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1 - Functionally Graded Materials: Processing Techniques and Applications
A Rabieifar V Abouei Mehrizi M Ghanbari HaghighiFunctionally graded materials (FGMs) revealed an immense growth with worldwide demand. This paper describes a brief review of the feasibility of production methods (solid, liquid, and gaseous methods) chosen for FGMs, with the aid of schematic diagrams. Advanced FGM fab أکثرFunctionally graded materials (FGMs) revealed an immense growth with worldwide demand. This paper describes a brief review of the feasibility of production methods (solid, liquid, and gaseous methods) chosen for FGMs, with the aid of schematic diagrams. Advanced FGM fabrication techniques such as additive manufacturing and laser deposition, which have been gaining importance are also explored. The evolution of fabrication techniques is correlated to the industrial requirements along with their merits and limitations. This review article also highlights some advanced engineering applications observed for FGMs. Comparing various fabrication technologies employed for FGMs, centrifugal casting was the most established and economically feasible method that met vast industrial product demands like hybrid and double-graded FGMs. Powder metallurgy was preferred for bulk gradation in spite of their sharp transitions across layers. Advanced FGM fabrication techniques like additive manufacturing, electrochemical gradation, and laser deposition techniques improved critical production parameters like precision, gradation control, etc. Thermal spraying successfully improved the heat insulation performance of FGMs. تفاصيل المقالة -
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2 - Experimental and Numerical Analysis of Titanium/HA FGM for Dental Implantation
Sina Sazesh Aazam Ghassemi Reza Ebrahimi Mohammad KhodaeiFGM dental implants are a very good alternative with respect to homogenous implants. In this study by focusing on mechanical property as one of the most important factors in implant design, the static behaviour of Ti/Nanostructure HA (hydroxyapatite) FGM dental implant أکثرFGM dental implants are a very good alternative with respect to homogenous implants. In this study by focusing on mechanical property as one of the most important factors in implant design, the static behaviour of Ti/Nanostructure HA (hydroxyapatite) FGM dental implant has been fabricated and investigated experimentally and numerically. At the first step, the nanostructure hydroxyapatite powders were synthesized by natural origin. At the second step, the initial powders were cold compacted in order to fabricate Ti/HA FGM samples for 4 different volume fraction exponents (N=1/3, 2/3, 1, 2). Then the compacted powders have been sintered using a vacuum furnace, in which compressive strength of each particular sample was finally assessed. A three-dimensional geometrical model of FGM dental implant system and surrounding bone was created by using the macro programming language in ANSYS software and then finite element analysis under static forces was performed. Finally the experimental results strength tests were compared with numerical solutions. According to the results, the FGM dental implants made of Ti/HA under static forces were sufficiently safe. As a result, FGM sample with volume fraction exponent of N=2/3 was chosen as the best sample. تفاصيل المقالة -
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3 - Stress Wave Propagation in 2D Functionally Graded Media: Optimization of Materials Distribution
Parham Rajabi Hossein Rahmani Alireza AmiriIn this paper, the analysis and optimization of the effect of the materials distribution on the behavior of 2D functionally graded media subjected to impacted loading has been investigated. First, it is assumed that there are two cases for distributing the components in أکثرIn this paper, the analysis and optimization of the effect of the materials distribution on the behavior of 2D functionally graded media subjected to impacted loading has been investigated. First, it is assumed that there are two cases for distributing the components in the FG material. In the first case, the power law is considered for materials distribution, and in the second case, the volume fractional changes of the components are made by third degree interpolation. Considering the elastodynamic behavior of the FG materials under loading, the general governing equations of the wave propagation are extracted for the case of properties variation in two dimensions and then the equations are solved using the finite difference method. Finally, an optimization has been made using a single objective genetic algorithm. The results show that the materials distribution has a considerable effect of stress wave propagation in FGMs. تفاصيل المقالة -
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4 - Evaluation of Critical Buckling Load in FG Plate using Analytical and Finite Elements Methods
Hossein Ahmadi Rashid AMIR GHIASVAND Maziar Mahdipour Jalilian Mahdi KazemiIn this paper, analytical and finite element solutions of mechanical buckling of a thick Functionally Graded (FG) plate have been investigated. Boundary conditions have been assumed as simply supported at all edges and three different loadings have been applied. In anal أکثرIn this paper, analytical and finite element solutions of mechanical buckling of a thick Functionally Graded (FG) plate have been investigated. Boundary conditions have been assumed as simply supported at all edges and three different loadings have been applied. In analytical section the procedure of developing the critical buckling force by third order shear theory has been presented and then the stability Equations have been reduced from 5 to 2. In continue, the problem has been solved using numerical simulation by ABAQUS. To validate the FEM, results have been compared and validated with analytical solution. The results show that the bi-axial compression loading case with the loading ratio of R to one and R to zero are the most possible and most unlikely case in buckling occurrence, respectively. تفاصيل المقالة -
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5 - Influence of Viscoelastic Foundation on Dynamic Behaviour of the Double Walled Cylindrical Inhomogeneous Micro Shell Using MCST and with the Aid of GDQM
A Mohammadi H Lashini M Habibi H SafarpourIn this article, dynamic modeling of double walled cylindrical functionally graded (FG) microshell is studied. Size effect of double walled cylindrical FG microshell are investigated using modified couple stress theory (MCST). Each layer of microshell is embedded in a v أکثرIn this article, dynamic modeling of double walled cylindrical functionally graded (FG) microshell is studied. Size effect of double walled cylindrical FG microshell are investigated using modified couple stress theory (MCST). Each layer of microshell is embedded in a viscoelasticmedium. For the first time, in the present study, has been considered, FG length scale parameter in double walled cylindrical FG microshells, which this parameter changes along the thickness direction. Taking into consideration the first-order shear deformation theory (FSDT), double walled cylindrical FG microshell is modeled and its equations of motions are derived using Hamilton's principle. The novelty of this study is considering the effects of double layers and MCST, in addition to considering the various boundary conditions of double walled cylindrical FG microshell. Generalized differential quadrature method (GDQM) is used to discretize the model and to approximate the equation of motions and boundary conditions. Also, for confirmation, the result of current model is validated with the results obtained from molecular dynamics (MD) simulation. Considering length scale parameter (l=R/3) on MCST show, the results have better agreement with MD simulation. The results show that, length, thickness, FG power index, Winkler and Pasternak coefficients and shear correction factor have important role on the natural frequency of double walled cylindrical FG microshell. تفاصيل المقالة -
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6 - A Generalized Thermo-Elastic Diffusion Problem in a Functionally Graded Rotating Media Using Fractional Order Theory
K Paul B MukhopadhyayA generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the th أکثرA generalized thermo-elastic diffusion problem in a functionally graded isotropic, unbounded, rotating elastic medium due to a periodically varying heat source in the context of fractional order theory is considered in our present work. The governing equations of the theory for a functionally graded material with GNIII model are established. Analytical solution of the problem is derived in Laplace-Fourier transform domain. Finally, numerical inversions are used to show the effect of rotation, non-homogeneity and fractional parameter on stresses, displacement, chemical potential, mass distribution, temperature, etc. and those are illustrated graphically. تفاصيل المقالة -
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7 - Vibrations of Inhomogeneous Viscothermoelastic Nonlocal Hollow Sphere under the effect of Three-Phase-Lag Model
S.R Sharma M.K Sharma D.K SharmaHerein, the free vibrations of inhomogeneous nonlocal viscothermoelastic sphere with three-phase-lag model of generalized thermoelasticity have been addressed. The governing equations and constitutive relations with three-phase-lag model have been solved by using non-di أکثرHerein, the free vibrations of inhomogeneous nonlocal viscothermoelastic sphere with three-phase-lag model of generalized thermoelasticity have been addressed. The governing equations and constitutive relations with three-phase-lag model have been solved by using non-dimensional quantities. The simple power law has been presumed to take the material in radial direction. The series solution has been established to derive the solution analytically. The relations of frequency equations for the continuation of viable modes are developed in dense form. The analytical results have been authenticated by the reduction of nonlocal and three–phase–lag parameters. To investigate the quality of vibrations, frequency equations are determined by applying the numerical iteration method. MATLAB software tools have been used for numerical computations and simulations to present the results graphically subject to natural frequencies, frequency shift, and thermoelastic damping. The numerical results clearly show that the variation of vibrations is slightly larger in case of nonlocal elastic sphere in contrast to elastic sphere. تفاصيل المقالة -
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8 - Elasticity Exact Solution for an FGM Cylindrical Shaft with Piezoelectric Layers Under the Saint-Venant Torsion by Using Prandtl’s Formulation
M. R Eslami M Jabbari A Eskandarzadeh SabetFunctionally graded materials (FGMs) belong to a noble family of composite material possess material properties varying gradually in a desired direction or orientation. In a past decade, functionally graded materials were remained in an interest of material investigator أکثرFunctionally graded materials (FGMs) belong to a noble family of composite material possess material properties varying gradually in a desired direction or orientation. In a past decade, functionally graded materials were remained in an interest of material investigators due to its prominent features, and have extensively used in almost every discipline of engineering which in turn significantly increases the number of research publication of FGM. In this paper the exact elasticity solution for an FGM circular shaft with piezo layers is analysed. piezoelectric layers are homogeneous and the modulus of elasticity for FGM varies continuously with the form of an exponential function. The shear modulus of the non-homogeneous FGM shaft is a given function of the Prandtl’s stress function of considered circular shaft when its material is homogeneous. state equations are derived. The Prandtl’s stress function and electric displacement potential function satisfy all conditions. The shearing stresses, torsional rigidity, torsional function for FGM layer and shearing stresses, electric displacements, torsional rigidity, electrical torsional rigidity ,torsional and electrical potential functions for piezoelectric layers are obtained. Exact analytical solution for hollow circular cross-section presented. At the end some graphs and conclusions are given. تفاصيل المقالة -
