Showing papers on "Functionally graded material published in 2016"

A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates

Abstract: In this article, a new five-variable refined plate theory for the free vibration analysis of functionally graded sandwich plates is developed. By dividing the transverse displacement into bending, shear, and thickness stretching parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or more in the case of other shear and normal deformation theories. The theory accounts for hyperbolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using a shear correction factor. Two common types of functionally graded material (FGM) sandwich plates, namely, the sandwich with FGM facesheet and homogeneous core and the sandwich with homogeneous facesheet and FGM core, are considered. The equations of motion are obtained using Hamilton's principle. Numerical resu...

Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory

Abstract: The hygro-thermo-mechanical bending behavior of sigmoid functionally graded material (S-FGM) plate resting on variable two-parameter elastic foundations is discussed using a four-variable refined plate theory. The material characteristics are distributed within the thickness direction according to the two power law variation in terms of volume fractions of the constituents of the material. By employing a four variable refined plate model, both a trigonometric distribution of the transverse shear strains within the thickness and the zero traction boundary conditions on the top and bottom surfaces of the plate are respected without utilizing shear correction factors. The number of independent variables of the current formulation is four, as against five in other shear deformation models. The governing equations are deduced based on the four-variable refined plate theory incorporating the external load and hygro-thermal influences. The results of this work are compared with those of other shear deformation models. Various numerical examples introducing the influence of power-law index, plate aspect ratio, temperature difference, elastic foundation parameters, and side-to-thickness ratio on the static behavior of S-FGM plates are investigated.

Effect of various thermal loadings on buckling and vibrational characteristics of nonlocal temperature-dependent functionally graded nanobeams

Abstract: In this article, the thermal effects on buckling and free vibrational characteristics of functionally graded (FG) size-dependent nanobeams subjected to various types of thermal loading are investigated by presenting a Navier-type solution for the first time. Temperature-dependent material properties of FG nanobeams vary continuously along the thickness according to the power-law form. The small-scale effect is taken into consideration based on Eringen's nonlocal elasticity theory. The nonlocal equations of motion are derived through Hamilton's principle and they are solved applying an analytical solution. It is revealed that the proposed modeling can provide accurate frequency results of the FG nanobeams.

Vibration analysis of nonlocal beams made of functionally graded material in thermal environment

Abstract: In this paper, thermal vibration behavior of functionally graded (FG) nanobeams exposed to various kinds of thermo-mechanical loading including uniform, linear and non-linear temperature rise embedded in a two-parameter elastic foundation are investigated based on third-order shear deformation beam theory which considers the influence of shear deformation without the need to shear correction factors. Material properties of FG nanobeam are supposed to be temperature-dependent and vary gradually along the thickness according to the Mori-Tanaka homogenization scheme. The influence of small scale is captured based on nonlocal elasticity theory of Eringen. The nonlocal equations of motion are derived through Hamilton’s principle and they are solved applying analytical solution. The comparison of the obtained results is conducted with those of nonlocal Euler-Bernoulli beam theory and it is demonstrated that the proposed modeling predicts correctly the vibration responses of FG nanobeams. The influences of some parameters including gradient index, nonlocal parameter, mode number, foundation parameters and thermal loading on the thermo-mechanical vibration characteristics of the FG nanobeams are presented.

On thermal stability of plates with functionally graded coefficient of thermal expansion

Abstract: In this article, a four-variable refined plate theory is presented for buckling analysis of functionally graded plates subjected to uniform, linear and non-linear temperature rises across the thickness direction. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. Young\'s modulus and Poisson ratio of the FGM plates are assumed to remain constant throughout the entire plate. However, the coefficient of thermal expansion of the FGM plate varies according to a power law form through the thickness coordinate. Equilibrium and stability equations are derived based on the present theory. The influences of many plate parameters on buckling temperature difference such ratio of thermal expansion, aspect ratio, side-to-thickness ratio and gradient index will be investigated.

Wave propagation analysis of quasi-3D FG nanobeams in thermal environment based on nonlocal strain gradient theory

Abstract: This article examines the application of nonlocal strain gradient elasticity theory to wave dispersion behavior of a size-dependent functionally graded (FG) nanobeam in thermal environment. The theory contains two scale parameters corresponding to both nonlocal and strain gradient effects. A quasi-3D sinusoidal beam theory considering shear and normal deformations is employed to present the formulation. Mori–Tanaka micromechanical model is used to describe functionally graded material properties. Hamilton’s principle is employed to obtain the governing equations of nanobeam accounting for thickness stretching effect. These equations are solved analytically to find the wave frequencies and phase velocities of the FG nanobeam. It is indicated that wave dispersion behavior of FG nanobeams is significantly affected by temperature rise, nonlocality, length scale parameter and material composition.

