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Showing papers on "Functionally graded material published in 2013"


Journal ArticleDOI
TL;DR: In this article, a non-classical microbeam model incorporating the material length scale parameter was proposed to capture the size effect of the FG microbeams and the governing equations and the related boundary conditions were derived using Hamilton's principle.

424 citations


Journal ArticleDOI
TL;DR: In this paper, a refined trigonometric shear deformation theory (RTSDT) is presented for the thermoelastic bending analysis of functionally graded sandwich plates, where the displacement components are expressed by trigonometrical series representation through the plate thickness to develop a two-dimensional theory and gives rise to transverse shear stress variation.

403 citations


Journal ArticleDOI
TL;DR: In this article, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates.

278 citations


Journal ArticleDOI
TL;DR: In this paper, the free vibration analysis of functionally graded material (FGM) beams subjected to different sets of boundary conditions is performed based on the classical and first order shear deformation beam theories.
Abstract: Present investigation is concerned with the free vibration analysis of functionally graded material (FGM) beams subjected to different sets of boundary conditions. The analysis is based on the classical and first order shear deformation beam theories. Material properties of the beam vary continuously in the thickness direction according to the power-law exponent form. Trial functions denoting the displacement components of the cross-sections of the beam are expressed in simple algebraic polynomial forms. The governing equations are obtained by means of Rayleigh–Ritz method. The objective is to study the effects of constituent volume fractions, slenderness ratios and the beam theories on the natural frequencies. To validate the present analysis, comparison studies are also carried out with the available results from the existing literature.

258 citations


Journal ArticleDOI
TL;DR: Based on the modified couple stress theory (MCST), a unified higher order beam theory which contains various beam theories as special cases is proposed for buckling of a functionally graded (FG) microbeam embedded in elastic Pasternak medium as mentioned in this paper.

194 citations


Journal ArticleDOI
TL;DR: In this article, a novel and effective formulation based on isogeometric approach (IGA) and higher-order deformation plate theory (HSDT) is presented to study the behavior of functionally graded material (FGM) plates.
Abstract: This paper presents a novel and effective formulation based on isogeometric approach (IGA) and higher-order deformation plate theory (HSDT) to study the behavior of functionally graded material (FGM) plates. HSDT model using C1 continuous element is able to improve the accuracy of solution and describe exactly the shear stress distribution without shear correction factors. IGA utilizes the non-uniform rational B-spline (NURBS) functions which allow us to achieve easily the smoothness with arbitrary continuity order. The present method hence fulfills the C1 – requirement of HSDT model. The effective material properties of the FGM plates, which property varies only through the thickness of plate, are calculated using the rule of mixture and the Mori–Tanaka homogenization technique. The static, dynamic and buckling analysis of rectangular and circular plates is investigated for different boundary conditions. Numerical results show high effectiveness of the present formulation.

180 citations


Journal ArticleDOI
TL;DR: In this article, the vibrational properties of functionally graded nanocomposite cylindrical panels reinforced by single-walled carbon nanotubes (SWCNTs) based on the three-dimensional theory of elasticity were investigated.

149 citations


Journal ArticleDOI
TL;DR: In this article, the buckling of heated functionally graded material (FGM) annular plates on an elastic foundation is studied analytically, and the equilibrium equations of an annular-shaped plate are obtained based on the classical plate theory.
Abstract: The buckling of heated functionally graded material (FGM) annular plates on an elastic foundation is studied analytically. A conventional Pasternak-type elastic foundation is assumed to be in contact with plate during deformation, which acts in both compression and tension. The equilibrium equations of an annular-shaped plate are obtained based on the classical plate theory. Each thermo-mechanical property of the plate is assumed to be graded across the thickness direction of plate based on the power law form, while Poisson’s ratio is kept constant. Among all combinations of free, simply-supported, and clamped boundary conditions, existence of bifurcation buckling for various edge supports is examined and stability equations are obtained by means of the adjacent equilibrium criterion. An exact analytical solution is presented to calculate the thermal buckling load by obtaining the eigenvalues of the stability equation. Three types of thermal loading, namely; uniform temperature rise, transversely linear temperature distribution and heat conduction across the thickness type are studied. Effects of thickness to outer radii, inner to outer radii, power law index, elastic foundation coefficient, and thermal loading type on critical buckling temperature of FG plates are presented.