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9 - Dynamic Stability Analysis of Bi-Directional Functionally Graded Beam with Various Shear Deformation Theories Under Harmonic Excitation and Thermal Environment
A Ghorbanpour Arani Sh Niknejad A Mihankhah I SafariIn this article, dynamic stability analysis of bi-directional functionally graded materials (BDFGMs) beam rested on visco-Pasternak foundation under harmonic excitation is studied. Also, BDFGMs beam is subjected to a transversely uniformly distributed temperature rising أکثرIn this article, dynamic stability analysis of bi-directional functionally graded materials (BDFGMs) beam rested on visco-Pasternak foundation under harmonic excitation is studied. Also, BDFGMs beam is subjected to a transversely uniformly distributed temperature rising and it is assumed that the material properties to be temperature-dependent. According to the exponential and power law distributions, thermo-mechanical properties of BDFGMs beam vary continuously in both the thickness and longitudinal directions. Based on various shear deformation theories (e.g. Euler-Bernoulli, Timoshenko, third order shear deformation and sinusoidal shear deformation theories), the stability equations of BDFGMs beam is derived by applying the Hamilton's principle. The generalized differential quadrature method (GDQM) in conjunction with the Bolotin method is utilized to solve the differential stability equations under SS, SC and CC boundary conditions. To validate the present analysis, a comparison study is carried out with the results found in the literature and a good agreement is observed compared to the reported results. Finally, numerical results are presented to study the influences of the gradient index, length-to-thickness ratio, temperature rise and foundation parameters on the dynamic stability region of BDFGMs beam. The results of presented paper can be used to the optimal design and assessment of the structural failure. تفاصيل المقالة -
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10 - Closed-Form Formulation for Bending Analysis of Functionally Graded Thick Plates
M Shaban M. J KhoshgoftarDue to their continuous material variation and eliminating the mismatch stress field in the thickness direction, Functionally Graded Materials (FGMs) have found wide applications in aerospace and mechanical engineering. This article presents closed-form solution for thi أکثرDue to their continuous material variation and eliminating the mismatch stress field in the thickness direction, Functionally Graded Materials (FGMs) have found wide applications in aerospace and mechanical engineering. This article presents closed-form solution for thick functionally graded plate based on three-dimensional elasticity theory. To this end, first, the characteristic equation of FG plate is derived and general closed-form is obtained analytically. Both positive and negative discriminant of characteristic equation is considered and solved. The presented method is validated with finite element results by considering isotropic thick plate. Several parametric studies are carried out to investigate the effect of geometric and material parameters. The aim of this research is to present analytical solution form for thick FG plate and work out the problem of inconsistency for corresponding displacements field. The presented solution can be used to examine accuracy of various plate theories such as first-order, third order shear deformation theories and other equivalent plate theories. تفاصيل المقالة -
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11 - An Efficient Co Finite Element Approach for Bending Analysis of Functionally Graded Ceramic-Metal Skew Shell Panels
G Taj A ChakrabartiIn this article, the prominence has been given to study the influence of skew angle on bending response of functionally graded material shell panels under thermo-mechanical environment. Derivation of governing equations is based on the Reddy’s higher-order shear d أکثرIn this article, the prominence has been given to study the influence of skew angle on bending response of functionally graded material shell panels under thermo-mechanical environment. Derivation of governing equations is based on the Reddy’s higher-order shear deformation theory and Sander’s kinematic equations. To circumvent the problem of C1 continuity requirement coupled with the finite element implementation, C0 formulation is developed. A nine noded isoparametric Lagrangian element has been employed to mesh the proposed shell element in the framework of finite element method. Bending response of functionally graded shell under thermal field is accomplished by exploiting temperature dependent properties of the constituents. Arbitrary distribution of the elastic properties follows linear distribution law which is a function of the volume fraction of ingredients. Different combinations of ceramic-metal phases are adopted to perform the numerical part. Different types of shells (cylindrical, spherical, hyperbolic paraboloid and hypar) and shell geometries are concerned to engender new-fangled results. Last of all, the influence of various parameters such as thickness ratio, boundary condition, volume fraction index and skew angle on the bending response of FGM skew shell is spotlighted. Some new results pertain to functionally graded skew shells are reported for the first time, which may locate milestone in future in the vicinity of functionally graded skew shells. تفاصيل المقالة -
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12 - Fractional Order Generalized Thermoelastic Functionally Graded Solid with Variable Material Properties
A Sur M KanoriaIn this work, a new mathematical model of thermoelasticity theory has been considered in the context of a new consideration of heat conduction with fractional order theory. A functionally graded isotropic unbounded medium is considered subjected to a periodically varyin أکثرIn this work, a new mathematical model of thermoelasticity theory has been considered in the context of a new consideration of heat conduction with fractional order theory. A functionally graded isotropic unbounded medium is considered subjected to a periodically varying heat source in the context of space-time non-local generalization of three-phase-lag thermoelastic model and Green-Naghdi models, in which the thermophysical properties are temperature dependent. The governing equations are expressed in Laplace-Fourier double transform domain and solved in that domain. Then the inversion of the Fourier transform is carried out by using residual calculus, where poles of the integrand are obtained numerically in complex domain by using Laguerre’s method and the inversion of Laplace transform is done numerically using a method based on Fourier series expansion technique. The numerical estimates of the thermal displacement, temperature and thermal stress are obtained for a hypothetical material. Finally, the obtained results are presented graphically to show the effect of non-local fractional parameter on thermal displacement, temperature and thermal stress. A comparison of the results for different theories (three-phase-lag model, GN model II, GN model III) is presented and the effect of non-homogeneity is also shown. The results, corresponding to the cases, when the material properties are temperature independent, agree with the results of the existing literature. تفاصيل المقالة -
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13 - Buckling Analyses of Rectangular Plates Composed of Functionally Graded Materials by the New Version of DQ Method Subjected to Non-Uniform Distributed In-Plane Loading
R Kazemi Mehrabadi V.R MirzaeianIn this paper, the new version of differential quadrature method (DQM), for calculation of the buckling coefficient of rectangular plates is considered. At first the differential equations governing plates have been calculated. Later based on the new version of differen أکثرIn this paper, the new version of differential quadrature method (DQM), for calculation of the buckling coefficient of rectangular plates is considered. At first the differential equations governing plates have been calculated. Later based on the new version of differential quadrature method, the existing derivatives in equation are converted to the amounts of function in the grid points inside the region. Having done that, the equation will be converted to an eigen value problem and the buckling coefficient is obtained. Solving this problem requires two kinds of loading: (1) unaxial half-cosine distributed compressive load and (2) uni-axial linearly varied compressive load. Having considered the answering in this case and the analysis of the effect of number of grid points on the solution of the problem, the accuracy of answering is considered, and also the effect of power law index over the buckling coefficient is investigated. Finally, if the case is an isotropic type, the results will be compared with the existing literature. تفاصيل المقالة -
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14 - A Semi-analytical Approach to Elastic-plastic Stress Analysis of FGM Pressure Vessels
A.T Kalali S Hadidi-MoudAn analytical method for predicting elastic–plastic stress distribution in a cylindrical pressure vessel has been presented. The vessel material was a ceramic/metal functionally graded material, i.e. a particle–reinforcement composite. It was assumed that th أکثرAn analytical method for predicting elastic–plastic stress distribution in a cylindrical pressure vessel has been presented. The vessel material was a ceramic/metal functionally graded material, i.e. a particle–reinforcement composite. It was assumed that the material’s plastic deformation follows an isotropic strain-hardening rule based on the von-Mises yield criterion, and that the vessel was under plane-stress conditions. The mechanical properties of the graded layer were modelled by the modified rule of mixtures. By assuming small strains, Hencky’s stress–strain relation was used to obtain the governing differential equations for the plastic region. A numerical method for solving those differential equations was then proposed that enabledthe prediction of stress state within the structure. Selected finite element results were also presented to establish supporting evidence for the validation of the proposed analytical modelling approach. Similar analyses were performed and solutions for spherical pressure made of FGMs were also provided. تفاصيل المقالة -
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15 - Comparison of Various Shell Theories for Vibrating Functionally Graded Cylindrical Shells
M JavadinejadThe classical shell theory, first-order shear deformation theory, and third-order shear deformation theory are employed to study the natural frequencies of functionally graded cylindrical shells. The governing equations of motion describing the vibration behavior of fun أکثرThe classical shell theory, first-order shear deformation theory, and third-order shear deformation theory are employed to study the natural frequencies of functionally graded cylindrical shells. The governing equations of motion describing the vibration behavior of functionally graded cylindrical shells are derived by Hamilton’s principle. Resulting equations are solved using the Navier-type solution method for a functionally graded cylindrical shell with simply supported edges. The effects of transverse shear deformation, geometric size, and configurations of the constituent materials on the natural frequencies of the shell are investigated. Validity of present formulation was checked by comparing the numerical results with the Love’s shell theory. تفاصيل المقالة -
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16 - Free Vibration Analysis of Moderately Thick Functionally Graded Plates with Multiple Circular and Square Cutouts Using Finite Element Method
