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Showing papers on "Functionally graded material published in 2012"


Proceedings Article
01 Jul 2012
TL;DR: An overview of fabrication processes, area of application, some recent research studies and the need to focus more research effort on improving the most promising FGM fabrication method (solid freeform SFF) is presented.
Abstract: Proceedings of the World Congress on Engineering 2012 Vol III (WCE 2012), London, UK, 4-6 July 2012

299 citations


Journal ArticleDOI
TL;DR: In this paper, a general nonlinear third-order plate theory that accounts for geometric nonlinearity, microstructure-dependent size effects, and two-constituent material variation through the plate thickness is presented using the principle of virtual displacements.

278 citations


Journal ArticleDOI
TL;DR: In this article, the bending and the free flexural vibration behavior of sandwich functionally graded material (FGM) plates are investigated using QUAD-8 shear flexible element developed based on higher order structural theory.

178 citations


Journal ArticleDOI
TL;DR: In this paper, a size-dependent functionally graded Euler-Bernoulli beam model is developed based on the strain gradient theory, a non-classical theory capable of capturing the size effect in micro-scaled structures.

163 citations


Journal ArticleDOI
TL;DR: In this article, a new four-variable refined plate theory for thermal buckling analysis of functionally graded material (FGM) sandwich plates is proposed, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors.
Abstract: The novelty of this paper is the use of a new four-variable refined plate theory for thermal buckling analysis of functionally graded material (FGM) sandwich plates. Unlike any other theory, the present new theory is variationally consistent and gives four governing equations. The number of unknown functions involved is only four, as against five in case of other shear deformation theories. In addition, the theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. Material properties and thermal expansion coefficient of the sandwich plate faces 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. ...

148 citations


Journal ArticleDOI
TL;DR: In this paper, a node-based strain smoothing is merged into shear-locking-free triangular plate elements for static, free vibration and mechanical/thermal buckling problems of FGM plates.
Abstract: This paper presents an improved finite element approach in which a node-based strain smoothing is merged into shear-locking-free triangular plate elements. The formulation uses only linear approximations and its implementation into finite element programs is quite simple and efficient. The method is then applied for static, free vibration and mechanical/thermal buckling problems of functionally graded material (FGM) plates. In the FGM plates, the material properties are assumed to vary across the thickness direction by a simple power rule of the volume fractions of the constituents. The behavior of FGM plates under mechanical and thermal loads is numerically analyzed in detail through a list of benchmark problems. The numerical results show high reliability and accuracy of the present method compared with other published solutions in the literature.

127 citations


Journal ArticleDOI
TL;DR: In this article, an efficient and simple refined theory is presented for buckling analysis of functionally graded plates, which accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors.

125 citations


Journal ArticleDOI
TL;DR: In this article, glass beads are placed within the adhesive layer at different densities along the joint to reduce the peel stress concentrations located near adherend discontinuities, and proof of concept testing is conducted to show the potential advantages of functionally graded adhesives.

112 citations


Journal ArticleDOI
TL;DR: In this paper, a microstructure-dependent nonlinear theory for axisymmetric bending of circular plates, which accounts for through-thickness power-law variation of a two-constituent material, is developed using the principle of virtual displacements.

109 citations


Journal ArticleDOI
TL;DR: In this article, a nonlinear governing equation for the functionally graded material beam with two clamped ends and surface-bonded piezoelectric actuators is derived by the Hamilton's principle.

106 citations


Journal ArticleDOI
TL;DR: In this article, titanium carbide (TiC) reinforcement particles were embedded in Inconel 690 with laser direct deposition to build functionally gradient metal matrix composites (FGMMCs) and microstructures of the MMC and distribution of TiC particles were characterized with an optical microscope, SEM and X-ray diffraction.
Abstract: Functionally gradient material (FGM) can be tailored to the structural requirements of the final product. In this study, titanium carbide (TiC) reinforcement particles were embedded in Inconel 690 with laser direct deposition to build functionally gradient metal matrix composites (FGMMCs). The microstructures of the MMC and distribution of TiC particles were characterized with an optical microscope, SEM and X-ray diffraction. There was a near absence of internal voids in the deposited TiC-Inconel 690 MMC. With the volume percentage of TiC particles in the depositions varied from 0 to 49%, a drastic evolution in the microstructure was observed and the presence of TiC particles over 30% yielded a refinement of the matrix microstructure and introduction of a finely dispersed crystalline phase. High-temperature dissolution of TiC was not detected under the conditions used. Micro-hardness and wear resistance tests showed a significant improvement with increased TiC content.