Fabrication of Fe-FeAl Functionally Graded Material Using the Wire-Arc Additive Manufacturing Process

Abstract: A functionally gradient iron-aluminum wall structure with aluminum composition gradient from 0 at. pct to over 50 at. pct is fabricated using a wire-arc additive manufacturing (WAAM) system. The as-fabricated alloy is investigated using optical microstructure analysis, hardness testing, tensile testing, X-ray diffraction phase characterization, and electron-dispersive spectrometry. The comprehensive analysis of the experimental samples has shown that the WAAM system can be used for manufacturing iron aluminide functionally graded material with full density, desired composition, and reasonable mechanical properties.

Free vibration of functionally graded carbon nanotube reinforced composite plates integrated with piezoelectric layers

Abstract: In the present research, free vibration behavior of carbon nanotube reinforced composite (CNTRC) plates integrated with piezoelectric layers at the bottom and top surfaces is analyzed. Plate is modeled according to the first order shear deformation plate theory. Distribution of CNTs across the plate thickness may be functionally graded (FG) or uniformly distributed (UD). Properties of the composite media are obtained according to a modified rule of mixtures approach which contains efficiency parameters. Distribution of electric potential across the piezoelectric thickness is assumed to be linear. The complete set of motion and Maxwell equations of the system are obtained according to the Ritz formulation suitable for arbitrary in-plane and out-of-plane boundary conditions. Besides, two types of electrical boundary conditions, namely, closed circuit and open circuit are considered for the free surfaces of the piezoelectric layers. Chebyshev polynomials are used as the basis functions in Ritz approximation. The resultant eigenvalue system is solved to obtain the frequencies of the system as well as the mode shapes. It is shown that, fundamental frequency of a closed circuit plate is always higher than a plate with open circuit boundary conditions.

Nonlinear finite element analysis of functionally graded circular plates with modified couple stress theory

Abstract: Finite element models of microstructure-dependent geometrically nonlinear theories for axisymmetric bending of circular plates, which accounts for through-thickness power-law variation of a two-constituent material, the von Karman nonlinearity, and the strain gradient effects are developed for the classical and first-order plate theories. The strain gradient effects are included through the modified couple stress theory that contains a single material length scale parameter which can capture the size effect in a functionally graded material plate. The developed finite element models are used to determine the effect of the geometric nonlinearity, power-law index, and microstructure-dependent constitutive relations on the bending response of functionally graded circular plates with different boundary conditions.

Nonlocal and surface effects on the buckling behavior of functionally graded nanoplates: An isogeometric analysis

Abstract: The size-dependent static buckling responses of circular, elliptical and skew nanoplates made of functionally graded materials (FGMs) are investigated in this article based on an isogeometric model. The Eringen nonlocal continuum theory is implemented to capture nonlocal effects. According to the Gurtin–Murdoch surface elasticity theory, surface energy influences are also taken into account by the consideration of two thin surface layers at the top and bottom of nanoplate. The material properties vary in the thickness direction and are evaluated using the Mori–Tanaka homogenization scheme. The governing equations of buckled nanoplate are achieved by the minimum total potential energy principle. To perform the isogeometric analysis as a solution methodology, a novel matrix-vector form of formulation is presented. Numerical examples are given to study the effects of surface stress as well as other important parameters on the critical buckling loads of functionally graded nanoplates. It is found that the buckling configuration of nanoplates at small scales is significantly affected by the surface free energy.

A unified solution for the vibration analysis of FGM doubly-curved shells of revolution with arbitrary boundary conditions

Abstract: This paper describes a unified solution for the vibration analysis of functionally graded material (FGM) doubly-curved shells of revolution with arbitrary boundary conditions. The solution is derived by means of the modified Fourier series method on the basis of the first order shear deformation shell theory considering the effects of the deepness terms. The material properties of the shells are assumed to vary continuously and smoothly along the normal direction according to general three-parameter power-law volume fraction functions. In summary, the energy functional of the shells is expressed as a function of five displacement components firstly. Then, each of the displacement components is expanded as a modified Fourier series. Finally, the solutions are obtained by using the variational operation. The convergence and accuracy of the solution are validated by comparing its results with those available in the literature. A variety of new vibration results for the circular toroidal, paraboloidal, hyperbolical, catenary, cycloidal and elliptical shells with classical and elastic boundary conditions as well as different geometric and material parameters are presented, which may serve as benchmark solution for future researches. Furthermore, the effects of the boundary conditions, shell geometric and material parameters on the frequencies are carried out.