J Vimal R.K Srivastava A.D Bhatt A.K SharmaA simple formulation for studying the free vibration of shear-deformable functionally graded plates of different shapes with different cutouts using the finite element method is presented. The aim is to fill the void in the available literature with respect to the free أکثرA simple formulation for studying the free vibration of shear-deformable functionally graded plates of different shapes with different cutouts using the finite element method is presented. The aim is to fill the void in the available literature with respect to the free vibration results of functionally graded plates of different shapes with different cutouts. The material properties of the plates are assumed to vary according to a power law distribution in terms of the volume fraction of the constituents. Validation of the formulation is done with the help of convergence studies with respect to the number of nodes and the results are compared with those from past investigations available only for simpler problems. In this paper rectangular, trapezoidal and circular plates with cutouts are studied and the effects of volume fraction index, thickness ratio and different external boundary conditions on the natural frequencies of plates are studied. تفاصيل المقالة -
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17 - Simple Solutions for Buckling of Conical Shells Composed of Functionally Graded Materials
A LavasaniUsing Donnell-type shell theory a simple and exact procedure is presented for linear buckling analysis of functionally graded conical shells under axial compressive loads and external pressure. The solution is in the form of a power series in terms of a particularly con أکثرUsing Donnell-type shell theory a simple and exact procedure is presented for linear buckling analysis of functionally graded conical shells under axial compressive loads and external pressure. The solution is in the form of a power series in terms of a particularly convenient coordinate system. By analyzing the buckling of a series of conical shells, under various boundary conditions and different material coefficients, the validity of the presented procedure is confirmed. تفاصيل المقالة -
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18 - Inhomogeneity Material Effect on Electromechanical Stresses, Displacement and Electric Potential in FGM Piezoelectric Hollow Rotating Disk
A Ghorbanpour Arani H Khazaali M Rahnama M DadkhahIn this paper, a radially piezoelectric functionally graded rotating disk is investigated by the analytical solution. The variation of material properties is assumed to follow a power law along the radial direction of the disk. Two resulting fully coupled differential e أکثرIn this paper, a radially piezoelectric functionally graded rotating disk is investigated by the analytical solution. The variation of material properties is assumed to follow a power law along the radial direction of the disk. Two resulting fully coupled differential equations in terms of the displacement and electric potential are solved directly. Numerical results for different profiles of inhomogeneity are also graphically displayed. تفاصيل المقالة -
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19 - Vibration Analysis of Functionally Graded Spinning Cylindrical Shells Using Higher Order Shear Deformation Theory
M MehrparvarIn this paper the vibration of a spinning cylindrical shell made of functional graded material is investigated. After a brief introduction of FG materials, by employing higher order theory for shell deformation, constitutive relationships are derived. Next, governing di أکثرIn this paper the vibration of a spinning cylindrical shell made of functional graded material is investigated. After a brief introduction of FG materials, by employing higher order theory for shell deformation, constitutive relationships are derived. Next, governing differential equation of spinning cylindrical shell is obtained through utilizing energy method and Hamilton’s principle. Making use of the principle of minimum potential energy, the characteristic equation of natural frequencies is derived. After verification of the results, the effect of changing different parameters such as material grade, geometry of shell and spinning velocity on the natural frequency are examined. تفاصيل المقالة -
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20 - Frequency Analysis of FG Sandwich Rectangular Plates with a Four-Parameter Power-Law Distribution
S Kamarian M.H Yas A PourasgharAn accurate solution procedure based on the three-dimensional elasticity theory for the free vibration analysis of Functionally Graded Sandwich (FGS) plates is presented. Since no assumptions on stresses and displacements have been employed, it can be applied to the fre أکثرAn accurate solution procedure based on the three-dimensional elasticity theory for the free vibration analysis of Functionally Graded Sandwich (FGS) plates is presented. Since no assumptions on stresses and displacements have been employed, it can be applied to the free vibration analysis of plates with arbitrary thickness. The two-constituent FGS plate consists of ceramic and metal graded through the thickness, from one surface of the each sheet to the other according to a generalized power-law distribution with four parameters. The benefit of using generalized power-law distribution is to illustrate and present useful results arising from symmetric, asymmetric and classic profiles. Using the Generalized Differential Quadrature (GDQ) method through the thickness of the plate, further allows one to deal with FG plates with an arbitrary thickness distribution of material properties. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The effects of different geometrical parameters such as the thickness-to-length ratio, different profiles of materials volume fraction and four parameters of power-law distribution on the vibration characteristics of the FGS plates are investigated. Interesting result shows that by utilizing a suitable four-parameter model for materials volume fraction, frequency parameter can be obtained more than the frequency parameter of the similar FGS plate with sheets made of 100% ceramic and at the same time lighter. Also, results show that frequencies of symmetric and classic profiles are smaller and larger than that of other types of FGS plates respectively. The solution can be used as benchmark for other numerical methods and also the refined plate theories. تفاصيل المقالة -
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21 - Application of Piezoelectric and Functionally Graded Materials in Designing Electrostatically Actuated Micro Switches
A Hosseinzadeh M.T AhmadianIn this research, a functionally graded microbeam bonded with piezoelectric layers is analyzed under electric force. Static and dynamic instability due to the electric actuation is studied because of its importance in micro electro mechanical systems, especially in micr أکثرIn this research, a functionally graded microbeam bonded with piezoelectric layers is analyzed under electric force. Static and dynamic instability due to the electric actuation is studied because of its importance in micro electro mechanical systems, especially in micro switches. In order to prevent pull-in instability, two piezoelectric layers are used as sensor and actuator. A current amplifier is used to supply input voltage of the actuator from the output of the sensor layer. Using Hamilton’s principle and Euler-Bernoulli theory, equation of motion of the system is obtained. It is shown that the load type (distributed or concentrated) applied to the micro beam from the piezoelectric layer, depends on the shape of the actuator layer (E.g. rectangle, triangular). Finite element method is implemented for evaluation of displacement field in the micro beam and dynamic response of the micro beam under electric force is calculated using finite difference method. Effect of squeeze film damping on pull-in voltage and time-response of the system is considered using nonlinear Reynolds equation. Effect of several parameters such as gain value between piezoelectric sensor and actuator layer, profile of functionally material, and geometry of the system is considered on dynamic behavior of the micro beam especially on pull-in instability. Results are verified for simple cases with previous related studies in the literature and good agreements were achieved. Results indicate that increasing gain value between sensor and actuator enhances stiffness of the system and will raise pull-in voltage. Also, dependency of dynamic properties of the system such as amplitude and frequency of vibration on functionally graded material profile is shown. The material distribution of the functionally graded material is designed in such a way that results in a specific pull-in voltage. تفاصيل المقالة -
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22 - A Power Series Solution for Free Vibration of Variable Thickness Mindlin Circular Plates with Two-Directional Material Heterogeneity and Elastic Foundations
M.M Alipour M ShariyatIn the present paper, a semi-analytical solution is presented for free vibration analysis of circular plates with complex combinations of the geometric parameters, edge-conditions, material heterogeneity, and elastic foundation coefficients. The presented solution cover أکثرIn the present paper, a semi-analytical solution is presented for free vibration analysis of circular plates with complex combinations of the geometric parameters, edge-conditions, material heterogeneity, and elastic foundation coefficients. The presented solution covers many engineering applications. The plate is assumed to have a variable thickness and made of a heterogeneous material whose properties vary in both radial and transverse directions. While the edge is simply-supported, clamped, or free; the bottom surface of the plate is resting on a two-parameter (Winkler-Pasternak) elastic foundation. A comprehensive sensitivity analysis including evaluating effects of various parameters is carries out. Mindlin theory is employed for derivation of the governing equations whereas the differential transform method is used to solve the resulted equations. In this regard, both the in-plane and rotary inertia are considered. Results show that degradations caused by a group of the factors (e.g., the geometric parameters) in the global behavior of the structure may be compensated by another group of factors of different nature (e.g, the material heterogeneity parameters). Moreover, employing the elastic foundation leads to higher natural frequencies and postponing the resonances. تفاصيل المقالة -
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23 - Generalized Differential Quadrature Method for Vibration Analysis of Cantilever Trapezoidal FG Thick Plate
K Torabi H AfshariThis paper presents a numerical solution for vibration analysis of a cantilever trapezoidal thick plate. The material of the plate is considered to be graded through the thickness from a metal surface to a ceramic one according to a power law function. Kinetic and strai أکثرThis paper presents a numerical solution for vibration analysis of a cantilever trapezoidal thick plate. The material of the plate is considered to be graded through the thickness from a metal surface to a ceramic one according to a power law function. Kinetic and strain energies are derived based on the Reissner-Mindlin theory for thick plates and using Hamilton's principle, the governing equations and boundary conditions are derived in the Cartesian coordinates. A transformation of coordinates is used to convert the equations and boundary conditions from the original coordinate into a new computational coordinates. Generalized differential quadrature method (GDQM) is selected as a strong method and natural frequencies and corresponding modes are derived. The accuracy and convergence of the proposed solution are confirmed using results presented by other authors. Finally, the effect of the power law index, angles and thickness of the plate on the natural frequencies are investigated. تفاصيل المقالة -
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24 - Buckling Analysis of FG Plate with Smart Sensor/Actuator
