Graded Material Layer Research Articles

Reduction in stress concentration around a pair of circular holes with functionally graded material layer

The stress concentration in an infinite panel having a pair of circular holes surrounded by a functionally graded material layer subjected to different load conditions using the extended finite element method is numerically analysed. Young’s modulus of the functionally graded material layer varies with a power law function, in the direction normal to the holes. To model the material properties and the hole boundary, a level set function is used. The relation of stress concentration factor with functionally graded material layer parameters (i.e. power law index, thickness of layer) and hole geometry parameters (i.e. normalised distance between holes, hole radius ratio) is discussed, and it is observed that the functionally graded material layer around the pair of circular holes results in a significant reduction in stress concentration. It is concluded that the proper selection of power law index and thickness of the functionally graded material layer helps in reducing the stress concentration factor to a great extent.

Reduction of stress concentration for a rounded rectangular hole by using a functionally graded material layer

This work aims to analyse the stress concentration in an infinite panel having a rounded rectangular hole reinforced with a functionally graded material layer using the extended finite element method. Young’s modulus of the functionally graded material layer varies in normal direction to the hole with a power law function. The relation of stress concentration factor with hole parameters, layer thickness, and power law index is presented for uniaxial, biaxial, and shear loads. It is noticed that the reinforcement of the functionally graded material layer around the hole has a significant influence on the stress distribution, and the controlled variation in the material properties of the layer can significantly reduce the stress concentration.

Exponential matrix method for the solution of exact 3D equilibrium equations for free vibrations of functionally graded plates and shells

The present paper analyzes the convergence of the exponential matrix method in the solution of three-dimensional equilibrium equations for the free vibration analysis of functionally graded material structures. The three-dimensional equilibrium equations are written in general orthogonal curvilinear coordinates for one-layered and sandwich plates and shells embedding functionally graded material layers. The resulting system of second-order differential equations is reduced to a system of first-order differential equations redoubling the variables. This system is exactly solved using the exponential matrix method and harmonic displacement components. In the case of functionally graded material plates, the differential equations have variable coefficients because of the material properties which depend on the thickness coordinate z. For functionally graded material shells, the differential equations have variable coefficients because of both changing material properties and curvature terms. Several mathematical layers M can be introduced to approximate the curvature terms and the variable functionally graded material properties to obtain differential equations with constant coefficients. The exponential matrix is applied to solve the resulting system of partial differential equations with constant coefficients, where the used expansion has a very fast convergence ratio. The present work investigates the convergence of the proposed method related to the order N used for the expansion of the exponential matrix and to the number of mathematical layers M used for the approximation of curvature shell terms and variable functionally graded material properties. Both N and M values are analyzed for different geometries, thickness ratios, materials, functionally graded material laws, lamination sequences, imposed half-wave numbers, frequency orders, and vibration modes.

Nonlinear thermomechanical response of pressure-loaded doubly curved functionally graded material sandwich panels in thermal environments including tangential edge constraints

This paper investigates the nonlinear response of doubly curved functionally graded material sandwich panels resting on elastic foundations, exposed to thermal environments and subjected to uniform external pressure. The material properties of both face sheets and core layer are assumed to be temperature dependent, and effective material properties of functionally graded material layers 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. Formulations are based on first-order shear deformation shell theory taking geometrical nonlinearity, initial geometrical imperfection, Pasternak type elastic foundations, and tangential edge constraints into consideration. Approximate solutions are assumed to satisfy simply supported boundary conditions and Galerkin procedure is applied to derive expressions of buckling loads and nonlinear load–deflection relation. The effects of material, geometry and foundation parameters, face sheet thickness ratio, initial geometrical imperfection, thermal environments and degree of tangential restraint of edges on the snap-through instability, and nonlinear response of spherical and cylindrical functionally graded material sandwich panels are analyzed and discussed in detail.

Propagation of Love waves in a prestressed Voigt-type viscoelastic orthotropic functionally graded layer over a porous half-space

The present paper investigates the theory of propagation of Voigt-type viscoelastic Love waves in a functionally graded material layer over an anisotropic porous half-space. The complex dispersion equation of Love waves has been expanded into real and imaginary parts. An assumption of the dissipation factor has been applied. Some particular cases have also been deduced, and it is noticed that the dispersion equation is in well agreement with the classical Love wave equation. In addition, to study the effect of initially stressed parameter, inhomogeneity parameter and porosity on phase velocity and dissipation function, some significant observations have been made by detailed numerical calculations and illustrated graphically. The results of this paper may present a deeper insight into the nature of the propagation behavior in elastic inhomogeneous functionally graded materials and can provide theoretical guidance for the design and optimization to the field of earthquake engineering.