Journal ArticleDOI
TL;DR: In this article, the free longitudinal vibration of axially functionally graded (AFG) tapered nanorods with variable cross-section based on the nonlocal elasticity theory is reported.

Journal ArticleDOI
TL;DR: In this article, an analytical method is proposed for solving the free vibration of cracked functionally graded material (FGM) beams with axial loading, rotary inertia and shear deformation.

Journal ArticleDOI
TL;DR: In this paper, a semi-analytical approach which makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is used to obtain the vibration frequencies.
Abstract: This paper deals with three-dimensional analysis of functionally graded annular plates through using state-space based differential quadrature method (SSDQM) and comparative behavior modeling by artificial neural network (ANN) for different boundary conditions. The material properties are assumed to have an exponent-law variation along the thickness. A semi-analytical approach which makes use of state-space method in thickness direction and one-dimensional differential quadrature method in radial direction is used to obtain the vibration frequencies. The state variables include a combination of three displacement parameters and three stress parameters. Numerical results are given to demonstrate the convergency and accuracy of the present method. Once the semi-analytical method is validated, an optimal ANN is selected, trained and tested by the obtained numerical results. In addition to the quantitative input parameters, support type is also considered as a qualitative input in NN modeling. Eventually the results of SSDQM and ANN are compared and the influence of thickness of the annular plate, material property graded index and circumferential wave number on the non-dimensional natural frequency of annular functionally graded material (FGM) plates with different boundary conditions are investigated. The results show that ANN can acceptably model the behavior of FG annular plates with different boundary conditions.

Journal ArticleDOI
TL;DR: In this article, the static, dynamic, and free vibration analysis of a doubly curved panel is investigated analytically in the Laplace domain and then inverted to the time domain following an analytical procedure.

Journal ArticleDOI
TL;DR: It is demonstrated, for the first time, that a PSO based optimizer outperforms classical mathematical programming based methods, such as active set and trust region algorithms, in the optimal design of functionally graded materials.
Abstract: A new method for the optimal design of Functionally Graded Materials (FGM) is proposed in this paper. Instead of using the widely used explicit functional models, a feature tree based procedural model is proposed to represent generic material heterogeneities. A procedural model of this sort allows more than one explicit function to be incorporated to describe versatile material gradations and the material composition at a given location is no longer computed by simple evaluation of an analytic function, but obtained by execution of customizable procedures. This enables generic and diverse types of material variations to be represented, and most importantly, by a reasonably small number of design variables. The descriptive flexibility in the material heterogeneity formulation as well as the low dimensionality of the design vectors help facilitate the optimal design of functionally graded materials. Using the nature-inspired Particle Swarm Optimization (PSO) method, functionally graded materials with generic distributions can be efficiently optimized. We demonstrate, for the first time, that a PSO based optimizer outperforms classical mathematical programming based methods, such as active set and trust region algorithms, in the optimal design of functionally graded materials. The underlying reason for this performance boost is also elucidated with the help of benchmarked examples.

Journal ArticleDOI
TL;DR: In this article, a 2D Unconstrained Third Order Shear Deformation Theory (UTSDT) is presented for the evaluation of tangential and normal stresses in moderately thick functionally graded cylindrical shells subjected to mechanical loadings.

Journal ArticleDOI
TL;DR: In this paper, the static analysis of plates and shells made of Functionally Graded Material (FGM), subjected to mechanical loads, is considered. And the results are compared with both benchmark solutions from literature and the results obtained using the Navier method that provides the analytical solution for simply supported structures subjected to sinusoidal pressure loads.

Journal ArticleDOI
TL;DR: In this paper, a finite strip method is applied for analyzing the buckling behavior of rectangular functionally graded plates (FGPs) under thermal loadings, where the material properties of FGPs are assumed to vary continuously through the thickness of the plate, according to the simple power law distribution.