N.S Viliani S.M.R Khalili H PorrostamiIn this paper, the active buckling control of smart functionally graded (FG) plates using piezoelectric sensor/actuator patches is studied. A simply supported FG rectangular plate which is bonded with piezoelectric rectangular patches on the top and/or the bottom surfac أکثرIn this paper, the active buckling control of smart functionally graded (FG) plates using piezoelectric sensor/actuator patches is studied. A simply supported FG rectangular plate which is bonded with piezoelectric rectangular patches on the top and/or the bottom surface(s) as actuators/sensors is considered. When a constant electric charge is imposed, the governing differential equations of motion are derived using the classical laminated plate theory (CLPT). The solution for the equation of motion is obtained using a Fourier series method and the effect of feedback gain on the critical buckling load for PZT-4 is studied .The buckling behavior of smart plate subjected to compressive load is also investigated. The sensor output is used to determine the input to the actuator using the feedback control algorithm. The forces induced by the piezoelectric actuators under the applied voltage field, enhance the critical buckling load تفاصيل المقالة -
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25 - Buckling Analysis of Simply-supported Functionally Graded Rectangular Plates under Non-uniform In-plane Compressive Loading
M MahdavianIn this research, mechanical buckling of rectangular plates of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM rectangular plate under uniform in-plane compression are derived. For isotropic materials, convergent buckling أکثرIn this research, mechanical buckling of rectangular plates of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM rectangular plate under uniform in-plane compression are derived. For isotropic materials, convergent buckling loads have been presented for non-uniformly compressed rectangular plates based on a rigorous superposition fourier solution for the in-plane Airy stress field and Galerkin’s approach for stability analysis. The results for isotropic case will be compared with reference articles and finite element method (FEM) solution. Finally, the results will be achieved for a sample of FGM material as well as the research on the effect of power law index on buckling coefficient. تفاصيل المقالة -
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26 - Calculation of Natural Frequencies of Bi-Layered Rotating Functionally Graded Cylindrical Shells
I Fakhari GolpayeganiIn this paper, an exact analytical solution for free vibration of rotating bi-layered cylindrical shell composed of two independent functionally graded layers was presented. The thicknesses of the shell layers were assumed to be equal and constant. The material properti أکثرIn this paper, an exact analytical solution for free vibration of rotating bi-layered cylindrical shell composed of two independent functionally graded layers was presented. The thicknesses of the shell layers were assumed to be equal and constant. The material properties of the constituents of bi-layered FGM cylindrical shell were graded in the thickness direction of the layers of the shell according to a volume fraction power-law distribution. In order to derive the equations of motion, the Sanders’ thin shell theory and Rayleigh-Ritz method were used. Also the results were extracted by considering Coriolis, centrifugal and initial hoop tension effects. Effects of rotating speed, geometrical parameters, and material distribution in the two functionally graded layers of the shell, circumferential and longitudinal wave number on the forward and backward natural frequencies were investigated. A comparison of the results was made with those available in the literature for the validity and accuracy of the present methodology. تفاصيل المقالة -
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27 - Influence of Rotation on Vibration Behavior of a Functionally Graded Moderately Thick Cylindrical Nanoshell Considering Initial Hoop Tension
H Safarpour M.M Barooti M GhadiriIn this research, the effect of rotation on the free vibration is investigated for the size-dependent cylindrical functionally graded (FG) nanoshell by means of the modified couple stress theory (MCST). MCST is applied to make the design and the analysis of nano actuato أکثرIn this research, the effect of rotation on the free vibration is investigated for the size-dependent cylindrical functionally graded (FG) nanoshell by means of the modified couple stress theory (MCST). MCST is applied to make the design and the analysis of nano actuators and nano sensors more reliable. Here the equations of motion and boundary conditions are derived using minimum potential energy principle and first-order shear deformation theory (FSDT). The formulation consists of the Coriolis, centrifugal and initial hoop tension effects due to the rotation. The accuracy of the presented model is verified with literatures. The novelty of this study is the consideration of the rotation effects along with the satisfaction of various boundary conditions. Generalized differential quadrature method (GDQM) is employed to discretize the equations of motion. Then the investigation has been made into the influence of some factors such as the material length scale parameter, angular velocity, length to radius ratio, FG power index and boundary conditions on the critical speed and natural frequency of the rotating cylindrical FG nanoshell. تفاصيل المقالة -
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28 - Analysis of Mode III Fraction in Functionally Graded Plate with Linearly Varying Properties
M.R TorshizianA model is provided for crack problem in a functionally graded semi-infinite plate under an anti-plane load. The characteristic of material behavior is assumed to change in a linear manner along the plate length. Also the embedded crack is placed in the direction of the أکثرA model is provided for crack problem in a functionally graded semi-infinite plate under an anti-plane load. The characteristic of material behavior is assumed to change in a linear manner along the plate length. Also the embedded crack is placed in the direction of the material change. The problem is solved using two separate techniques. Primary, by applying Laplace and Fourier transformation, the governing equation for the crack problem is converted to the solution of a singular integral equation system. Then, finite element technique is employed to analyze this problem by considering quadrilateral eight nodded singular element near the crack tips. The effects of material non-homogeneity and crack length on the stress intensity factor are studied and the results of two methods are judged against each other. تفاصيل المقالة -
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29 - Thermal Creep Analysis of Functionally Graded Thick-Walled Cylinder Subjected to Torsion and Internal and External Pressure
S Sharma S Yadav R SharmaSafety analysis has been done for the torsion of a functionally graded thick-walled circular cylinder under internal and external pressure subjected to thermal loading. In order to determine stresses the concept of Seth’s transition theory based on generalized pri أکثرSafety analysis has been done for the torsion of a functionally graded thick-walled circular cylinder under internal and external pressure subjected to thermal loading. In order to determine stresses the concept of Seth’s transition theory based on generalized principal strain measure has been used. This theory simplifies the set of mechanical equations by mentioning the order of the measure of deformation. This theory helps to achieve better agreement between the theoretical and experimental results. Results have been analyzed with or without thermal effects for functionally graded and homogeneous cylinder with linear and nonlinear strain measure.From the analysis, it has been concluded that in creep torsion cylinder made up of less functionally graded material (FGM) under pressure is better choice for designing point of view as compared to homogeneous cylinder. This is due to shear stresses which are maximum for cylinder made up of functionally graded material as compared to homogeneous material. تفاصيل المقالة -
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30 - Analytical Solutions of the FG Thick Plates with In-Plane Stiffness Variation and Porous Substances Using Higher Order Shear Deformation Theory
M karimi darani A GhasemiThis paper presents the governing equations on the rectangular plate with the variation of material stiffness through their thick using higher order shear deformation theory (HSDT). The governing equations are obtained by using Hamilton's principle with regard to variat أکثرThis paper presents the governing equations on the rectangular plate with the variation of material stiffness through their thick using higher order shear deformation theory (HSDT). The governing equations are obtained by using Hamilton's principle with regard to variation of Young's modulus in through their thick with regard sinusoidal variation of the displacement field across the thickness. In addition, the effects of the substances in FG-porous plate are investigated. تفاصيل المقالة -
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31 - Stress Analysis of Two-directional FGM Moderately Thick Constrained Circular Plates with Non-uniform Load and Substrate Stiffness Distributions
M.M Alipour M ShariyatIn the present paper, bending and stress analyses of two-directional functionally graded (FG) circular plates resting on non-uniform two-parameter foundations (Winkler-Pasternak foundations) are investigated using a first-order shear-deformation theory. To enhance the a أکثرIn the present paper, bending and stress analyses of two-directional functionally graded (FG) circular plates resting on non-uniform two-parameter foundations (Winkler-Pasternak foundations) are investigated using a first-order shear-deformation theory. To enhance the accuracy of the results, the transverse stress components are derived based on the three dimensional theory of elasticity. The solution is obtained by employing the differential transform method (DTM). The material properties are assumed to vary in both transverse and radial directions according to power and exponential laws, respectively. Intensity of the transverse load is considered to vary according to a second-order polynomial. The performed convergence analysis and the comparative studies demonstrate the high accuracy and high convergence rate of the approach. A sensitivity analysis consisting of evaluating effects of different parameters (e.g., exponents of the material properties, thickness to radius ratio, trend of variations of the foundation stiffness, and edge conditions) is carried out. Results reveal that in contrast to the available constitutive-law-based solutions, present solution guarantees continuity of the transverse stresses at the interfaces between layers and may also be used for stress analysis of the sandwich panels. The results are reported for the first time and are discussed in detail. تفاصيل المقالة -
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32 - Effects of Geometric Nonlinearity on Stress Analysis in Large Amplitude Vibration of Moderately Thick Annular Functionally Graded Plate
M.H Amini A Rastgoo M SoleimaniThis paper deals with the nonlinear free vibration of thick annular functionally graded material plates. The thickness is assumed to be constant. Material properties are assumed to be graded in the thickness direction according to a simple power law distribution in term أکثرThis paper deals with the nonlinear free vibration of thick annular functionally graded material plates. The thickness is assumed to be constant. Material properties 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 formulations are based on the first-order shear deformation plate theory and von Kármán-type equation. For harmonic vibrations, by using assumed-time-mode method sinusoidal oscillations are assumed, then the time variable is eliminated by applying Kantorovich averaging method. Thus, the basic governing equations for the problem are reduced to a set of ordinary differential equations in term of radius. The results reveal that vibration amplitude and volume fraction have significant effects on the resultant stresses in large amplitude vibration of the functionally graded thick plate. تفاصيل المقالة -
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33 - Theoretical Formulations for Finite Element Models of Functionally Graded Beams with Piezoelectric Layers
