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In this paper, the thermal buckling behavior of circular plates with variable thicknesses made of bimorph functionally graded materials, under uniform thermal loading circumstances, considering the first-order shear deformation plate theory and also assumptions of von Karman has been studied. The material characteristics are symmetric to the middle surface of the plate and, based on the power law, vary along with thickness; where the middle surface is intended pure metal, and the sides are pure ceramic. In order to determine the distribution of pre-buckling force in the radial direction, the membrane equation is solved using the shooting method. And the stability equations are solved numerically, with the help of pseudo-spectral method by choosing Chebyshev functions as basic functions. The numerical results in clamped and simply supported boundary conditions and the linear and parabolic thickness variations are presented. And the influence of various parameters like volume fraction index, the thickness profile and side ratio on the buckling behavior of these plates has been evaluated.

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In this paper, the Meshless Local Petrov-Galerkin (MLPG) method is used to analyze the fracture of an isotropic FGM plate. The stress intensity factor of Mode I and Mode II are determined under the influence of various non-homogeneity ratios, crack length and material gradation angle. Both the moving least square (MLS) and the direct method have been applied to estimate the shape function and to impose the essential boundary conditions. The enriched weight function method is used to simulate the displacement and stress field around the crack tip. Normalized stress intensity factors (NDSIF) are calculated using the path independent integral, J*, which is formulated for the non-homogeneous material. The Edge-Cracked FGM plate is considered here and analyzed under the uniform load and uniform fixed grip conditions. To validate results, at first, homogeneous and FGM plate with material gradation along crack length was analyzed and compared with exact solution. Results showed good agreement between MLPG and exact solution.

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The main purpose of this study is to investigate nonlinear bending and buckling analysis of radially functionally graded annular plates subjected to uniform in-plane compressive loads by Dynamic Relaxation method. The mechanical properties of plates assumed to vary continuously along the radial direction by the Mori–Tanaka distribution. The nonlinear formulations are based on first order shear deformation theory (FSDT) and large deflection von Karman equations. The dynamic relaxation (DR) method combined with the finite difference discretization technique is employed to solve the equilibrium equations. Due to the lack of similar research for the bending and buckling of functionally graded annular plates with material variation in the radial direction, some results are compared with the ones obtained by the Abaqus finite element software. Furthermore, some comparison study is carried out to compare the current solution with the results reported in the literature for annular isotropic plates. The achieved good agreements between the results indicate the accuracy of the present numerical method. Finally, numerical results for the maximum displacement and critical buckling load for various boundary conditions, effects of grading index, thickness-to-radius ratio and inner radius -to-outer radius ratio are presented.

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Functionally graded materials have been taken into consideration by many researchers in the last two decades. Gradual changes of mechanical properties in FGMs decrease stress concentration, crack initiation and propagation and delamination. Many of the present and potential applications of FGM contain contact loading.This kind of loading causes surface crack initiation which is followed by subcritical crack propagation.Thus, propagation of surface cracks is one of the most important failure mechanisms in FG structures. In this article two dimensional sliding contact of a rigid flat punch on a homogeneous substrate with an FGM coating is studied. Plane strain condition is considered in this problem. The Properties of the substrate and the FGM layer are assumed to be elastic and the Poisson’s ratio is assumed to be constant. The modulus of elasticity in the graded layer is calculated based on TTO model approximation. This model defines a parameter q which considers the microstructural interactions. The governing equations are solved by Finite Difference method by means of MATLAB software. The influence of different parameters such nonhomogeneity,q, the dimensions of the punch, the thickness of the graded layer and the coefficient of friction on the mode I and II stress intensify factors are investigated.

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This paper presents the first and third order shear deformation plate theory and von Karman theories to solve Thermo-elastic problems of functionally graded hollow rotating disk. The material properties of the disk are assumed to be graded in the direction of the thickness by a power law distribution of volume fractions of the constituents. New set of equilibrium equations with small and large deflections are developed. Using small deflection theory an exact solution for displacement field is given. Solutions are obtained in series form in case of large deflection. Numerical results are presented for various percentages of ceramic-metal volume fractions and have been compared with those obtained using first-and third-order shear deformation plate theories. Also the results are verified with ABAQUS soft, simulink method and the known data in the literature.