Size-dependent thermo-mechanical vibration and instability of conveying fluid functionally graded nanoshells based on Mindlin's strain gradient theory

Abstract: The free vibration and instability characteristics of nanoshells made of functionally graded materials (FGMs) with internal fluid flow in thermal environment are studied in this paper based upon the first-order shear deformation shell theory. In order to capture the size effects, Mindlin's strain gradient theory (SGT) is utilized. The mechanical and thermal properties of FG nanoshell are determined by the power-law relation of volume fractions. The Knudsen number is considered to analyze the slip boundary conditions between the flow and wall of nanoshell, and the average velocity correction parameter is used to obtain the modified flow velocity of nano-flow. The governing partial differential equations of motion and associated boundary conditions are derived by Hamilton's principle. An analytical solution method is also employed to solve the governing equations under the simply-supported end conditions. Then, some numerical examples are presented to investigate the effects of fluid velocity, longitudinal and circumferential mode numbers, length scale parameters, material properties, temperature difference and compressive axial loads on the natural frequencies, critical flow velocities and instability of system.

An efficient shear deformation theory for wave propagation of functionally graded material plates

Abstract: An efficient shear deformation theory is developed for wave propagation analysis of an infinite functionally graded plate in the presence of thermal environments. By dividing the transverse displacement into bending and shear parts, the number of unknowns and governing equations of the present theory is reduced, and hence, makes it simple to use. The thermal effects and temperature-dependent material properties are both taken into account. The temperature field is assumed to be a uniform distribution over the plate surface and varied in the thickness direction only. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton\'s principle and the physical neutral surface concept. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The analytic dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The effects of the volume fraction distributions and temperature on wave propagation of functionally graded plate are discussed in detail. It can be concluded that the present theory is not only accurate but also simple in predicting the wave propagation characteristics in the functionally graded plate. The results carried out can be used in the ultrasonic inspection techniques and structural health monitoring.

A simplified shear and normal deformations nonlocal theory for bending of functionally graded piezomagnetic sandwich nanobeams in magneto-thermo-electric environment

Abstract: A simplified three-unknown shear and normal deformations nonlocal beam theory for thermo-electro-magneto mechanical bending analysis of a nanobeam with a functionally graded material core and two functionally piezomagnetic layers is studied in this paper. The assumed structure is subjected to mechanical, thermal, electrical, and magnetic loads. An initial applied voltage and magnetic load is considered on the functionally graded piezomagnetic material layers. Eringen’s nonlocal constitutive equations are considered in the analysis. Governing equations are derived according to the present refined theory using the principle of virtual displacements. The numerical results including the deflection, electric, and magnetic potential distribution are calculated in terms of important parameters of the problem such as applied electric and magnetic potentials, two parameters of temperature distribution, and nonlocal parameter. The numerical results indicate that increase in applied electric potential increases the ...

An improved Moving Kriging-based meshfree method for static, dynamic and buckling analyses of functionally graded isotropic and sandwich plates

Abstract: A meshfree method with a modified distribution function of Moving Kriging (MK) interpolation is investigated. This method is then combined with a high order shear deformation theory (HSDT) for static, dynamic and buckling analyses of functionally graded material (FGM) isotropic and sandwich plates. A meshfree method uses the normalized form of MK interpolation under a new quartic polynomial correlation to build the basis shape functions in high order approximations. The Galerkin weak form is used to separate the system equations which is numerically solved by meshfree method. A rotation-free technique extracted from isogeometric analysis is introduced to eliminate the degrees of freedom of slopes. Then, the method retains a highly computational effect with a lower number of degrees of freedom. In addition, the requirement of shear correction factors is ignored and the traction free is at the top and bottom surfaces of FGM plates. Various thickness ratios, boundary conditions and material properties are studied to validate the numerical analyses of the rectangular and circular plates. The numerical results show that the present theory is more stable and well accurate prediction as compared to three-dimensional (3D) elasticity solution and other meshfree methods in the literature.