142 citations


Journal ArticleDOI
TL;DR: In this paper, a higher order shear and normal deformation theory is developed to simulate the thermoelastic bending of functionally graded material (FGM ) sandwich plates, which is relevant to aerospace, chemical process and nuclear engineering structures which may be subjected to intense thermal loads.

132 citations


Journal ArticleDOI
TL;DR: In this article, a modified couple stress theory (MCST) was used for static bending analysis of FG microbeams and the equilibrium equations and the related boundary conditions were derived by using the principal of the minimum total potential energy.

132 citations


Journal ArticleDOI
TL;DR: In this paper, a bi-directional evolutionary structural optimization technique in the form of inverse homogenization is used for the design of the FGM for specified variation in bulk or shear modulus.
Abstract: Design of functionally graded material (FGM), in which the mechanical property varies along one direction, is the focus of this study. It is assumed that the microstructure of the FGM is composed of a series of base cells in the variation direction and self-repeated in other directions. Bi-directional evolutionary structural optimization technique in the form of inverse homogenization is used for the design of the FGM for specified variation in bulk or shear modulus. Instead of designing a series of base cells simultaneously, the base cells are optimized progressively by considering three base cells at each stage. Thus, the proper connections between adjacent base cells can be achieved with high computational efficiency. Numerical examples demonstrate the effectiveness of the proposed method for designing microstructures of 2D and 3D FGMs with specified variation in bulk or shear modulus. The proposed algorithm can also be easily extended to design FGMs with other functional properties.

Journal ArticleDOI
TL;DR: In this paper, a mesh-free analysis of carbon nanotube reinforced composite (CNTRC) cylinders was performed by using an axisymmetric model and the transformation method was used for the imposition of essential boundary conditions.

Journal ArticleDOI
TL;DR: In this paper, the critical buckling load of a functionally graded material (FGM) Timoshenko beam and that of the corresponding homogeneous Euler-Bernoulli beam subjected to axial compressive load have been derived for clamped-clamped (C-C), simply supported-simply supported (S-S), and clamped free (C -F) edges.

Journal ArticleDOI
TL;DR: In this article, thermal buckling and postbuckling analysis of Functionally Graded Material (FGM) Timoshenko beams resting on a non-linear elastic foundation are examined.

Journal ArticleDOI
TL;DR: In this paper, an isogeometric finite element approach (IGA) in combination with the third-order deformation plate theory (TSDT) was proposed for thermal buckling analysis of functionally graded material (FGM) plates.

Journal ArticleDOI
TL;DR: This discussion is intended to give the readers about successful and obstacles fabrication of FGM and porous FGM in dental implants that will bring state-of-the-art technology to the bedside and develop quality of life and present standards of care.
Abstract: Functionally graded material (FGM) is a heterogeneous composite material including a number of constituents that exhibit a compositional gradient from one surface of the material to the other subsequently, resulting in a material with continuously varying properties in the thickness direction. FGMs are gaining attention for biomedical applications, especially for implants, owing to their reported superior composition. Dental implants can be functionally graded to create an optimized mechanical behavior and achieve the intended biocompatibility and osseointegration improvement. This review presents a comprehensive summary of biomaterials and manufacturing techniques researchers employ throughout the world. Generally, FGM and FGM porous biomaterials are more difficult to fabricate than uniform or homogenous biomaterials. Therefore, our discussion is intended to give the readers about successful and obstacles fabrication of FGM and porous FGM in dental implants that will bring state-of-the-art technology to the bedside and develop quality of life and present standards of care.