J.N Reddy S Doshi A MulianaIn this paper an overview of functionally graded materials and constitutive relations of electro elasticity for three-dimensional deformable solids is presented, and governing equations of the Bernoulli–Euler and Timoshenko beam theories which account for through- أکثرIn this paper an overview of functionally graded materials and constitutive relations of electro elasticity for three-dimensional deformable solids is presented, and governing equations of the Bernoulli–Euler and Timoshenko beam theories which account for through-thickness power-law variation of a two-constituent material and piezoelectric layers are developed using the principle of virtual displacements. The formulation is based on a power-law variation of the material in the core with piezoelectric layers at the top and bottom. Virtual work statements of the two theories are also developed and their finite element models are presented. The theoretical formulations and finite element models presented herein can be used in the analysis of piezolaminated and adaptive structures such as beams and plates. تفاصيل المقالة -
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34 - On the Analysis of FGM Beams: FEM with Innovative Element
M Zakeri A Modarakar Haghighi R AttarnejadThis paper aims at presenting a new efficient element for free vibration and instability analysis of Axially Functionally Graded Materials (FGMs) non-prismatic beams using Finite Element Method (FEM). Using concept of Basic Displacement Functions (BDFs), two- node eleme أکثرThis paper aims at presenting a new efficient element for free vibration and instability analysis of Axially Functionally Graded Materials (FGMs) non-prismatic beams using Finite Element Method (FEM). Using concept of Basic Displacement Functions (BDFs), two- node element extends to three-node element for obtaining much more exact results using FEM. First, BDFs are introduced and computed using energy method such as unit-dummy load method. Afterward, new efficient shape functions are developed in terms of BDFs during the procedure based on the mechanical behavior of the element in which presented shape functions benefit generality and accuracy from stiffness and force method, respectively. Finally, deriving structural matrices of the beam with respect to new shape functions; free vibration and instability analysis of the FGM beam are studied using finite element method for all types of AFGM beams and the convergence of FEM has been studied. The results from both free vibration and instability analysis are in perfect agreement with those of previously published. تفاصيل المقالة -
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35 - First-Order Formulation for Functionally Graded Stiffened Cylindrical Shells Under Axial Compression
A HasaniThe buckling analysis of stiffened cylindrical shells by rings and stringers made of functionally graded materials subjected to axial compression loading is presented. It is assumed that the material properties vary as a power form of the thickness coordinate variable. أکثرThe buckling analysis of stiffened cylindrical shells by rings and stringers made of functionally graded materials subjected to axial compression loading is presented. It is assumed that the material properties vary as a power form of the thickness coordinate variable. The fundamental relations, the equilibrium and stability equations are derived using the first order shear deformation theory. Resulting equations are employed to obtain the critical buckling loads. The effects of the material properties and geometry of shell on the critical buckling loads are examined. Excellent agreement with the results in the literature indicates the correctness of the proposed closed form solution. تفاصيل المقالة -
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36 - Effect of Exponentially-Varying Properties on Displacements and Stresses in Pressurized Functionally Graded Thick Spherical Shells with Using Iterative Technique
M Zamani Nejad A Rastgoo A HadiA semi-analytical iterative method as one of the newest analytical methods is used for the elastic analysis of thick-walled spherical pressure vessels made of functionally graded materials subjected to internal pressure. This method is accurate, fast and has a reasonabl أکثرA semi-analytical iterative method as one of the newest analytical methods is used for the elastic analysis of thick-walled spherical pressure vessels made of functionally graded materials subjected to internal pressure. This method is accurate, fast and has a reasonable order of convergence. It is assumed that material properties except Poisson’s ratio are graded through the thickness direction of the sphere according to an exponential distribution. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and von Mises equivalent stress, as a function of radial direction, are obtained. A numerical solution, using finite element method (FEM), is also presented. Good agreement was found between the semi-analytical results and those obtained through FEM. تفاصيل المقالة -
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37 - Elastic-Plastic Transition of Pressurized Functionally Graded Orthotropic Cylinder using Seth’s Transition Theory
S Sharma R PanchalIn this paper the radial deformation and the corresponding stresses in a functionally graded orthotropic hollow cylinder with the variation in thickness and density according to power law and rotating about its axis under pressure is investigated by using Seth's transit أکثرIn this paper the radial deformation and the corresponding stresses in a functionally graded orthotropic hollow cylinder with the variation in thickness and density according to power law and rotating about its axis under pressure is investigated by using Seth's transition theory. The material of the cylinder is assumed to be non-homogeneous and orthotropic. This theory helps to achieve better agreement between experimental and theoretical results. Results has been mentioned analytically and numerically. From the analysis, it has been concluded that cylinder made up of orthotropic material whose thickness increases radially and density decreases radially is on the safer side of the design as circumferential stresses are high for cylinder made up of isotropic material as compared to orthotropic material. This paper is based on elastic-plastic behavior which plays important role in practical design of structures for safety factor. تفاصيل المقالة -
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38 - Vibration Analysis of FG Nanoplate Based on Third-Order Shear Deformation Theory (TSDT) and Nonlocal Elasticity
M.M Najafizadeh M Raki P YousefiIn present study, the third-order shear deformation theory has been developed to investigate vibration analysis of FG Nano-plates based on Eringen nonlocal elasticity theory. The materials distribution regarding to the thickness of Nano-plate has been considered based o أکثرIn present study, the third-order shear deformation theory has been developed to investigate vibration analysis of FG Nano-plates based on Eringen nonlocal elasticity theory. The materials distribution regarding to the thickness of Nano-plate has been considered based on two different models of power function and exponential function. All equations governing on the vibration of FG Nano-plate have been derived from Hamilton’s principle. It has been also obtained the analytical solution for natural frequencies and corresponding mode shapes of simply supported FG Nano-plates. In addition, the general form of stiffness and mass matrix elements has been expressed based on this theory. The effect of different parameters such as power and exponential indexes of targeted function , nonlocal parameter of Nano-plate, aspect ratio and thickness to length ratio of Nano-plate on non-dimensional natural frequencies of free vibration responses have been investigated. The obtained analytical results show an excellent agreement with other available solutions of previous studies. The formulation and analytical results obtained from proposed method can be used as a benchmark for further studies to develop this area of research. تفاصيل المقالة -
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39 - Edge Crack Studies in Rotating FGM Disks
H EskandariThis article focused on the stress analysis of an edge crack in a thin hallow rotating functionally graded material (FGM) disk. The disk is assumed to be isotropic with exponentially varying elastic modulus in the radial direction. A comprehensive study is carried out f أکثرThis article focused on the stress analysis of an edge crack in a thin hallow rotating functionally graded material (FGM) disk. The disk is assumed to be isotropic with exponentially varying elastic modulus in the radial direction. A comprehensive study is carried out for various combinations of the crack length and orientation with the different gradation of materials. The effect of non-uniform coefficient of thermal expansion on the distribution of stress intensity factor is also studied. The results which are normalized for the advantage of non-dimensional analysis show that the material gradation, the crack orientation and the crack length have significant influence on the amount of stress intensity factors. تفاصيل المقالة -
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40 - Elastic Analysis of Functionally Graded Variable Thickness Rotating Disk by Element Based Material Grading
A.K Thawait L Sondhi Sh Sanyal Sh BhowmickThe present study deals with the elastic analysis of concave thickness rotating disks made of functionally graded materials (FGMs).The analysis is carried out using element based gradation of material properties in radial direction over the discretized domain. The resul أکثرThe present study deals with the elastic analysis of concave thickness rotating disks made of functionally graded materials (FGMs).The analysis is carried out using element based gradation of material properties in radial direction over the discretized domain. The resulting deformation and stresses are evaluated for free-free boundary condition and the effect of grading index on the deformation and stresses is investigated and presented. The results obtained show that there is a significant reduction of stresses in FGM disks as compared to homogeneous disks and the disks modeled by power law FGM have better strength. تفاصيل المقالة -
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41 - Time-Dependent Hygro-Thermal Creep Analysis of Pressurized FGM Rotating Thick Cylindrical Shells Subjected to Uniform Magnetic Field
A Bakhshizadeh M Zamani Nejad M Davoudi KashkoliTime-dependent creep analysis is presented for the calculation of stresses and displacements of axisymmetric thick-walled cylindrical pressure vessels made of functionally graded material (FGM). For the purpose of time-dependent stress analysis in an FGM pressure vessel أکثرTime-dependent creep analysis is presented for the calculation of stresses and displacements of axisymmetric thick-walled cylindrical pressure vessels made of functionally graded material (FGM). For the purpose of time-dependent stress analysis in an FGM pressure vessel, material creep behavior and the solutions of the stresses at a time equal to zero (i.e. the initial stress state) are needed. This corresponds to the solution of the problem considering linear elastic behavior of the material. Therefore, using equations of equilibrium, stress–strain and strain–displacement, a differential equation for displacement is obtained and subsequently the initial elastic stresses at a time equal to zero are calculated. Assuming that the Magneto-hygro-thermoelastic creep response of the material is governed by Norton’s law, using the rate form of constitutive differential equation, the displacement rate is obtained and then the stress rates are calculated. Once the stress rates are known, the stresses at any time are calculated iteratively. The analytical solution is obtained for the plane strain condition. The pressure, inner radius and outer radius are considered to be constant and the magnetic field is uniform. Material properties are considered as power law function of the radius of the cylinder and the poisson’s ratio as constant. Following this, profiles are plotted for different values of material exponent for the radial, circumferential and effective stresses as a function of radial direction and time. The in-homogeneity exponent have significant influence on the distributions of the creep stresses. تفاصيل المقالة -
