Showing papers on "Functionally graded material published in 2018"

Closed-form solutions in stress-driven two-phase integral elasticity for bending of functionally graded nano-beams

Abstract: Strain-driven and stress-driven integral elasticity models are formulated for the analysis of the structural behaviour of fuctionally graded nano-beams. An innovative stress-driven two-phases constitutive mixture defined by a convex combination of local and nonlocal phases is presented. The analysis reveals that the Eringen strain-driven fully nonlocal model cannot be used in Structural Mechanics since it is ill-posed and the local-nonlocal mixtures based on the Eringen integral model partially resolve the ill-posedeness of the model. In fact, a singular behaviour of continuous nano-structures appears if the local fraction tends to vanish so that the ill-posedness of the Eringen integral model is not eliminated. On the contrary, local-nonlocal mixtures based on the stress-driven theory are mathematically and mechanically appropriate for nanosystems. Exact solutions of inflected functionally graded nanobeams of technical interest are established by adopting the new local-nonlocal mixture stress-driven integral relation. Effectiveness of the new nonlocal approach is tested by comparing the contributed results with the ones corresponding to the mixture Eringen theory.

Characterization of wire arc additively manufactured titanium aluminide functionally graded material: Microstructure, mechanical properties and oxidation behaviour

Abstract: In this paper, titanium-aluminide functionally graded material with a designed composition range from pure Ti to Ti-50 at% Al is successfully fabricated using the double-wire arc additive manufacturing method (WAAM). Due to the influence of Al concentration, the morphology, microstructure, mechanical properties and oxidation behaviour vary greatly along the gradient direction of the manufactured bulk. With increasing Al content from the bottom to the top, the bulk exhibits a layered structure consisting of α–β duplex structure, α-α2 lamellar structure, large α2 grains, α2-γ duplex lamellar structure and γ interdendrities structure in sequence from the bottom to the top. Microhardness and tensile strength exhibit similar trends and are comparable to those of mono-composition components. The oxidation resistance degrades at an increasing rate with decreasing Al content due to oxide breakaway occurring in the TiAl alloy matrix that consists of single α2 or α2 + α. The experimental results indicate that the WAAM method is able to produce defect free TiAl functionally graded material with the desired composition gradient, suitable mechanical properties and acceptable oxidation behaviour.

Influence of Porosity on the Flexural and Free Vibration Responses of Functionally Graded Plates in Thermal Environment

Abstract: This paper examines the influence of porosities on the flexural and free vibration response of functionally graded material (FGM) plates based on the authors’ recently developed non-polynomial higher-order shear and normal deformation theory. The theory accommodates the nonlinear variation in the in-plane and transverse displacements in the thickness coordinates. It also contains the hyperbolic shear strain shape function in the displacement field with only four unknowns. A new mathematical model has also been proposed to incorporate the effects of porosity in the FGM plate. Various numerical examples have been solved to ascertain the accuracy, efficiency, and applicability of the present formulation. The effects of porosity, volume fraction index, plate thickness, aspect ratio, boundary conditions and temperature have been discussed in details. The obtained results can be treated as a benchmark for future studies.

Small scale effects on buckling and postbuckling behaviors of axially loaded FGM nanoshells based on nonlocal strain gradient elasticity theory

Abstract: By means of a comprehensive theory of elasticity, namely, a nonlocal strain gradient continuum theory, size-dependent nonlinear axial instability characteristics of cylindrical nanoshells made of functionally graded material (FGM) are examined. To take small scale effects into consideration in a more accurate way, a nonlocal stress field parameter and an internal length scale parameter are incorporated simultaneously into an exponential shear deformation shell theory. The variation of material properties associated with FGM nanoshells is supposed along the shell thickness, and it is modeled based on the Mori-Tanaka homogenization scheme. With a boundary layer theory of shell buckling and a perturbation-based solving process, the nonlocal strain gradient load-deflection and load-shortening stability paths are derived explicitly. It is observed that the strain gradient size effect causes to the increases of both the critical axial buckling load and the width of snap-through phenomenon related to the postbuckling regime, while the nonlocal size dependency leads to the decreases of them. Moreover, the influence of the nonlocal type of small scale effect on the axial instability characteristics of FGM nanoshells is more than that of the strain gradient one.

Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities

Abstract: The free thermal vibration of functionally graded material (FGM) cylindrical shells containing porosities is investigated. Both even distribution and uneven distribution are taken into account. In addition, three thermal load types, i.e., uniform temperature rise (UTR), nonlinear temperature rise (NLTR), and linear temperature rise (LTR), are researched to explore their effects on the vibration characteristics of porous FGM cylindrical shells. A modified power-law formulation is used to describe the material properties of FGM shells in the thickness direction. Love’s shell theory is used to formulate the strain-displacement equations, and the Rayleigh-Ritz method is utilized to calculate the natural frequencies of the system. The results show that the natural frequencies are affected by the porosity volume fraction, constituent volume fraction, and thermal load. Moreover, the natural frequencies obtained from the LTR have insignificant differences compared with those from the NLTR. Due to the calculation complexity of the NLTR, we propose that it is reasonable to replace it by its linear counterpart for the analysis of thin porous FGM cylindrical shells. The present results are verified in comparison with the published ones in the literature.