Journal ArticleDOI
TL;DR: In this article, the authors derived the equilibrium and compatibility equations of imperfect sandwich plates with FGM face sheets under uniform temperature rise loading, and employed the single mode approach combined with Galerkin technique to calculate the critical buckling temperature and post-buckling equilibrium path of the plate.
Abstract: Post-buckling behaviour of sandwich plates with functionally graded material (FGM) face sheets under uniform temperature rise loading is considered. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation, which acts in both compression and tension. The derivation of equations is based on the first-order shear deformation plate theory. Thermomechanical non-homogeneous properties of FGM layers vary smoothly by the distribution of power law across the thickness, and temperature dependency of material constituents is taken into account. Using the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect sandwich plates with FGM face sheets are derived. The boundary conditions for the plate are assumed to be simply supported in all edges. The governing equations are reduced to two coupled equation in terms of stress function and lateral deflection. Employing the single mode approach combined with Galerkin technique, an approximate closed-form solution is presented to calculate the critical buckling temperature and post-buckling equilibrium path of the plate. Presented numerical examples contain the influences of power law index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation coefficients.

Journal ArticleDOI
TL;DR: In this paper, the authors presented an analysis of functionally graded material doubly curved panels with rectangular planform under the action of thermal and mechanical loads, based on first-order shear deformation theory of modified Sanders assumptions, five coupled partially differential equations (PDEs) are established as equations of motion.
Abstract: The paper presents an analysis of functionally graded material doubly curved panels with rectangular planform under the action of thermal and mechanical loads. Based on the first-order shear deformation theory of modified Sanders assumptions, five coupled partially differential equations (PDEs) are established as equations of motion. Each thermo-mechanical property of the shell follows the power law distribution across the thickness, except Poisson’s ratio, which is kept constant through the panel. Assuming that four edges of the shell-panel are simply supported, a Navier-based solution is adopted to reduce the PDEs into time-dependent ODEs. Applying the Laplace transformation, the equations of motion are transformed into the Laplace domain. With the aid of analytical Laplace inverse method, solutions of stresses, strains, and displacements are obtained in time domain and expressed in explicit phrases. Dynamic, free vibration, and thermo-mechanical bending analysis of the panel is carried out for various geometries. Obtained results are validated with the well-known available data reported in the literature.

Journal ArticleDOI
TL;DR: In this paper, the effects of the different profiles describing the graded properties of the materials on the stress and displacement fields were analyzed for a set of cylinders subjected to internal and external pressure in which the entire wall is made of functionally graded material or of only a thin functionally graded coating present on the internal homogeneous wall.

Journal ArticleDOI
TL;DR: In this article, an analytical solution for a plate made of functionally graded materials based on the third-order shear deformation theory and subjected to lateral thermal shock is presented for the analytical solution is obtained under coupled thermoelasticity assumptions.
Abstract: In this paper, the analytical solution is presented for a plate made of functionally graded materials based on the third-order shear deformation theory and subjected to lateral thermal shock. The material properties of the plate, except Poisson's ratio, are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The solution is obtained under the coupled thermoelasticity assumptions. The temperature profile across the plate thickness is approximated by a third-order polynomial in terms of the variable z with four unknown multiplier functions of ( x , y , t ) to be calculated. The equations of motion and the conventional coupled energy equation are simultaneously solved to obtain the displacement components and the temperature distribution in the plate. The governing partial differential equations are solved using the double Fourier series expansion. Using the Laplace transform, the unknown variables are obtained in the Laplace domain. Applying the analytical Laplace inverse method, the solution in the time domain is derived. Results are presented for different power law indices and the coupling coefficients for a plate with simply supported boundary conditions. The results are validated based on the known data for thermomechanical responses of a functionally graded plate reported in the literature.

Journal ArticleDOI
TL;DR: In this article, an analytical investigation into the nonlinear response of thick functionally graded double-curved shallow panels resting on elastic foundations and subjected to thermal and thermomechanical loads is presented.
Abstract: An analytical investigation into the nonlinear response of thick functionally graded double-curved shallow panels resting on elastic foundations and subjected to thermal and thermomechanical loads is presented. Young’s modulus and Poisson’s ratio are both graded in the thickness direction according to a simple power-law distribution in terms of volume fractions of constituents. All formulations are based on the classical shell theory with account of geometrical nonlinearity and initial geometrical imperfection in the cases of Pasternak-type elastic foundations. By applying the Galerkin method, explicit relations for the thermal load–deflection curves of simply supported curved panels are found. The effects of material and geometrical properties and foundation stiffness on the buckling and postbuckling load-carrying capacity of the panels in thermal environments are analyzed and discussed.