Journal ArticleDOI
TL;DR: In this article, an investigation of fatigue crack growth of interfacial cracks in bi-layered materials using the extended finite element method is presented, which reveals that the crack propagates into the FGM layer under all types of loads.
Abstract: An investigation of fatigue crack growth of interfacial cracks in bi-layered materials using the extended finite element method is presented. The bi-material consists of two layers of dissimilar materials. The bottom layer is made of aluminium alloy while the upper one is made of functionally graded material (FGM). The FGM layer consists of 100 % aluminium alloy on the left side and 100 % ceramic (alumina) on the right side. The gradation in material property of the FGM layer is assumed to be exponential from the alloy side to the ceramic side. The domain based interaction integral approach is extended to obtain the stress intensity factors for an interfacial crack under thermo-mechanical load. The edge and centre cracks are taken at the interface of bi-layered material. The fatigue life of the interface crack plate is obtained using the Paris law of fatigue crack growth under cyclic mode-I, mixed-mode and thermal loads. This study reveals that the crack propagates into the FGM layer under all types of loads.

Journal ArticleDOI
TL;DR: In this paper, an analytical approach is presented to investigate the nonlinear static and dynamic buckling of imperfect eccentrically stiffened functionally graded thin circular cylindrical shells subjected to axial compression.

Journal ArticleDOI
TL;DR: In this article, the buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic (FGMETE) circular cylindrical shell are carried out.

Journal ArticleDOI
TL;DR: In this article, the effect of frequency and duty cycle changes on the microstructure of the nano alumina particles has been studied for the synthesis of functionally graded nickel-nano Al 2 O 3 composite coatings.

Journal ArticleDOI
TL;DR: In this article, the free bending vibration of rotating axially functionally graded (FG) Timoshenko tapered beams (TTB) with different boundary conditions are studied using Differential Transformation method (DTM) and differential quadrature element method of lowest order (DQEL).

Journal ArticleDOI
TL;DR: In this article, the electromagneto-thermoelastic analysis of an infinite functionally graded material (FGM) hollow cylinder based upon Lord and Shulman's (LS) theory is presented.

Journal ArticleDOI
TL;DR: In this paper, the buckling analysis of symmetric sandwich plates with functionally graded material (FGM) face sheets resting on an elastic foundation based on the first-order shear deformation plate theory was presented.
Abstract: This paper presents an analytical investigation on the buckling analysis of symmetric sandwich plates with functionally graded material (FGM) face sheets resting on an elastic foundation based on the first-order shear deformation plate theory (FSDT) and subjected to mechanical, thermal and thermo-mechanical loads. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. An analytical approach is used to reduce the governing equations of stability and then solved using an analytical solution which is named as power series Frobenius method for symmetric sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of the plate aspect ratio, side-to-thickness ratio, loading type, sandwich plate type, volume fraction index, elastic foundation coefficients and boundary conditions on the buckling response of FGM sandwich plates. This has not been done before and serves to fill the gap of knowledge in this area.

Journal ArticleDOI
TL;DR: In this article, the authors investigated the nonlinear buckling and post-buckling behavior of functionally graded stiffened thin circular cylindrical shells subjected to external pressure by the analytical approach and derived equilibrium equations based on the smeared stiffeners technique and the classical shell theory with the geometrical nonlinearity in von Karman sense.
Abstract: The nonlinear buckling and post-buckling behavior of functionally graded stiffened thin circular cylindrical shells subjected to external pressure are investigated by the analytical approach in this paper. The shells are reinforced by eccentrically rings and stringers attached to the inside and material properties of shell and stiffeners are assumed to be continuously graded in the thickness direction. Fundamental relations, equilibrium equations are derived based on the smeared stiffeners technique and the classical shell theory with the geometrical nonlinearity in von Karman sense. Approximate three-terms solution of deflection is more correctly chosen and explicit expression to finding critical load and post-buckling pressure-deflection curves are given by using the Galerkin's method. The numerical results show the effectiveness of stiffeners in enhancing the stability of shells.