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42 - Free Vibration of Functionally Graded Cylindrical Shell Panel With and Without a Cutout
k.S Sai Ram K Pratyusha P KiranmayiThe free vibration analysis of the functionally graded cylindrical shell panels with and without cutout is carried out using the finite element method based on a higher-order shear deformation theory. A higher-order theory is used to properly account for transverse shea أکثرThe free vibration analysis of the functionally graded cylindrical shell panels with and without cutout is carried out using the finite element method based on a higher-order shear deformation theory. A higher-order theory is used to properly account for transverse shear deformation. An eight noded degenerated isoparametric shell element with nine degrees of freedom at each node is considered. The stiffness and mass matrices are derived based on the principle of minimum potential energy. The stiffness and mass matrices of the element are evaluated by performing numerical integration using the Gaussian quadrature. The effect of volume fraction exponent on the fundamental natural frequency of simply supported and clamped functionally graded cylindrical shell panel without a cutout is studied for various aspect ratios and arc-length to thickness ratios. Results are presented for variation of the fundamental natural frequency of the cylindrical shell panel with cutout size for simply supported and clamped boundary conditions. تفاصيل المقالة -
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43 - One-Dimensional Transient Thermal and Mechanical Stresses in FGM Hollow Cylinder with Piezoelectric Layers
S.M Mousavi M Jabbari M.A KianiIn this paper, an analytical method is developed to obtain the solution for the one dimensional transient thermal and mechanical stresses in a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers. The FGM properties are assumed to depend o أکثرIn this paper, an analytical method is developed to obtain the solution for the one dimensional transient thermal and mechanical stresses in a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r but the Poisson’s ratio is assumed to be constant. Transient temperature distribution, as a function of radial direction and time with general thermal boundary conditions on the inside and outside surfaces, is analytically obtained for different layers, using the method of separation of variables and generalized Bessel function. A direct method is used to solve the Navier equations, using the Euler equation and complex Fourier series. This method of solution does not have the limitations of the potential function or numerical methods as to handle more general types of the mechanical and thermal boundary conditions. تفاصيل المقالة -
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44 - Delamination of Two-Dimensional Functionally Graded Multilayered Non-Linear Elastic Beam - an Analytical Approach
V RizovDelamination fracture of a two-dimensional functionally graded multilayered four-point bending beam that exhibits non-linear behaviour of the material is analyzed. The fracture is studied analytically in terms of the strain energy release rate. The beam under considerat أکثرDelamination fracture of a two-dimensional functionally graded multilayered four-point bending beam that exhibits non-linear behaviour of the material is analyzed. The fracture is studied analytically in terms of the strain energy release rate. The beam under consideration has an arbitrary number of layers. Each layer has individual thickness and material properties. A delamination crack is located arbitrary between layers. The material is two-dimensional functionally graded in the cross-section of each layer. The beam mechanical behaviour is described by a power-law stress-strain relation. The fracture is analyzed also by applying the J-integral approach in order to verify the solution derived for the strain energy release rate. The effects of crack location, material gradient and non-linear behaviour of material on the delamination fracture are evaluated. It is found that the material non-linearity leads to increase of the strain energy release rate. Therefore, the material non-linearity should be taken into account in fracture mechanics based safety design of two-dimensional functionally graded multilayered structural members. It is found also that the delamination behaviour can be effectively regulated by using appropriate material gradients in the design stage of functionally graded multilayered structural members and components. تفاصيل المقالة -
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45 - Biaxial Buckling Analysis of Symmetric Functionally Graded Metal Cored Plates Resting on Elastic Foundation under Various Edge Conditions Using Galerkin Method
M Rezaei S Ziaee S ShojaIn this paper, buckling behavior of symmetric functionally graded plates resting on elastic foundation is investigated and their critical buckling load in different conditions is calculated and compared. Plate governing equations are derived using the principle of minim أکثرIn this paper, buckling behavior of symmetric functionally graded plates resting on elastic foundation is investigated and their critical buckling load in different conditions is calculated and compared. Plate governing equations are derived using the principle of minimum potential energy. Afterwards, displacement field is solved using Galerkin method and the proposed process is examined through numerical examples. Effect of FGM power law index, plate aspect ratio, elastic foundation stiffness and metal core thickness on critical buckling load is investigated. The accuracy of this approach is verified by comparing its results to those obtained in another work, which is performed using Fourier series expansion. تفاصيل المقالة -
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46 - An Investigation of Stress and Deformation States of Rotating Thick Truncated Conical Shells of Functionally Graded Material
A Thawait L Sondhi Sh Bhowmick Sh SanyalThe present study aims at investigating stress and deformation behavior of rotating thick truncated conical shells subjected to variable internal pressure. Material prpperties of the shells are graded along the axial direction by Mori-tanaka scheme, which is achieved by أکثرThe present study aims at investigating stress and deformation behavior of rotating thick truncated conical shells subjected to variable internal pressure. Material prpperties of the shells are graded along the axial direction by Mori-tanaka scheme, which is achieved by elemental gradation of the properties.Governing equations are derived using principle of stsionary total potential (PSTP) and shells are subjected to clamped- clamped boundary conditions. Aluminum-zirconia, metal-ceramic and ceramic-metal FGM is considered and effects of grading index of material properties and pressure distribution are analyzed. Distribution of Radial displacement and circumferential stress in both radial and axial direction is presented. Further a comparison of behaviors of different FGM shells and homogeneous shells are made which shows, a significant reduction in stresses and deformations of FGM shells as compared to homogeneous shell. FGM shell having value of grading parameter n = 2 is most suitable for the purpose of rotating conical shells having variable pressure distribution as compared to homogeneous shell and shell having other values of grading parameter n. تفاصيل المقالة -
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47 - Effect of Material Gradient on Stresses of FGM Rotating Thick-Walled Cylindrical Pressure Vessel with Longitudinal Variation of Properties under Non-uniform Internal and External Pressure
Mehdi Jabbari Mohammad Zamani Nejad Mehdi GhannadThe present paper provides a semi-analytical solution to obtain the displacements and stresses in a functionally graded material (FGM) rotating thick cylindrical shell with clamped ends under non-uniform pressure. Material properties of cylinder are assumed to change al أکثرThe present paper provides a semi-analytical solution to obtain the displacements and stresses in a functionally graded material (FGM) rotating thick cylindrical shell with clamped ends under non-uniform pressure. Material properties of cylinder are assumed to change along the axial direction according to a power law form. It is also assumed that the Poisson’s ratio is constant. Given the existence of shear stress in the thick cylindrical shell due to material and pressure changes along the axial direction, the governing equations are obtained based on first-order shear deformation theory (FSDT). These equations are in the form of a set of general differential equations with variable coefficients. Given that the FG cylinder is divided into n homogenous disks, n sets of differential equations with constant coefficients are obtained. The solution of this set of equations, applying the boundary conditions and continuity conditions between the layers, yields displacements and stresses. The problem was also solved, using the finite element method (FEM), the results of which were compared with those of the multi-layered method (MLM). Finally, some numerical results are presented to study the effects of applied pressure, non-homogeneity index, and power law index of FGM on the mechanical behavior of the cylindrical shell. تفاصيل المقالة -
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48 - Effects of Power-Law Distribution and Exponential with Uniform Pressures on Vibration Behavior of Reinforced Cylindrical Shell Made of Functionally Graded Materials under Symmetric Boundary Conditions
Mohammad Reza IsvandzibaeiIn this paper, the influence of the constituent volume fractions by changing the values of the power-law exponent with uniform pressure on the vibration frequencies of reinforced functionally graded cylindrical shells is studied. The FGM shell with ring is developed in أکثرIn this paper, the influence of the constituent volume fractions by changing the values of the power-law exponent with uniform pressure on the vibration frequencies of reinforced functionally graded cylindrical shells is studied. The FGM shell with ring is developed in accordance to the volume fraction law from two constituents namely stainless steel and nickel. These constituents are graded through the thickness direction, from one surface of the shell to the other and are controlled by power-law volume fraction distribution. The reinforced FGM shell equations with ring and uniform pressure are established based on first order shear deformation theory. The governing equations of motion were employed, using energy functional and by applying Ritz method. The boundary conditions represented by end conditions of the FGM cylindrical shell are simply supported-simply supported, clamped-clamped and free-free. Effects of the different values of the power-law exponent, uniform pressure, reinforced ring and different symmetric boundary conditions on natural frequencies characteristics are studied. To check the validity of the present study, the results obtained are compared with those available in the literature. تفاصيل المقالة -
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49 - Creep and Stress Redistribution Analysis of Thick-Wall FGM Spheres Subjected to Mechanical Load and Heat Flux – An Analytical Approach
Ali Ziaei-Asl Mohammad Reza Saviz Javad PourabdollahIn this paper, creep analysis of a thick-walled spherical pressure vessel made of Functionally Graded Material (FGM) under thermo-mechanical loadings has been investigated based on Bailey-Norton Law. Considering the nonlinearity of the creep behavior, there is no analyt أکثرIn this paper, creep analysis of a thick-walled spherical pressure vessel made of Functionally Graded Material (FGM) under thermo-mechanical loadings has been investigated based on Bailey-Norton Law. Considering the nonlinearity of the creep behavior, there is no analytical solution that can accurately determine the stresses of an FGM as a function of time and thermal boundaries, thus in this paper, a new method based on the Taylor Series expansion of the creep strain rate is developed to solve the Beltrami-Michell equation by employing an asymptotic method. The resulting quantities are compared with the numerical ones and show good accuracy. The impacts of FGM constants and wall-thickness, and series order on the creep stress and strain distributions are evaluated. The results are depicted graphically and reveal that even for vessels with high wall thickness and FGM constants, the proposed method equipped with high orders of the Taylor series produces accurate results. Also, due to the agreement of both numerical and analytical methods, this method can be generalized to study the creep of other symmetric FGM structures. تفاصيل المقالة -
