Showing papers on "Functionally graded material published in 2015"

A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates

Abstract: In this research, a simple but accurate sinusoidal plate theory for the thermomechanical bending analysis of functionally graded sandwich plates is presented. The main advantage of this approach is that, in addition to incorporating the thickness stretching effect, it deals with only 5 unknowns as the first order shear deformation theory (FSDT), instead of 6 as in the well-known conventional sinusoidal plate theory (SPT). The material properties of the sandwich plate faces are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The core layer is made of an isotropic ceramic material. Comparison studies are performed to check the validity of the present results from which it can be concluded that the proposed theory is accurate and efficient in predicting the thermomechanical behavior of functionally graded sandwich plates. The effect of side-to-thickness ratio, aspect ratio, the volume fraction exponent, and the loading conditions on the thermomechanical response of functionally graded sandwich plates is also investigated and discussed.

Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect

Abstract: This paper addresses theoretically the bending and buckling behaviors of size-dependent nanobeams made of functionally graded materials (FGMs) including the thickness stretching effect. The size-dependent FGM nanobeam is investigated on the basis of the nonlocal continuum model. The nonlocal elastic behavior is described by the differential constitutive model of Eringen, which enables the present model to become effective in the analysis and design of nanostructures. The present model incorporates the length scale parameter (nonlocal parameter) which can capture the small scale effect, and furthermore accounts for both shear deformation and thickness stretching effects by virtue of a sinusoidal variation of all displacements through the thickness without using shear correction factor. The material properties of FGM nanobeams are assumed to vary through the thickness according to a power law. The governing equations and the related boundary conditions are derived using the principal of minimum total potential energy. A Navier-type solution is developed for simply-supported boundary conditions, and exact expressions are proposed for the deflections and the buckling load. The effects of nonlocal parameter, aspect ratio and various material compositions on the static and stability responses of the FGM nanobeam are discussed in detail. The study is relevant to nanotechnology deployment in for example aircraft structures.

Transverse vibration analysis of rotating porous beam with functionally graded microstructure using the differential transform method

Abstract: This study presents free vibration analysis of rotating functionally graded Timoshenko beam made of porous material using the semi-analytical differential transform method.The material properties are supposed to vary along the thickness direction of the beam according to the rule of mixture, which is modified to approximate the material properties with the porosity phases. The frequency equation is obtained using Hamilton’s principle. It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of porous FG rotating beams. The good agreement between the results of this article and those available in literature validated the presented approach. Detailed mathematical derivations are presented and numerical investigations are performed, while emphasis is placed on investigating the effect of the several parameters such as porosity, functionally graded microstructure, thickness ratio, rotational speed and hub radius on the normalized natural frequencies of porous FG rotating beams in detail.

Application of the differential transformation method for nonlocal vibration analysis of functionally graded nanobeams

Abstract: In this study, the applicability of differential transformation method (DTM) in investigations on vibrational characteristics of function- ally graded (FG) size-dependent nanobeams is examined. The material properties of FG nanobeam vary over the thickness based on the power law. The nonlocal Eringen theory, which takes into account the effect of small size, enables the present model to be effective in the analysis and design of nanosensors and nanoactuators. Governing equations are derived through Hamilton's principle. The obtained re- sults exactly match the results of the presented Navier-based analytical solution as well as those available in literature. The DTM is also demonstrated to have high precision and computational efficiency in the vibration analysis of FG nanobeams. The detailed mathematical derivations are presented and numerical investigations performed with emphasis placed on investigating the effects of several parameters, such as small scale effects, volume fraction index, mode number, and thickness ratio on the normalized natural frequencies of the FG nanobeams. The study also shows explicitly that vibrations of FG nanobeams are significantly influenced by these effects. Numerical results are presented to serve as benchmarks for future analyses of FG nanobeams.

Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory

Abstract: In this work, a layerwise finite element formulation is presented for the first time for dynamic analysis of two types of functionally graded material (FGM) sandwich plates with nonlinear temperature variation along the thickness and the FGM having temperature dependent material properties. Natural frequencies of sandwich plates made of FGM in thermal environment are presented using a layerwise theory. Two configurations of sandwich plate, one with homogenous facesheets and functionally graded core and the second with functionally graded facesheets and homogenous core are considered. The material properties of both types of FGM sandwich plates are varied according to Mori–Tanaka (MT) scheme and the rule of mixture (ROM). The layerwise theory used in this work is based on the assumption of the first order shear deformation theory in each layer and the displacement continuity is satisfied at each layer interface. In the present investigation, it is seen that the natural frequencies converge with lesser number of elements and the results are found to be accurate. Natural frequencies are presented for FGM sandwich plates with different geometric and elastic properties, thermal load and boundary conditions.