Analysis of functionally graded sandwich plates using a higher-order layerwise theory

Abstract: A higher-order layerwise finite element formulation is presented for static and dynamic analyses of functionally graded material (FGM) sandwich plates. A higher-order displacement field is assumed for core and first-order displacement field is assumed for top and bottom facesheets maintaining a continuity of displacement at layer interface. An eight noded isoparametric element using a C0 based finite element formulation with thirteen degrees of freedom per node has been considered in the present work. Two configurations of FGM sandwich plates, one with FGM core and homogenous facesheets and second having top and bottom layers made of FGM and homogenous core are considered. Effective material properties of the FGM are computed using rule of mixture (ROM). In order to establish the correctness of the present finite element formulation for wide range of problems for two configurations of FGM sandwich plates, comparison studies are presented. Next, parametric studies are taken up to investigate the effects of volume fraction index, span to thickness ratio and boundary conditions on static and dynamic behavior of FGM sandwich plate. It is shown here that present formulation is simple, straightforward and accurate for static and dynamic analyses of functionally graded material (FGM) sandwich plates.

Free vibration of functionally graded beams resting on Winkler-Pasternak foundation

Abstract: In the present study, the free vibration of functionally graded beams resting on two parameter elastic foundation was examined. The properties of the functionally graded materials were presumed to vary continuously along the thickness direction. The foundation medium was assumed to be linear, homogeneous, and isotropic, and it was modeled by the Winkler-Pasternak model with two parameters for describing the reaction of the elastic foundation on the beam. The functionally graded beam was modeled with classical beam theory. The governing equation including the effects of functionally graded material properties, Winkler-Pasternak elastic foundation was solved using separation of variables. The eigenvalues of yielding fundamental equation versus clamped-clamped, clamped-free, clamped-simply supported, and simply supported-simply supported boundary conditions were found. To corroborate the results, comparisons were carried out with available results for homogeneous and functionally graded beams. The effects of Winkler-Pasternak type elastic foundation and functionally graded material properties on the values of dimensionless frequency parameter of beams were discussed. Briefly, it was found that the dimensionless frequency parameters of beam change according to material properties, presence of elastic foundation, and boundary conditions; moreover, the separate effects of these quantities on each other are interesting.

Material distribution and sizing optimization of functionally graded plate-shell structures

Abstract: A high order shear deformation theory is used to develop a discrete model for the structural and sensitivity analyses allowing for the material distribution and sizing optimization of functionally graded material (FGM) structures. The finite element formulation for general FGM plate-shell type structures is presented, and a non-conforming triangular flat plate/shell element with 24° of freedom for the generalized displacements is used. The formulation accounts for geometric and material nonlinear behaviour, free vibrations and linear buckling analyses, and their analytical gradient based sensitivities. The p-index of the power–law material distribution and the thickness are the design variables. Mass, displacement, fundamental frequency and critical load are the objective functions or constraints. The optimization solutions, obtained by a Feasible Arc Interior Point gradient-based algorithm, for some plate-shell examples are presented for benchmarking purposes.

A novel four variable refined plate theory for wave propagation in functionally graded material plates

Abstract: In This work an analysis of the propagation of waves of functionally graduated plates is presented by using a high order hyperbolic (HSDT) shear deformation theory. This theory has only four variables, which is less than the theory of first order shear deformation (FSDT). Therefore, a shear correction coefficient is not required. Unlike other conventional shear deformation theories, the present work includes a new field of displacement which introduces indeterminate integral variables. The properties of materials are supposed classified in the direction of the thickness according to two simple distributions of a power law in terms of volume fractions of constituents. The governing equations of the wave propagation in the functionally graded plate are derived by employing the Hamilton's principle. The analytical dispersion relation of the functionally graded plate is obtained by solving an eigenvalue problem. The convergence and the validation of the proposed theoretical numerical model are performed to demonstrate the efficacy of the model.

A new 3-unknown hyperbolic shear deformation theoryfor vibration of functionally graded sandwich plate

Abstract: In this work, a simple but accurate hyperbolic plate theory for the free vibration analysis of functionally graded material (FGM) sandwich plates is developed. The significant feature of this formulation is that, in addition to including the shear deformation effect, it deals with only 3 unknowns as the classical plate theory (CPT), instead of 5 as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM face sheet and the homogeneous core and the sandwich with the homogeneous face sheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton‟s principle. The closed form solutions are obtained by using the Navier technique. The fundamental frequencies are found by solving the eigenvalue problems. Numerical results of the present theory are compared with the CPT, FSDT, order shear deformation theories (HSDTs), and 3D solutions. Verification studies show that the proposed theory is not only accurate and simple in solving the free vibration behaviour of FGM sandwich plates, but also comparable with the higher-order shear deformation theories which contain more number of unknowns.