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50 - Numerical and Analytical Investigation of a Cylinder Made of Functional Graded Materials under Thermo-Mechanical Fields
Javad Jafari Fesharaki Seyed Ghasem Madani Sa’id GolabiThis research develops thermo-elastic analysis of a functionally graded cylinder under thermo-mechanical loadings. Heat conduction equation in cylindrical coordinate system is solved. Thermal conductivity coefficient is graded along the radial direction. By considering أکثرThis research develops thermo-elastic analysis of a functionally graded cylinder under thermo-mechanical loadings. Heat conduction equation in cylindrical coordinate system is solved. Thermal conductivity coefficient is graded along the radial direction. By considering a symmetric distribution of temperature, loading and boundary conditions, strain-displacement and stress-strain relations can be developed. Material properties such as modulus of elasticity are graded along the radial direction. For validation of the obtained results; a complete numerical analysis using finite element approach is presented. تفاصيل المقالة -
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51 - Stress Concentration Factor in a Functionally Graded Material Plate around a Hole
Javad Jafari Fesharaki Seyed Ghasem Madani Davood SeydaliStress concentration factors have been examined in a functionally graded material (FGM) plate withcentral holes in different shapes in this essay. The material properties change along the thickness ofplate. ABAQUS software has been utilized for modeling of problem in wh أکثرStress concentration factors have been examined in a functionally graded material (FGM) plate withcentral holes in different shapes in this essay. The material properties change along the thickness ofplate. ABAQUS software has been utilized for modeling of problem in which subroutine ofABAQUS sub-program was used for modeling of the targeted material. The considering shapes forhole in plate are circular and elliptical in which stress concentration factors have been studied indifferent modes in respective of ellipse diameters. Similarly, stress concentration factors have beenanalyzed in the plate for various coefficients of FGM function. The results show that changes inmaterial properties and the shape of hole in plate affect the stress concentration factor around thehole. An experiment was implemented to determine verification of results from Finite ElementMethod (EFM). تفاصيل المقالة -
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52 - تحلیل تیر FGM در اثر ضربه با سرعت کم به روش FEM با آباکوس
مهدی قهیه ئی سید علیرضا مهاجرانی سعید جعفری مهر آبادی بهناز قهیه ئیآسیب ضربه با سرعت کم از مهمترین مسائلی است که در مواد کامپوزیتی صنایع نظامی و عمران بکار گرفته میشود. کامپوزیتهای فیبری ورقهای محکمی هستند که در معرض تنشهای ناشی از بار ضربه استفاده میشوند تا آسیب ضربه را با استفاده از رزینهای سخت و مقاوم کاهش دهند. در این مقاله ب أکثرآسیب ضربه با سرعت کم از مهمترین مسائلی است که در مواد کامپوزیتی صنایع نظامی و عمران بکار گرفته میشود. کامپوزیتهای فیبری ورقهای محکمی هستند که در معرض تنشهای ناشی از بار ضربه استفاده میشوند تا آسیب ضربه را با استفاده از رزینهای سخت و مقاوم کاهش دهند. در این مقاله برخورد گلوله با سرعت کم به 6 تیر با لایهبندی FGM که مدول الاستیسیته در ضخامت تیر از سرامیک تا فلز متغیر است و پاسخ تیر در برابر ضربه با سرعت کم به روش اجزای محدود به کمک نرمافزار آباکوس بررسی شده است. تنشها و خیز و کرنش تیر در دو حالت لایه آخر فلز و سرامیک – فلز تحلیل شده است، نمودارهایی از تنش، خیز و کرنش در طول تیر برای شش تیر بدست آمده و مشاهده گردید در حالتی که درجه خواص فلز نسبت به سرامیک بیشتر باشد، میزان خیز و تنش بالاتر است و کرنش در تیر با افزایش درجه خواص سرامیک نسبت به فلز کاهش مییابد. تفاصيل المقالة -
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53 - A FSDT model for vibration analysis of Nano rectangular FG plate based on Modified Couple Stress Theory under moving load
یونس امینIn present paper, vibration of Nano FGM plate based on modified couple stress and First Order Shear Deformation Theories (FSDT) under moving load has been developed. Basic equations and linear strains are introduced by first order shear deformation theory and Mori Tanak أکثرIn present paper, vibration of Nano FGM plate based on modified couple stress and First Order Shear Deformation Theories (FSDT) under moving load has been developed. Basic equations and linear strains are introduced by first order shear deformation theory and Mori Tanaka’s model is used for the plate. The module of elasticity and density are assumed to vary only through thickness of plate. Governing Equations are derived according to the modified couple stress theory and Hamilton’s principle. Constitutive equations are also derived based on modified couple stress and finally, analytical solution for simply supported Nano rectangular FG plate is obtained by using of Navier solution. Examples of length scales parameter and power law index are presented to show effect of this parameter on plate behaviors. Results show that plate’s deflection enhances with power law index increasing and by increasing of length scale parameter, deflection decreases, and for frequencies, the deflection with both raising of power law index and length parameter scales, are reduced تفاصيل المقالة -
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54 - The method of fundamental solutions for transient heat conduction in functionally graded materials: some special cases
M. Nili Ahmadabadi M. Arab F. M. Maalek GhainiIn this paper, the Method of Fundamental Solutions (MFS) is extended to solvesome special cases of the problem of transient heat conduction in functionally graded materials. First, the problem is transformed to a heat equation with constant coefficients usinga suitable أکثرIn this paper, the Method of Fundamental Solutions (MFS) is extended to solvesome special cases of the problem of transient heat conduction in functionally graded materials. First, the problem is transformed to a heat equation with constant coefficients usinga suitable new transformation and then the MFS together with the Tikhonov regularizationmethod is used to solve the resulting equation. تفاصيل المقالة -
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55 - Vibration Analysis of FG Micro-Beam Based on the Third Order Shear Deformation and Modified Couple Stress Theories
Mehdi Alimoradzadeh Mehdi Salehi Sattar Mohammadi EsfarjaniIn this paper, free vibration analysis and forced vibration analysis of FG doubly clamped micro-beams is studied based on the third order shear deformation and modified couple stress theories. The size dependent dynamic equilibrium equations and both the classical and n أکثرIn this paper, free vibration analysis and forced vibration analysis of FG doubly clamped micro-beams is studied based on the third order shear deformation and modified couple stress theories. The size dependent dynamic equilibrium equations and both the classical and non-classical boundary conditions are derived using a variational approach. It is assumed that all properties of the FG micro-beam follow a power law form through thickness. The motion equations are solved by employing Furrier series in conjunction with Galerkin method. Also, effects of aspect ratio, power index and dimensionless length scale parameter on the natural frequencies and amplitude-excite frequency curves are investigated. Findings indicate that dimensionless frequencies are strongly dependent on the values of the material length scale parameter and power index. The numerical results of this study indicate that if the thickness of the beam is in the order of the material length scale parameter, size effects are more significant. تفاصيل المقالة -
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56 - Asymmetric buckling analysis of the circular FGM plates with temperature-dependent properties under elastic medium
علیرضا نداف اسکویی هادی محمدی هویه وحید علایی خداداد واحدیIn this paper, Asymmetric buckling analysis of functionally graded (FG) Circular plates with temperature dependent property that subjected to the uniform radial compression and thermal loading is investigated. This plate is on an elastic medium that simulated by Winkler أکثرIn this paper, Asymmetric buckling analysis of functionally graded (FG) Circular plates with temperature dependent property that subjected to the uniform radial compression and thermal loading is investigated. This plate is on an elastic medium that simulated by Winkler and Pasternak foundation. Mechanical properties of the plate are assumed to vary nonlinearly by temperature change. The equilibrium equations are obtained using the classical plate theory (CPT), Von Karman geometric nonlinearity and virtual displacement method. Existence of bifurcation buckling is examined and stability equations are obtained by means of the adjacent equilibrium criterion. The effects of elastic foundation coefficient, thickness to radius, power law index, and temperature-dependency of the material properties on critical buckling load of FG plates are presented. The results of the present work have been compared with the results of other investigator and the results of the comparison are very good. It is found that by increasing temperature, critical buckling load decreases. It is also concluded that the critical buckling load of (FG) Circular plates increases with an increase in the Winkler and Pasternak constants of elastic foundation. تفاصيل المقالة -
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57 - Free vibration analysis of circular sandwich plates with clamped FG face sheets
یونس محمدی کیوان حسینی صفری محسن رحمانیFree vibration of sandwich plates with temperature dependent functionally graded (FG) face sheets in various thermal environments is investigated. The material properties of FG face sheets are assumed to be temperature-dependent and vary continuously through the thickne أکثرFree vibration of sandwich plates with temperature dependent functionally graded (FG) face sheets in various thermal environments is investigated. The material properties of FG face sheets are assumed to be temperature-dependent and vary continuously through the thickness according to a power-law distribution in terms of the volume fractions of the constituents. Also, the material properties of the core are assumed to be temperature dependent. The governing equations of motion in polar system and in free natural vibration are derived using Hamilton’s principle and Galerkin method is used to solve the equations and obtain the natural frequency. In-plane stresses of the core that usually are ignored in the vibration characteristics of the sandwich structures are considered in this formulation. The results obtained by Galerkin method for symmetric circular sandwich plate with fixed support is compared with finite element method that obtained by ABAQUS and good agreement is found. The results show that varying the power-law index and temperature have important effects on natural frequency. تفاصيل المقالة -
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58 - Thermo-elastic Analysis of Functionally Graded Thick- Walled Cylinder with Novel Temperature – Dependent Material Properties using Perturbation Technique