Journal ArticleDOI
TL;DR: In this paper, a two-dimensional elastic analysis of functionally graded materials (FGMs) is conducted using the proposed boundary integral based graded element formulation, which is based on independent internal and frame field approximations.
Abstract: A two-dimensional (2D) elastic analysis of functionally graded materials (FGMs) is conducted using the proposed boundary integral based graded element formulation. The graded element model is based on independent internal and frame field approximations. The elemental stiffness contains element boundary integrals only and is calculated using the exact expression of the graded material property. In the construction of the element model, the fundamental solutions of functionally graded plate with quadratic variation of elastic properties are employed to construct the internal approximation and then the graded element is constructed, in which the material definition entails naturally graded variation. Three numerical examples are considered: verification of fundamental solutions, a functionally graded cantilever beam, and a functionally graded link bar, to assess the performance of the hybrid graded model and to show the advantages of FGMs over homogeneous materials.

Journal ArticleDOI
TL;DR: In this paper, the pull-in instability and free vibration of functionally graded poly-SiGe micro-beams under combined electrostatic force, intermolecular force and axial residual stress, with an emphasis on the effects of ground electrode shape, position-dependent material composition, and geometrically nonlinear deformation of the micro-beam.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the thermal postbuckling behavior of FGM cylindrical shells in a Pasternak-type elastic medium and provided a closed-form solution to the equilibrium and stability equations.
Abstract: M IRZAVAND and Eslami [1] have presented the thermal buckling analysis of simply supported functionally graded material (FGM) cylindrical shells that are integratedwith the surfacebonded piezoelectric actuators. Shen [2] reported the thermal postbuckling behavior of FGM cylindrical shells based on the thirdorder theory of shell via a singular perturbation method. Shen et al. [3,4] also made a study on the postbuckling response of an FGM cylindrical shell embedded in a Pasternak elastic medium and under mechanical load in thermal environments. The buckling analysis of FGM truncated conical shells subjected to combined axial extension loads and hydrostatics pressure and resting on the Pasternak-type elastic foundationwere studied analytically by Sofiyev [5]. Recently, the present authors reported the explicit expressions for mechanical buckling loads of thick FGM cylindrical shells in contact with a Pasternak-type elastic medium [6]. In the present Note, buckling of cylindrical shells made of FGM in contact with the Pasternak elastic foundation subjected to uniform temperature rise is investigated. The material properties of an FGM shell are assumed to be temperature-dependent and vary continuously as a power form through the thickness of a shell. The boundary conditions are assumed to be a fixed simply supported type. The equilibrium and stability equations are obtained, and stability equations are reduced to one equation. The investigation ends in a closed-form solution for the FGM cylindrical shells under uniform thermal load, and numerical results are presented.

Journal ArticleDOI
TL;DR: In this paper, a high order theory for functionally graded (FG) axisymmetric cylindrical shells based on the expansion of the linear elasticity for functional graded materials (FGMs) into Fourier series in terms of Legendre's polynomials is presented.

Journal ArticleDOI
TL;DR: In this article, the authors presented analytical solutions to predict the deformation behavior of such functionally graded shape memory alloy wires, and closed-form solutions were derived for nominal stress-strain variations that are closely validated by experimental data for shape memory effect and pseudoelastic behaviour of NiTi wires.

Journal ArticleDOI
TL;DR: In this paper, the Bernoulli-Euler and Timoshenko beam theories are reformulated using a modified couple stress theory and through-thickness power-law variation of a two-constituent material [functionally graded material (FGM)].
Abstract: The Bernoulli–Euler and Timoshenko beam theories are reformulated using a modified couple stress theory and through-thickness power-law variation of a two-constituent material [functionally graded material (FGM)]. The model contains a material length scale parameter that can capture the size effect in a FGM. The equations are then used to develop algebraic relationships for the deflections, slopes, stress resultants of the Timoshenko beam theory (TBT) for microstructure-dependent FGM beams in terms of the same quantities of the conventional Bernoulli–Euler beam theory (BET). The relationships allow determination of the solutions of the TBT for microstructure-dependent FGM beams whenever solutions based on the BET are available. Examples of the use of the relationships are presented using straight beams with simply supported and clamped boundary conditions.