Size-dependent vibration and instability of fluid-conveying functionally graded microshells based on the modified couple stress theory

Abstract: In this article, the vibration and dynamic instability of cylindrical microshells made of functionally graded materials (FGMs) and containing flowing fluid are studied. In order to take the size effects into account, the modified couple stress elasticity theory is used in conjunction with the classical first-order shear deformation shell theory. The material properties of FGM microshells are considered to be graded in the thickness direction on the basis of the power-law function. By using Hamilton’s principle, the non-classical governing differential equations of motion and related boundary conditions are derived. Subsequently, a Navier-type exact solution method is carried out to obtain the imaginary and real parts of natural frequencies of different modes for various values of fluid velocity, length scale parameter, material property gradient index, compressive axial load, and length-to-radius ratio. It is found that for microshells with lower length-to-radius ratios, the system diverges at lower values of fluid velocity. Also, it is demonstrated that by increasing the value of material property gradient index of FGM microshell, the natural frequency of the first mode and the critical flow velocity of the system increase.

Size-dependent electromechanical buckling of functionally graded electrostatic nano-bridges

Abstract: This study explored the electromechanical buckling (EMB) of beam-type nanoelectromechanical systems (NEMS) by considering the nonlinear geometric effect and intermolecular forces (Casimir force and van der Walls force) based on modified couple stress theory. To model the system, a slender nanobeam made of functionally graded material (FGM) with clamped-guided boundary conditions, which is under compressive or tensile axial loads as well as symmetric and nonlinear electrostatic and intermolecular transverse loads, is used. Considering the Euler–Bernoulli beam theory and using the principle of minimum potential energy and the variational approach, the governing equation as well as the related boundary conditions is derived. To discretize the equation and its related boundary conditions, and to solve the equations, the generalized differential quadrature method (GDQM) is employed. Finally, after validation of the results, the effects of size, length, power law index, and the distance between the two fixed and movable electrodes on the bucking of the system are discussed and examined.

Buckling analysis of functionally graded nanobeams based on a nonlocal third-order shear deformation theory

Abstract: In this paper, a general third-order beam theory that accounts for nanostructure-dependent size effects and two-constituent material variation through the nanobeam thickness, i.e., functionally graded material (FGM) beam is presented. The material properties of FG nanobeams are assumed to vary through the thickness according to the power law. A detailed derivation of the equations of motion based on Eringen nonlocal theory using Hamilton’s principle is presented, and a closed-form solution is derived for buckling behavior of the new model with various boundary conditions. The nonlocal elasticity theory includes a material length scale parameter that can capture the size effect in a functionally graded material. The proposed model is efficient in predicting the shear effect in FG nanobeams by applying third-order shear deformation theory. The proposed approach is validated by comparing the obtained results with benchmark results available in the literature. In the following, a parametric study is conducted to investigate the influences of the length scale parameter, gradient index, and length-to-thickness ratio on the buckling of FG nanobeams and the improvement on nonlocal third-order shear deformation theory comparing with the classical (local) beam model has been shown. It is found out that length scale parameter is crucial in studying the stability behavior of the nanobeams.

Thermal buckling of temperature-dependent FGM conical shells with arbitrary edge supports

Abstract: Bifurcation behavior of heated conical shell made of a through-the-thickness functionally graded material is investigated in the present research. Properties of the shell are obtained based on a power law form across the thickness. Temperature dependency of the constituents is also taken into account. The heat conduction equation of the shell is solved based on an iterative generalized differential quadrature method (GDQM). General nonlinear equilibrium equations and the associated boundary conditions are obtained using the virtual displacement principle in the Donnell sense. The prebuckling solution of the shell is obtained under the assumption of linear membrane deformations. The stability equations are extracted via the concept of the adjacent equilibrium criterion. A semi-analytical solution employing the GDQM and trigonometric expansion is implemented to solve the stability equations. Numerical results of the present research are compared and validated with the known available data through the open literature. Some parametric studies are conducted to investigate the influences of various involved parameters, such as the cone semi-vertex angle, boundary conditions, power law index of composition rule, length to thickness ratio, and the radius to thickness ratio.