Alireza Nadafoskoue hadi mohammadi hooyehIn this work, thermo – elastic analysis for functionally graded thick – walled cylinder with temperature - dependent material properties at steady condition is carried out. The length of cylinder is infinite and loading is consist of internal hydrostatic pre أکثرIn this work, thermo – elastic analysis for functionally graded thick – walled cylinder with temperature - dependent material properties at steady condition is carried out. The length of cylinder is infinite and loading is consist of internal hydrostatic pressure and temperature gradient. All of physical and mechanical properties expect the Poisson's ratio are considered as multiplied an exponential function of temperature and power function of radius. With these assumptions, the nonlinear differential equations for temperature distribution at cylindrical coordinate is obtained. Temperature distribution is achieved by solving this equation using classical perturbation method. With considering strain – displacement, stress – strain and equilibrium relations and temperature distribution that producted pervious, the constitutive differential equation for cylinder is obtained. By employing mechanical boundary condition the radial displacement is yield. With having radial displacement, stresses distribution along the thickness are achieved. The results of this work show that by increasing the order of temperature perturbation series the convergence at curves is occurred and also dimensionless radial stress decrease and other stresses with dimensionless radial displacement increase. تفاصيل المقالة -
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59 - Modified Fixed Grid Finite Element Method to Solve 3D Elasticity Problems of Functionally Graded Materials
محمد جواد کاظم زاده پارسی فرهنگ دانشمندIn the present paper, applicability of the modified fixed grid finite element method in solution of three dimensional elasticity problems of functionally graded materials is investigated. In the non-boundary-fitted meshes, the elements are not conforming to the domain b أکثرIn the present paper, applicability of the modified fixed grid finite element method in solution of three dimensional elasticity problems of functionally graded materials is investigated. In the non-boundary-fitted meshes, the elements are not conforming to the domain boundaries and the boundary nodes which are used in the traditional finite element method for the application of boundary conditions no longer exist. Therefore, special techniques are needed for computation of the stiffness matrix of boundary intersecting elements and application of boundary conditions.The stiffness matrix of boundary intersecting elements are calculated via integration of strain energy over the internal parts of these elements. Essential boundary conditions are applied using penalty function method. To examine the effectiveness of the proposed method, some numerical examples are solved and results are compared with those obtained using the standard finite element method. تفاصيل المقالة -
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60 - Applying Differential Transform Method on the Effect of the Elastic Foundation on the out - Plane Displacement of the Functionally Graded Circular Plates
سمیه عباسی فاطمه فرهت نیا سعید رسولی جزیIn this paper, the effect of elastic foundation on the out of plane displacement of functionally graded circular plates using differential transform method is presented. Differential transform method is a semi-analytical-numerical solution technique that is capable to s أکثرIn this paper, the effect of elastic foundation on the out of plane displacement of functionally graded circular plates using differential transform method is presented. Differential transform method is a semi-analytical-numerical solution technique that is capable to solve various types of differential equations. Using this method, governing differential equations are transformed into recursive relations and boundary conditions are changed into algebraic equations. Since the problem of plates on elastic foundation have a great practical importance in modern engineering structures and Winkler foundation model is widely used, plate is assumed on Winkler elastic foundation. In this article functionally graded plate is considered in which material properties vary through the thickness direction by power-law distribution. Analysis results of out of plane displacement of plate on elastic foundation under uniform transverse loads are obtained in different terms of foundation stiffness, material properties and boundary conditions. In order to validate the solution technique, results obtained are compared with the results of the finite element method (FEM). تفاصيل المقالة -
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61 - Disk Vibration Analysis of Functionally Graded Materials
محبوبه روائی حسن نحویPerforated discs have many applications in different parts of industry. By making such disks of functionally graded materials, more capabilities can be obtained from them. Vibration analysis of these kinds of disks can help us make them more efficient. In this paper, mo أکثرPerforated discs have many applications in different parts of industry. By making such disks of functionally graded materials, more capabilities can be obtained from them. Vibration analysis of these kinds of disks can help us make them more efficient. In this paper, modeling and evaluation of disk vibration of functionally graded materials with regard to thickness were carried out using Abaqus software. Since no certain element has been defined regarding functionally graded materials for the design and analysis of a particular element in Abaqus software, molding of such materials has been used in this application. In order to verify the results, the results obtained from ABAQUS analysis have been compared with those available in the literature. The obtained results show that by defining more layers with regard to changes in properties, the obtained results approach the exact solutions. تفاصيل المقالة -
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62 - Fluid-structure Interaction Vibration Analysis of Vertical Cylindrical Containers with Elastic Bottom Plate Made of Functionally Graded Materials
علی اکبر شفیعی مجتبی محزون احسان عسکریIn the present paper a method is proposed to investigate the free vibration of a partially liquid-filled cylindrical tank. The mechanical properties of the container are assumed to change continuously along the thickness according to volume fraction Power-law, Sigmoid o أکثرIn the present paper a method is proposed to investigate the free vibration of a partially liquid-filled cylindrical tank. The mechanical properties of the container are assumed to change continuously along the thickness according to volume fraction Power-law, Sigmoid or Exponential distribution. The liquid is supposed to be incompressible and in viscid and its velocity potential is formulated by using Eigen function expansions. The interaction between the liquid and the plate was considered and the dynamic characteristics of the plate are extracted by using the Rayleigh–Ritz method. The results from the proposed method are in good agreement with experimental and numerical solutions available in the literature. A finite element analysis is also applied to check the validity of the results. Furthermore, the influence of various variables such as the number of nodal circles and diameters, volume fractions of functionally graded materials and liquid level on the dynamic behavior of the coupled system is investigated. تفاصيل المقالة -
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63 - Buckling of Rectangular Functionally Graded Material Plates under Various Edge Conditions
متین لطیفی فاطمه فرهت نیا محمود کدخدائیIn the present paper, the buckling problem of rectangular functionally graded (FG) plate with arbitrary edge supports is investigated. The present analysis is based on the classical plate theory (CPT) and large deformation is assumed for deriving stability equations. Th أکثرIn the present paper, the buckling problem of rectangular functionally graded (FG) plate with arbitrary edge supports is investigated. The present analysis is based on the classical plate theory (CPT) and large deformation is assumed for deriving stability equations. The plate is subjected to bi-axial compression loading. Mechanical properties of FG plate are assumed to vary continuously along the thickness of the plate according to differentvolume of fractionfunctions of constituents. These functions are assumed to have power law distributions. The displacement function is assumed to have the form of doubleFourier series, of which derivatives are legitimized using Stokes’ transformation method. The advantage of using this method is the capability of considering effect of anypossible combination of boundary conditionson the buckling loads. The out-plane displacement distribution is assumed using Fourier Sinus Series. This results in a general eigenvalue problem which can be used for evaluating the buckling load under different edge conditions, plate aspect ratios and various volume fraction functions. For generality of problem, plate is elastically restrained using some rotational and translational springs at four edges. Some numerical examples are presented and compared the to numerical results of finite element method using ABAQUS and other researchers’ results to validate the proposed method. It has been shown that there is good agreement between them تفاصيل المقالة -
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64 - Dynamic Stability of Nano FGM Beam Using Timoshenko Theory
شهاب صفاری محمد هاشمیانBased on the nonlocal Timoshenko beam theory, the dynamic stability of functionally gradded (FG) nanoeams under axial load is studied in thermal environment, with considering surface effect. It is used power law distribution for FGM and the surface stress effects are co أکثرBased on the nonlocal Timoshenko beam theory, the dynamic stability of functionally gradded (FG) nanoeams under axial load is studied in thermal environment, with considering surface effect. It is used power law distribution for FGM and the surface stress effects are considered based on Gurtin-Murdoch continuum theory. Using Von Karman geometric nonlinearity, governing equations are derived based on Hamilton’s principle. The developed nonlocal models have the capability to interpret small scale effects. Winkler and Pasternak types elastic foundation are employed to represent the interaction of the nano FG beam and the surrounding elastic medium. A parametric study is conducted to investigate the influences of the static load factor, temperature change, nonlocal elastic parameter, slenderness ratio, surface effect and springs constant of the elastic medium on the dynamic stability characteristics of the FG beam, with simply-supported boundary conditions. It is found that the difference between instability regions predicted by local and nonlocal beam theories is significant for nanobeams with lower aspect ratios. Moreover, it is observed that in contrast to high temperature environments, at low temperatures, increasing the temperature change moves the origins of the instability regions to higher excitation frequencies and leads to further stability of the system at lower excitation frequencies, considering surface stress effect shifts the FG beam to higher frequency zone تفاصيل المقالة -
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65 - Nonlinear buckling analysis of clamped-free porous FG sandwich beams with temperature dependent materials
Mohsen RahmaniAnalysing the buckling behaviour of the two kinds of sandwich beams, the first one with functionally graded material faces and homogeneous core and the second one with functionally graded material core and homogeneous faces are presented in this paper based on a high or أکثرAnalysing the buckling behaviour of the two kinds of sandwich beams, the first one with functionally graded material faces and homogeneous core and the second one with functionally graded material core and homogeneous faces are presented in this paper based on a high order sandwich beam theory. Properties of the constituent materials are assumed temperature dependent and functionally graded materials are modelled by a power law rule. Even and uneven porosity distributions are considered to improve the accuracy of the model. Minimum potential energy principle is used to obtain the govern equations and Galerkin method is applied used to solve the equations in a clamped free boundary conditions. Lateral displacement, and thermal stresses of the core and Lagrange strains are considered. To verify the procedure, the results of the present study are compared with the literature. Thickness, length, porosity, wave number and temperature effect on the critical load are investigated too. تفاصيل المقالة
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