The axisymmetric stress analysis of double contact problem for functionally graded materials layer with arbitrary graded materials properties

In this paper, the axisymmetric double contact problems for a functionally graded layer indented by a rigid cylindrical indenter and a rigid spherical indenter are considered. A linear multi-layered model is applied to model the functionally graded layer whose shear modulus varies as an arbitrary function. The Hankel integral transform technique and the transfer matrix method are applied to convert the double contact problem to a system of coupled singular integral equations which are solved by the numerical method. The numerical results show that the stiffness ratio and the gradient index have great effect on the contact region and the contact pressure.

Stress intensity factor of semi-elliptical surface crack in a thermo-mechanically loaded cylinder with hoop wrapped FGM layer

This article focused on three dimensional fracture analyses of a pressurized cylinder with hoop wrapped functionally graded material layer, which contains a longitudinal semielliptical internal surface crack and subjected to temperature gradient. The effect of non-uniform coefficient of thermal expansion and the hoop wrapped layer thickness on the distribution of the stress intensity factor along the crack front for different crack profiles is also studied. The results, which are normalized for the advantage of non-dimensional analysis show that the hoop wrapped functionally graded material cylinder, can significantly influence on the amount and distribution of stress intensity factors along the crack front.

Free vibration and vibrational displacements analysis of thick elastically supported laminated curved panels with power-law distribution functionally graded layers and finite length via 2D GDQ method

This paper deals with free vibration and vibrational displacements analysis of thick laminated curved panels with finite length resting on two-parameter elastic foundations based on the three-dimensional elasticity theory. Because of using two-dimensional generalized differential quadrature method, the present approach makes possible vibration analysis of cylindrical panels with two opposite axial edges simply supported and arbitrary boundary conditions including free, simply supported and clamped at the curved edges. The material properties vary continuously through the layers’ thickness according to a three-parameter power-low distribution. It is assumed that the inner surfaces of the functionally graded sheets are metal rich, while the outer surfaces of the layers can be metal rich, ceramic rich or made of a mixture of two constituents. The benefit of using the considered power-law distribution is to illustrate and present useful results arising from symmetric and asymmetric profiles. The effects of two-parameter elastic foundation modulus, geometrical and material parameters together with the boundary conditions on the frequency parameters of the laminated functionally graded panels are investigated. The obtained results show that the outer functionally graded material layers have significant effect on the vibration behavior of cylindrical panels. This study serves as a benchmark for assessing the validity of numerical methods or two-dimensional theories used to analysis of laminated curved panels.

Thermal Buckling Analysis of Circular Plates Made of Piezoelectric and Saturated Porous Functionally Graded Material Layers

AbstractThis study presents the thermal buckling of a radially solid sandwich circular plate made of a piezoelectric actuator and porous material. The porous material properties vary through the thickness of the plate for a specific function. The general thermoelastic nonlinear equilibrium and linear stability equations are derived using the variational formulations to obtain the governing equations of the piezoelectric porous plate. The geometrical nonlinearities are considered along with the higher-order shear deformation plate theory. The problem is simplified to an axisymmetric one, and then closed-form solutions for circular plates subjected to temperature load are obtained. The buckling temperatures that are derived for solid circular plates under uniform temperature rise through the thickness for an immovable clamped edge of the boundary conditions. The effects of the porous plate thickness, piezoelectric thickness, applied actuator voltage, and variation of porosity on the critical temperature loa...

Functionally graded materials for impedance matching in elastic media

Abstract When functionally graded material layers are inserted between two impedance mismatching media, passbands with extremely large bandwidths can appear in these layered systems. An accurate and effective iterative method is developed to deal with these layered systems with extremely large layer number.