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This paper presents an analytical solution for a FGPM hollow cylinder subjected to two dimensional electro thermo mechanical fields. All material properties except the Poisson’s ratio are assumed to be varied with power low function along the thickness of cylinder. For analytical solution, using Fourier series expansions with separate variable method, the Navier’s equations are solved. Then, with special boundary conditions, the results for a FGPM cylinder are presented. The results show the proper power index has a significant influence on electro thermo mechanical response of cylinder as a sensor or actuators. The main idea in this paper is using the Fourier series to solve the equations that caused this method be suitable for considering any complicated and simply conditions for problem.

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In this paper, elastic-plastic deformation of a rotating hollow FGM cylinder is analytically studied based on small strain theory and for plane-strain state. Variation of elasticity modulus, density and yield stress are assumed to obey power-law functions of radial coordinate. Material was assumed to obey Tresca yield criterion and its associated flow rule. To evaluate and validate the presented analysis, numerical results were compared with previously published results for homogeneous and also FGM cylinder with constant density and yield stress, as two special cases. Then the effect of density and yield stress variation, which was not considered in the previous researches, was investigated on the elastic-plastic deformation of the FGM rotating cylinder. The results show that when the variation of density and yield stress is ignored, considerable differences may arise not only in the magnitude of computed radial displacement and stress and strain components, but also in predicting the pattern of yield initiation and also plastic zone development.

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In this study, numerical solution of non-Fourier heat conduction is discussed by a fractional single phase lag model in an inhomogeneous hollow cylinder made of a functionally graded material. For this purpose, all material properties of the media are assumed to vary continuously according to a power-law formulation except the phase lag and fractional order considered as constants. It is assumed that the cylinder is one-dimensional, symmetric and without any heat source. The governing equation has been solved numerically in a try and error algorithm to find the phase lag and the fractional order using an implicit numerical method. In order to validate the results, the numerical solutions of the fractional single phase lag model and the dual phase lag model are compared to the results of semi-analytical dual-phase lag. In the following the influence of non-homogeneity parameters is studied on the maximum transient temperature and thermal wave transmission speed. The temperature distribution is investigated from wave creation instance to steady state thermal distribution. Finally, the effect of different time delays and fraction orders on the temperature distribution is investigated.

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This study is investigated vibration analysis of a FG rectangular plate partially contacting with a bounded fluid. Wet dynamic transverse displacement of the plates is approximated by a set of admissible trial functions which is required to satisfy the clamped (CL) and simply supported moveable (SSM) and simply supported immoveable (SSI) geometric boundary conditions. The oscillatory behavior of fluid is obtained by solving the Laplace equation and satisfies the boundary conditions. The natural frequencies and mode shapes of the plate coupled with sloshing fluid modes are calculated by using the Rayleigh–Ritz method based on minimizing the Rayleigh quotient. The proposed method is validated with available data in the literature. In the numerical results, the effects of volume fraction coefficient, thickness ratios and aspect ratios of the FG plates and depth of the fluid, width of the tank, and boundary conditions on the wet natural frequencies are examined and discussed in detail.

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This paper presents an elastic parametric analysis for the purpose of investigating the limit angular speed, displacement and stresses in rotating disks made of functionally graded materials (FGMs) based on Tresca yield criterion. The material properties obey the power law in radial direction. The Poisson’s ratio due to slight variations in engineering materials is assumed constant. For different values of inhomogeneity constant, limit angular speed, displacement and stresses in radial direction are plotted and for the commencement of the plastic flow, different states are investigated. state1: onset of plastic flow at the inner radius, state2: onset of plastic flow at the outer radius, state3: onset of plastic flow as the simultaneously at both radii and state4: onset of plastic flow between the inner and outer radii. To the best of the researchers’ knowledge, so far, in the papers which have been dealing with the investigation of onset yield analysis, the density and yield stress has been assumed constant; however, in this paper by assuming varying density and yield stress in rotating disks made of functionally graded materials and comparing results obtained by fixing these parameters, it has been observed that taking the density as a constant value is wrong and varying it has significant effects on the stresses.

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In this study, static and free vibration behaviors of two type of sandwich plates based on the three dimensional theory of elasticity are investigated. The core layer of one type is functionally graded (FG) with the homogeneous face sheets where as in second type the core layer is isotropic with the face sheets FG material. Plate is under uniform pressure at the top surface and free from traction in the bottom surface. The effective material properties of FG layers are estimated to vary continuously through the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. State space differential equations are obtained from equilibrium equations and constitutive relations. The obtained governing differential equations are solved by using Fourier series expansion along the in plane directions and state space technique across the thickness direction. Accuracy and exactness of the present approach is validated by comparing the numerical results with the published results. Furthermore it is possible to validate the exactness of the conventional two dimensional theories. Finally the influences of volume fraction, width-to-thickness ratios and aspect ratio on the vibration and static behaviors of plate are investigated.

