbitrarily varying cross-sectional area. Assuming polynomial distributions of modulus of elasticity and mass density, the competency of the element is examined in stability analysis, free longitudinal vibration and free transverse vibration of double tapered beams with different boundary conditions and the convergence rate of the element is then investigated.

Journal ArticleDOI
TL;DR: In this paper, a fabrication process to produce functionally graded porous polymer via supercritical carbon dioxide (ScCO2) foaming is reported, which utilizes a partial gas saturation technique to obtain non-equilibrium gas concentration profiles in thermoplastic polymer.
Abstract: A fabrication process to produce functionally graded porous polymer via supercritical carbon dioxide (ScCO2) foaming is reported in this paper. It utilizes a partial gas saturation technique to obtain non-equilibrium gas concentration profiles in thermoplastic polymer. Once foamed the polymer material obtains a graded foam–solid-foam structure with varying pore size distributions. This functionally graded material fabrication method was studied with polymethyl methacrylate (PMMA) under a ScCO2 saturation condition. A diffusion model was developed to estimate the gas diffusion coefficient and to predict the gas concentration profiles inside the polymer samples. Scanning electron microscopy images were used to analyze the effects of partial saturation on the graded porous structure. Mechanical properties of the foamed samples were characterized using a three-point bending test. It was found that the gas concentration profiles resulted from partial saturation corresponded well to the graded structure after foaming. The proportion of the foam and solid regions inside the polymer sample can be manipulated by controlling the partial saturation profile. The test results also suggested that the graded foam structure could be optimized to achieve desirable mechanical properties.

Journal ArticleDOI
TL;DR: In this paper, the Euler-Bernoulli theory and Haar matrices were used to investigate the vibrational properties of non-uniform and functionally graded beams with various boundary conditions and varying cross-sections.

Journal ArticleDOI
Lazreg Hadji1, Hassen Ait Atmane1, Abdelouahed Tounsi1, Ismail Mechab1, E.A. Adda Bedia1 
TL;DR: In this paper, the authors used the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates, which is variationally consistent and strongly similar to the classical plate theory in many aspects.
Abstract: This paper uses the four-variable refined plate theory (RPT) for the free vibration analysis of functionally graded material (FGM) sandwich rectangular plates. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The theory presented is variationally consistent and strongly similar to the classical plate theory in many aspects. It does not require the shear correction factor, and gives rise to the transverse shear stress variation so that the transverse shear stresses vary parabolically across the thickness to satisfy free surface conditions for the shear stress. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. The validity of the theory is shown by comparing the present results with those of the classical, the first-order, and the other higher-order theories. The proposed theory is accurate and simple in solving the free vibration behavior of the FGM sandwich plates.

Journal ArticleDOI
01 Mar 2011
TL;DR: In this paper, an exact analytical solution for free vibration characteristics of thin functionally graded rectangular plates with different boundary conditions is presented. But the authors do not consider the effects of aspect ratio, thickness, length ratio, power law index, and boundary conditions on the vibration characteristics.
Abstract: The aim of this article is to find an exact analytical solution for free vibration characteristics of thin functionally graded rectangular plates with different boundary conditions. The governing equations of motion are obtained based on the classical plate theory. Using an analytical method, three partial differential equations of motion are reformulated into two new decoupled equations. Based on the Navier solution, a closed-form solution is presented for natural frequencies of functionally graded simply supported rectangular plates. Then, considering Levy-type solution, natural frequencies of functionally graded plates are presented for various boundary conditions. Three mode shapes of a functionally graded rectangular plate are also presented for different boundary conditions. In addition, the effects of aspect ratio, thickness—length ratio, power law index, and boundary conditions on the vibration characteristics of functionally graded rectangular plates are discussed in details. Finally, it has been...

Journal ArticleDOI
TL;DR: In this article, the free vibration characteristics of side-cracked rectangular functionally graded material (FGM) thick plates are reported, and a novel Ritz procedure is developed incorporating special admissible functions that properly account for the stress singularity behaviors in the neighborhood of a crack tip, and that properly accounts for the discontinuities of displacements and slops across a crack.

Journal ArticleDOI
TL;DR: In this paper, the authors presented a two-variable refined plate theory for the analysis of the thermoelastic bending of functionally graded sandwich plates, where the number of unknown functions involved is only four, as against five in case of other shear deformation theories.
Abstract: The thermoelastic bending analysis of functionally graded sandwich plates using the two-variable refined plate theory is presented in this paper Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, 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 The sandwich plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson's ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents The core layer is still homogeneous and made of an isotropic ceramic

Journal ArticleDOI
TL;DR: In this article, buckling analysis of functionally graded material (FGM) beams with or without surface-bonded piezoelectric layers subjected to both thermal loading and constant voltage is studied.
Abstract: In this article, buckling analysis of functionally graded material (FGM) beams with or without surface-bonded piezoelectric layers subjected to both thermal loading and constant voltage is studied. Thermal and mechanical properties of FGM layer is assumed to follow the power law distribution in thickness direction, except Poisson’s ratio which is considered constant. The Timoshenko beam theory and nonlinear strain-displacement relations are used to obtain the governing equations of piezoelectric FGM beam. Beam is assumed under three types of thermal loading and various types of boundary conditions. For each case of boundary conditions, existence of bifurcation-type buckling is examined and for each case of thermal loading and boundary conditions, closed-form solutions are obtained which are easily usable for engineers and designers. The effects of the applied actuator voltage, beam geometry, boundary conditions, and power law index of FGM beam on critical buckling temperature difference are examined.