Nonlinear torsional buckling and postbuckling of eccentrically stiffened FGM cylindrical shells in thermal environment

Abstract: The main aim of this paper is to investigate the nonlinear buckling and post-buckling of functionally graded stiffened thin circular cylindrical shells surrounded by elastic foundations in thermal environments and under torsional load by analytical approach Shells are reinforced by closely spaced rings and stringers in which material properties of shell and the stiffeners are assumed to be continuously graded in the thickness direction The elastic medium is assumed as two-parameter elastic foundation model proposed by Pasternak Based on the classical shell theory with von Karman geometrical nonlinearity and smeared stiffeners technique, the governing equations are derived Using Galerkin method with three-term solution of deflection, the closed form to find critical torsional load and post-buckling load–deflection curves are obtained The effects of temperature, stiffener, foundation, material and dimensional parameters are analyzed

Micro-scratch and corrosion behavior of functionally graded HA-TiO2 nanostructured composite coatings fabricated by electrophoretic deposition.

Abstract: In the present study, functionally graded coatings of HA/TiO 2 nanoparticles and HA-TiO 2 nanocomposite coatings with 0, 10 and 20 wt% of TiO 2 were fabricated by electrophoretic deposition on Ti–6Al–4V substrate. The functionally graded structure of HA/TiO 2 coatings was formed by gradual addition of HA suspension into the deposition cell containing TiO 2 nanoparticles. Micro-scratch test results showed the highest critical distances of crack initiation and delamination, normal load before failure and critical contact pressures for functionally graded coating. It was observed that the improvement of adhesion strength and fracture toughness of functionally graded coatings would be due to the reduction of thermal expansion coefficient mismatch between Ti–6Al–4V substrate and HA. The results of potentiodynamic polarization measurements showed that the graded structure of the coating could efficiently increase the corrosion resistance of substrate.

Analyses of Circular Magnetoelectroelastic Plates with Functionally Graded Material Properties

Abstract: A meshless method based on the local Petrov–Galerkin approach is proposed for plate bending analysis with material containing functionally graded magnetoelectroelastic properties. Material properties are considered to be continuously varying along the plate thickness. Axial symmetry of geometry and boundary conditions for a circular plate reduces the original 3D boundary value problem into a 2D problem in axial cross section. Both stationary and transient dynamic conditions for a pure mechanical load are considered in this article. The local weak formulation is employed on circular subdomains in the axial cross section. Subdomains surrounding nodes are randomly spread over the analyzed domain. The test functions are taken as unit step functions in derivation of the local integral equations (LIEs). The moving least-squares (MLS) method is adopted for the approximation of the physical quantities in the LIEs. After performing the spatial integrations, one obtains a system of ordinary differential equations f...

A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations:

Abstract: This paper deals with the thermo-mechanical deformation behaviour of shear deformable functionally graded sandwich plates resting on a two-parameter (Pasternak model) elastic foundation. By dividin...

Nonlinear dynamic analysis of imperfect functionally graded material double curved thin shallow shells with temperature-dependent properties on elastic foundation

Abstract: This paper presents an analytical investigation on the nonlinear dynamic analysis of functionally graded double curved thin shallow shells using a simple power-law distribution (P-FGM) with temperature-dependent properties on an elastic foundation and subjected to mechanical load and temperature. The formulations are based on the classical shell theory, taking into account geometrical nonlinearity, initial geometrical imperfection, temperature-dependent properties and unlike other publications, Poisson ratio is assumed to be varied smoothly along the thickness ν=ν(z). The nonlinear equations are solved by the Bubnov-Galerkin and Runge-Kutta methods. The obtained results show the effects of temperature, material and geometrical properties, imperfection and elastic foundation on the nonlinear vibration and nonlinear dynamical response of double curved FGM shallow shells. Some results were compared with those of other authors.

Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method

Abstract: This study presents static and free vibration behaviors of two type of sandwich plates based on the three dimensional theory of elasticity. The core layer of one type is functionally graded material (FGM) with the isotropic face sheets whereas in second type, the core layer is isotropic with the face sheets FGM. The effective material properties of FGM layers are estimated to vary continuously through the thickness direction according to a power-law distribution of the volume fractions of the constituents. By using differential equilibrium equations and/or equations of motion as well as constitutive relations, state-space differential equation can be derived. In the case of simply supported condition, applying Fourier series to the quantities along the in-plane coordinates, governing equation can be solved analytically and for the other edges condition, a semi analytical solution can be obtained by using differential quadrature method (DQM) along the in-plane coordinate as well as state spaces technique in the thickness direction. Accuracy and exactness of the present approach is validated by comparing the numerical results with the results of published literature. Moreover, the influences of volume fraction, width-to-thickness ratios and aspect ratio on the vibration and static behaviors of plate are investigated.