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In this paper the three dimensional dynamic analysis and stress wave propagation in thick functionally graded plate subjected to impact loading is studied. Material properties (elasticity modulus and density) are assumed to vary continuously through the thickness direction of the plate according to a simple power law distributions and the Poisson’s ratio is assumed to be constant. The equations of motion are based on three dimensional theory of elasticity. The three dimensional Graded Finite Element Method (GFEM) based on Rayleigh-Ritz energy formulation and Newmark direct integration method has been applied to solve the equations in time and space domains. It is assumed that in dynamic loading the upper surface of the plate is subjected to a pressure load that varies linearly with time, and suddenly is unloaded at a specified time. This unloading acts as an impact loading. Afterward, the time histories of displacement through the thickness, stresses in three dimensions and velocity of stress wave propagation for different values of power law exponents, various boundary conditions and thickness to length ratios have been investigated. The obtained results are in agreement with available data in literature.

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In this paper the creep behavior of a functionally graded (FG) rotating disc made of Aluminum 6061 and Silicon Carbide is investigated and the optimum volume fraction of FG disc and its profile has been obtained. For this purpose, the temperature gradiant along the disc radius is obtained by solving the govering heat transfer differential equation. All the thermal properties of the material are assumed to be the function of temperature and volume fraction. To obtain material properties, two models of Mori-Tanaka and Hashin-Schtrickman are used. To validate the results, they are compared with those given in the literature. Two solution methods: semi-analytical and closed form are employed and the results are compared. The optimum design is carried out with one, and multi-objective methods which are based on genetic algorithm. The objectives are increasing the factor of safety, reducing the weight of the disc and reducing the range between minimum and maximum safety factors. The design variables are percentage of volume fraction, the power of material distribution formula, and the thickness of the disc. The results show that two solution methods compare well. Also, it has been shown that high fraction of Silicon Carbide in the outer side the disc provide optimum results. Also, contradiction of the objectives is reviled, hence the results are presented as Pareto front.

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To investigate, understanding and predicting dynamic fracture behavior of a cracked body, dynamic stress intensity factors (DSIFs) are important parameters. In the present work interaction integral method is presented to compute static and dynamic stress intensity factors for three-dimensional cracks contained in the functionally graded materials (FGMs), and is implemented in conjunction with the finite element method (FEM). By a suitable definition of the auxiliary fields, the interaction integral method which is not related to derivatives of material properties can be obtained. For the sake of comparison, center, edge and elliptical cracks in homogeneous and functionally graded materials under static and dynamic loading are considered. Then material gradation is introduced in an exponential form in the two directions in and normal to the crack plane. Then the influence of the graded modulus of elasticity on static and dynamic stress intensity factors is investigated. It has been shown that, material gradation has considerable reduce influence on DSIFs of functionally graded material in comparison with homogenous material. While, static stress intensity factors can decrease or increase, depend on the direction of gradation material property.

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In this paper, three dimensional frequency analysis of moderately thick plate with considering the effect of a circular hole is presented by using of Three Dimensional theory of Elasticity and a numerical mesh-less method with radial point interpolation functions. Using this numerical method, the field variable (such as displacement) is interpolated just using nodes scattered in the plate domain. Because there is no relation between nodes, they can be scattered arbitrarily in the problem domain. The plate is made of a functionally graded material that is consists of two different phases of metal and ceramic. Mechanical properties of the plate change independently in the length, width and thickness directions of it using (according to) Mori-Tanaka model. The effects of radius of holes, different volume fraction exponents of functionally graded plate in three directions and different boundary conditions on natural frequencies of the plate is investigated by using of the code written in MATLAB and simulation in ABAQUS. The results have been compared with results in available papers and it shows the high accuracy of the method used in this present work.

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This study deals with thermo-elasto-plastic behaviour of functionally graded thick-walled cylinder that is exposed to internal pressure and temperature gradient. For this purpose, Von-Mises yield criterion and Prandtl-Reuss flow-rule under state of plane strain are utilized. The modulus of elasticity, the thermal conductivity and thermal expansion coefficients are assumed to obey the power function in the radial position according to Erdogan’s model. In this work, the presented approach leads to the definition of new formulation to determine the elastic limit pressure and predict the onset radius of yielding, spread and growth of plastic zone. The governing equilibrium equation of cylindrical shell in axi-symmetrical status is solved in order to determine the distribution of radial, circumferential stresses and radial displacement. Various examples are handled to investigate the effect of FG-power law parameters on the yield pattern and distribution of plastic zone. The distribution of radial displacement, radial and circumferential stresses are expressed as the functions of radial position. The numerical results show that by the appropriate choice of the FG parameters and the specified thermal gradient, the plastic zone can commence simultaneously from inside and outside or intermediate radius.