Wave Propagation of Porous Nanoshells

Abstract: This study aims at investigating the wave propagation of porous nanoshells. The Bi-Helmholtz non-local strain gradient theory is employed in conjunction with a higher-order shear deformation shell theory, in order to include the size-dependent effects. The nanoshells are made of a porous functionally graded material (P-FGM), whose properties vary continuously along the thickness direction. A variational approach is here applied to handle the governing equations of the problem, which are solved analytically to compute the wave frequencies and phase velocities as function of the wave numbers. The sensitivity of the wave response is analyzed for a varying porosity volume fraction, material properties, non-local parameters, strain gradient length scales, temperature, humidity, and wave numbers. Based on the results, it is verified that the size-dependence of the response is almost the same to the one of plates, beams and tubes.

Geometrically nonlinear analysis of functionally graded shallow curved tubes in thermal environment

Abstract: Present research aims to analyze the nonlinear bending response of the functionally graded material curved tube subjected to the uniform lateral pressure. The effect of thermal environment is also included. Properties of the arch are distributed through the radial direction using a power law function. Thermomechanical properties of the media are assumed to be temperature dependent. The governing nonlinear equilibrium equations of the arch are obtained by means of the von Karman assumption and a higher order shear deformation tube theory which satisfies the traction free boundary conditions on the inner and outer surfaces of the tube. The three coupled nonlinear equations of the tube are reduced to new two ones in a dimensionless presentation. These two equations are solved using the two step perturbation technique for pin ended and clamped ended boundary conditions. Closed form and accurate expressions are provided to estimate the deflection of the arch as a function of the thermal and mechanical load parameters. Numerical results are provided to explore the effect of different parameters such as the power law index of the FGM tube, boundary conditions of the tube, thermal environment, and three geometrical parameters.

A four-variable refined shear-deformation beam theory for thermo-mechanical vibration analysis of temperature-dependent FGM beams with porosities

Abstract: This article proposes a four-variable shear deformation refined beam theory for thermo-mechanical vibration characteristics of porous, functionally graded (FG) beams exposed to various kinds of thermal loadings by using an analytical method. Thermo-mechanical properties of functionally graded material (FGM) beams are supposed to vary through the thickness direction, and are estimated through the modified power-law rule in which the porosities with even and uneven types are approximated. The material properties of FGM beams are supposed to be temperature dependent. Porosities possibly occur inside FGMs during fabrication because of technical problems that lead to the creation of microvoids in these materials. The variation of pores along the thickness direction influences the mechanical properties. Thus, it is incumbent to predict the effect of porosities on the thermo-mechanical vibration behavior of FG beam in the present study. Four types of thermal loading, namely, uniform, linear, nonlinear, a...

Nonlinear vibration and buckling of functionally graded porous nanoscaled beams

Abstract: Although many researchers have studied the vibration and buckling behavior of porous materials, the behavior of porous nanobeams is still a needed issue to be studied. This paper is focused on the buckling and nonlinear vibration of functionally graded (FG) porous nanobeam for the first time. Nonlinear Von Karman strains are put into consideration to study the nonlinear behavior of nanobeam based on the Euler–Bernoulli beam theory. The nonlocal Eringen’s theory is used to study the size effects. The mechanical properties of ceramic and metal are used to model the functionally graded material through thickness, and the boundary conditions are considered as clamped–clamped (CC) and simply supported–simply supported (SS). The generalized differential quadrature method (GDQM) is used in conjunction with the iterative method to solve the equations. The parametric study is done to examine the effects of nonlinearity, porosity, sized effect, FG index, etc., on the vibration and buckling of porous nanobeam.

Influence of initial geometric imperfections and porosity on the stability of functionally graded material plates

Abstract: In the present paper, the effect of initial geometric imperfections and porosity on the stability of functionally graded material (FGM) plates is investigated. The formulations are based on the rec...

Nonlinear thermo-mechanical dynamic analysis and vibration of higher order shear deformable piezoelectric functionally graded material sandwich plates resting on elastic foundations:

Abstract: Used the Reddy's higher-order shear deformation plate theory, the nonlinear dynamic analysis and vibration of imperfect functionally graded sandwich plates in thermal environment with piezoelectric actuators (PFGM) on elastic foundations subjected to a combination of electrical, damping loadings and temperature are investigated in this article. One of the salient features of this work is the consideration of temperature on the piezoelectric layer, and the material properties of the PFGM sandwich plates are assumed to be temperature-dependent. The governing equations are established based on the stress function, the Galerkin method, and the Runge–Kutta method. In the numerical results, the effects of geometrical parameters; material properties; imperfections; elastic foundations; electrical, thermal, and damping loads on the vibration and nonlinear dynamic response of the PFGM sandwich plates are discussed. The obtained natural frequencies are verified with the known results in the literature.