Journal ArticleDOI
TL;DR: In this article, the propagation behavior of Lamb waves in a thermal stress relaxation type functionally graded material (FGM) plate with material parameters that vary continuously along the thickness was investigated for theoretical derivations.
Abstract: To investigate the propagation behavior of Lamb waves in a thermal stress relaxation type functionally graded material (FGM) plate with material parameters that vary continuously along the thickness, the power series technique, which has been proved to have good convergence and high precision, is employed for theoretical derivations. The influence of the gradient coefficients of FGM on the dispersion curves is illustrated. The numerical results also reveal differences between the properties of Lamb wave propagation in the FGM plate and the corresponding properties in a homogenous plate. In terms of results, we find that both the normal and anomalous dispersions exist in the first and the second modes of the Lamb wave that propagates in the FGM plate, while only the anomalous dispersion is in the first mode and only the normal dispersion is in the second mode for the homogenous plate. The wave structure is asymmetric due to the asymmetric properties of the material. The dominance of in-plane and out-plane displacements is different between the metal-rich and ceramic-rich surfaces. All these results give theoretical guidance not only for experimental measurement of material properties but also for nondestructive evaluation using an ultrasonic wave generation device.

Journal ArticleDOI
TL;DR: In this article, a rigid punch is sliding over the surface of the FGM coating with a constant velocity, and friction heating, with its value proportional to contact pressure, friction coefficient and sliding velocity, is generated at the interface between the punch and the FGF coating.

Journal ArticleDOI
TL;DR: In this paper, the von Karman nonlinear strain-displacement relationship is used to account for the large deflection of the plate, and two control algorithms are employed: classical displacement-velocity feedback control and robust H2 control.
Abstract: In this paper, large amplitude vibration control of functionally graded material (FGM) plates under thermal gradient and transverse mechanical loads using integrated piezoelectric sensor/actuator layers is investigated. In this regard, finite element formulation based on higher order shear deformation plate theory is developed. The von Karman nonlinear strain-displacement relationship is used to account for the large deflection of the plate. The material properties of FGM are assumed to be temperature-dependent and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The temperature field is assumed to be constant in the plane and varied only in the thickness direction of the plate. In order to control the large amplitude vibration of the plate, two control algorithms are employed: classical displacement-velocity feedback control and robust H2 control. Also, the uncertainty which arises from external disturbances (low-frequenc...

Journal ArticleDOI
TL;DR: In this paper, the linear free flexural vibrations of functionally graded material plates with a through center crack were studied using an 8-noded shear flexible element, where the material properties were assumed to be temperature dependent and graded in the thickness direction.

Journal ArticleDOI
TL;DR: In this paper, a finite element formulation based on higher order shear deformation plate theory is developed to analyze nonlinear natural frequencies, time and frequency responses of functionally graded plate with surface-bonded piezoelectric layers under thermal, electrical and mechanical loads.

Journal ArticleDOI
TL;DR: In this paper, a dynamic solution for the propagating viscoelastic waves in functionally graded material (FGM) plates subjected to stress-free conditions is presented in the context of the Kelvin-Voigt theory.

Journal ArticleDOI
TL;DR: In this paper, an exact analytical solution for buckling of functionally graded rectangular plates subjected to non-uniformly distributed in-plane loading acting on two opposite simply supported edges is developed.
Abstract: In this research work, an exact analytical solution for buckling of functionally graded rectangular plates subjected to non-uniformly distributed in-plane loading acting on two opposite simply supported edges is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the classical plate theory based on exact neutral surface position is employed to derive the governing stability equations. Considering Levy-type solution, the buckling equation reduces to an ordinary differential equation with variable coefficients. An exact analytical solution is obtained for this equation in the form of power series using the method of Frobenius. By considering sufficient terms in power series, the critical buckling load of functionally graded plate with different boundary conditions is determined. The accuracy of presented results is verified by appropriate convergence study, and the results are checked with those available in related literature. Furthermore, the effects of power of functionally graded material, aspect ratio, foundation stiffness coefficients and in-plane loading configuration together with different combinations of boundary conditions on the critical buckling load of functionally graded rectangular thin plate are studied.

Journal ArticleDOI
TL;DR: In this article, the effect of compositional gradient exponent and impactor velocity on the elasto-plastic impact response of functionally graded (FG) circular plates under low-velocity impact loads is investigated.

Journal ArticleDOI
TL;DR: In this article, thermal buckling analysis of functionally graded material (FGM) plates resting on two-parameter Pasternak's foundations is investigated and equilibrium and stability equations of FGM plates are derived based on the trigonometric shear deformation plate theory and includes the plate foundation interaction and thermal effects.
Abstract: In this article, thermal buckling analysis of functionally graded material (FGM) plates resting on two-parameter Pasternak's foundations is investigated. Equilibrium and stability equations of FGM plates are derived based on the trigonometric shear deformation plate theory and includes the plate foundation interaction and thermal effects. The material properties vary according to a power law form through the thickness coordinate. The governing equations are solved analytically for a plate with simply supported boundary conditions and subjected to uniform temperature rise and gradient through the thickness. Resulting equations are employed to obtain the closed-form solution for the critical buckling load for each loading case. The influences of the plate aspect ratio, side-to-thickness ratio, gradient index, and elastic foundation stiffnesses on the buckling temperature difference are discussed.

Journal ArticleDOI
TL;DR: In this article, large amplitude free flexural vibration analysis of shear deformable functionally graded material (FGM) plates is investigated, where the material properties of FGM plates are assumed to vary through the thickness of the plate by a simple power-law distribution in terms of the volume fractions of the constituents.