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In this article, the buckling of multilayer rectangular thick plate made of functionally graded, transversely isotropic and piezoelectric materials in both closed and open circuit conditions are investigated. Based on the shear and normal higher-order deformation theory, the governing equilibrium equations of plate are obtained using the principle of minimum total potential energy and Maxwell’s equation. Using an analytical approach, the governing stability equations of functionally graded rectangular plates with piezoelectric layers have been presented in terms of displacement components and electric potentials. In order to obtain the stability equations, the adjacent equilibrium criterion is used. The stability equations are then solved analytically, assuming simply support boundary condition along all edges. Finally after ensuring the validation of the results, the effects of different parameters such as different loading conditions, functionally graded power law index, thickness-to-length ratio and aspect ratio, on the critical buckling loads of plates are studied in details. Furthermore, the effect of piezoelectric thickness on the plate critical buckling loads has been studied. The results present better accuracy in comparison with the classic and third order shear theories.

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In this paper, pull-in instability of a cantilever beam type nanoactuator made of the functionally graded material (FGM) based on higher order modified strain gradient theory investigated. It is assumed that the functionally graded beam, made of germanium and silicon, follows the volume fraction definition and law of mixtures, and its properties change as a power function through its thickness. By changing the germanium constituent volume fraction percent of the nano-beam, five different types of the nano-beams are investigated. The influences of the volume fraction index, length scale parameter and the intermolecular forces, on the pull-in instability are examined. Principle of minimum total potential energy used to derive the nonlinear governing differential equation and consistent boundary conditions which is then solved using the differential quadrature method (DQM). The present analysis is validated through direct comparisons with published other research methods and experimental results and after comparison excellent agreement has been achieved between new solution method and other experimental and numerical solution results. Besides, the results demonstrate that size effect and amount of volume fraction have a substantial impact on the pull-in instability behavior of beam-type nanoactuator.

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The major concern in Shallow arches behavior under lateral loading is their instability at a critical load, which can make the structure to collapse or displace to another stable configuration, a phenomenon called snap through. By introduction of functionally graded materials in recent years, and incorporating them into this problem, interesting results can be obtained which can give structures with favorable stability properties. In this work, dynamic stability of the hinged-hinged functionally graded shallow arch under implusive loading is investigated. Material properties vary through the thickness by power law. Nonlinear governing equations are derived using Euler-Bernoulli beam assumption and equations of motion are expressed by a nonlinear differential-integral equation. The solution utilizes a Fourier form of response. The procedure of analysis of dynamic stability that is followed in this work uses the total energy of the system and the Lyapunov function in the phase space that consists of essentially three steps: First, one finds all the possible equilibrium configurations of the shallow arch. Next, the local dynamic stability of each of the equilibrium configurations is studied.. Last, when the preferred configuration from which a snap through may occur is locally stable and when there is at least one other locally stable equilibrium configuration, then we proceed to find a sufficient, condition for stability against snap through. The effect of gradation on stability and critical load of the arch is investigated in detail.

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In this paper a method has been developed to obtain an optimum material distribution for a cylindrical shell with Functionally Graded (FG) material and additional piezoelectric outer layer. The objective of the optimization is to satisfy full stress loading criterion. For this purpose; firstly, a solution method has been outlined in which, the governing equations are developrd by combining First order Shear Deformation Theory (FSDT) and Maxwell equations, with the use of Hamilton principle. Dynamic analysis is a major concern in this solution method because of the significant dynamic displacements, strains and stresses due to the effect of moving load. Hence, the time dependent transient responses of the structure and stress distribution have been obtained. At the next stage, a methodology has been introduced to obtain the optimum material distribution. In this method, instead of using pre-assumed material distribution functions which impose limitations to the manufacturing of the shell and also to the optimization solution, control points with Hermite functions are used. The thickness of the shell and volume fraction of the FG material at these points have been regarded as optimization variables. The optimization method is based on the genetic algorithm and to reduce the solution time, calculations are carried out using parallel processing in four cores. The results show that the developed method is capable of analyzing the FG structures and provide optimum solution. The major advantage of this method is its flexibility in providing volume fraction distribution of the material.