Journal ArticleDOI
TL;DR: In this paper, a computational method based on the extended finite element method (XFEM) is implemented for fracture analysis of isotropic and orthotropic functionally graded materials (FGMs) under mechanical and steady state thermal loadings.
Abstract: A computational method based on the extended finite element method (XFEM) is implemented for fracture analysis of isotropic and orthotropic functionally graded materials (FGMs) under mechanical and steady state thermal loadings. The aim is set to include the thermal effects in loading, governing equations, and the interaction integral for inhomogeneous materials with a complementary study on available crack propagation criteria in orthotropic FGMs under thermal loading conditions. The isotropic and orthotropic crack tip enrichments are applied to reproduce the singular stress field near crack tips. Mixed-mode stress intensity factors are evaluated in isotropic and orthotropic FGMs by means of the interaction integral. In addition, the mesh dependency and number of elements around the crack tip are substantially reduced in comparison with the standard finite element method with the same level of accuracy. Both mode-I and mixed-mode fracture problems with various types of mechanical and thermo-mechanical functionally graded material properties are simulated and discussed to assess the accuracy and efficiency of the proposed numerical method. Good agreements are observed between the predicted results and the reference results available in the literature with far lower degrees of freedom.

Journal ArticleDOI
TL;DR: In this article, the free bending vibration of rotating axially functionally graded (FG) Euler-Bernoulli tapered beams (ETB) with different boundary conditions are studied using Differential Transformation method (DTM) and differential quadrature element method of lowest order (DQEL).

Journal ArticleDOI
TL;DR: In this paper, a semi-analytical approach is presented to investigate the nonlinear dynamic of imperfect eccentrically stiffened functionally graded shallow shells taking into account the damping subjected to mechanical loads.

Journal ArticleDOI
TL;DR: In this article, a co-rotational beam element taking the effects of the material inhomogeneity, shear deformation and nonuniform cross section into account is formulated and employed in computing the response of the beams.
Abstract: The large displacement response of tapered cantilever beams made of axially functionally graded material is investigated by the finite element method. A co-rotational beam element taking the effects of the material inhomogeneity, shear deformation and nonuniform cross section into account is formulated and employed in computing the response of the beams. The numerical results show that the large displacement response of the beam is governed by the material distribution, the taper ratio and taper type. The axial displacement at the free end of the beam is most sensitive to the taper ratio, and the transverse displacement at the point is least affected by this parameter. The influence of the length to height ratio is also investigated and highlighted.

Journal ArticleDOI
TL;DR: In this article, a mixed static and dynamic optimization of four-parameter functionally graded material (FGM) doubly curved shells and panels is presented, where particle swarm optimization, Monte Carlo and genetic algorithm approaches are applied to define the optimum volume fraction profile for optimizing the first natural frequency and the maximum static deflection of the considered shell structure.
Abstract: This study deals with a mixed static and dynamic optimization of four-parameter functionally graded material (FGM) doubly curved shells and panels. The two constituent functionally graded shell consists of ceramic and metal, and the volume fraction profile of each lamina varies through the thickness of the shell according to a generalized power-law distribution. The Generalized Differential Quadrature (GDQ) method is applied to determine the static and dynamic responses for various FGM shell and panel structures. The mechanical model is based on the so-called First-order Shear Deformation Theory (FSDT). Three different optimization schemes and methodologies are implemented. The Particle Swarm Optimization, Monte Carlo and Genetic Algorithm approaches have been applied to define the optimum volume fraction profile for optimizing the first natural frequency and the maximum static deflection of the considered shell structure. The optimization aim is in fact to reach the frequency and the static deflection targets defined by the designer of the structure: the complete four-dimensional search space is considered for the optimization process. The optimized material profile obtained with the three methodologies is presented as a result of the optimization problem solved for each shell or panel structure.

Journal ArticleDOI
TL;DR: In this paper, a structural optimization problem with the objective of maximizing the crush force efficiency is solved by response surface method (RSM), where the thickness and density of each layer are selected as design variables and the optimum design shows gradually decreasing density distribution.