Random Dynamic Analysis of a Crack in a Functionally Graded Materials Layer for Plane Problem Using Shear Stress

Dynamic analysis is performed for a crack in a functionally graded materials layer for plane problem using shear stress. The material properties of the functionally graded materials layer vary randomly in the thickness direction, and the cracks are parallel to the materials faces. A pair of dynamic loadings applied on the elastic planes faces are treated as stationary stochastic processes of time. By dividing the functionally graded materials layer into several sub-layers, this problem is reduced to the analysis of laminated composites containing a crack, the material properties of each layer being random variables. A fundamental problem is constructed for the solution. Based on the use of Laplace and Fourier transforms, the boundary conditions are reduced to a set of singular integral equations, which can be solved by the Chebyshev polynomial expansions. The stress intensity factor history with its statistics is analytically derived. Numerical calculations are provided to show the effects of related parameters.

Reissner’s mixed variational theorem-based finite cylindrical layer methods for the three-dimensional free vibration analysis of sandwich circular hollow cylinders with an embedded functionally graded material layer

Based on Reissner’s mixed variational theorem (RMVT), finite cylindrical layer methods (FCLMs) were developed for the three-dimensional (3D) free vibration analysis of simply supported, functionally graded material (FGM) sandwich circular hollow cylinders. The FGM sandwich cylinder consists of a thick and soft FGM core bounded with two thin and stiff homogeneous material face sheets, in which the material properties of the FGM core are assumed to obey an exponent-law varying exponentially with the thickness coordinate. In this formulation, the FGM sandwich cylinder is divided into a number of equal-thickness cylindrical layers, where the trigonometric functions and Lagrange polynomials are used to interpolate the in- and out-of-surface variations of the field variables of each individual layer, respectively. An h-refinement process instead of a p-refinement one is adopted to yield the convergent solutions in this study, and the layerwise linear, quadratic or cubic function distribution through the thickness coordinate is thus assumed for the related field variables. The accuracy and convergence of the RMVT-based FCLMs developed in this article are assessed by comparing their solutions with the exact 3D solutions available in the literature.

Random dynamic response of crack in functionally graded materials layer for plane problem

In order to dynamically analyze a crack in a functionally graded materials layer for plane problem under dynamic loadings, a stochastic model is established for plane problem in which the material properties of the functionally graded materials layer vary randomly in the thickness direction, and the crack is parallel to the materials faces. A pair of dynamic loadings applied on the crack faces are treated as stationary stochastic processes of time. By dividing the functionally graded materials layer into several sub-layers, this problem is reduced to the analysis of laminated composites containing a crack, the material properties of each layer being random variables. A fundamental problem is constructed for the solution. Based on the use of Laplace and Fourier transforms, the boundary conditions are reduced to a set of singular integral equations, which can be solved by the Chebyshev polynomial expansions. The stress intensity factor history with its statistics is analytically derived. Numerical calculations are provided to show the effects of the related parameters. The results show that the increase of crack length, random field parameter β and crack location ratio h2/h leads to the increase of the mathematical expectation and standard deviation of normalized stress intensity factor history.

Effects of electrorheological fluid core and functionally graded layers on the vibration behavior of a rotating composite beam

Vibration properties of a rotating Functionally Graded Electro-Rheological (FGER) beam are investigated. In the composition of three layered beam, an electrorheological fluid layer is embedded between two functionally graded material layers. Classical beam theory is applied in the analysis of Functionally Graded Material (FGM) layers. Using Hamilton’s principle and finite element method (FEM), equations of motion of the FGER beam are derived. The effects of various parameters such as FGM volume fraction index, rotating speed, thickness of the viscoelastic core and electric field on the resonant frequencies and modal loss factors are studied. The results quantify the significant effect of the FGM distribution and the ER core on the vibration suppression of the rotating composite beam.

Random dynamic response and reliability of a crack in a functionally graded material layer between two dissimilar elastic half-planes

Abstract An analytical approach is presented for the random dynamic analysis of a functionally graded material (FGM) layer between two dissimilar elastic half-planes. This FGM layer contains a crack and its material properties vary randomly in the thickness direction, while their mean values are exponential functions of field position. The transient loadings applied on the crack faces are assumed to be stochastic processes of time. In order to obtain the solution, the FGM layer is divided into several sub-layers, and the material properties of each layer are reduced to random variables by an average method. A fundamental problem is constructed for the solution. Based on the use of Laplace and Fourier transforms, the boundary conditions are reduced to a set of singular integral equations, which can be solved by the Chebyshev polynomial expansions. Both stress intensity factor history with its statistics and dynamic reliability are analytically derived. Numerical calculations are provided to show the effects of related parameters.

Effect of the volume of a functionally graded material layer on frictionally excited thermoelastic instability

A finite element model is used to identify the effect of the volume of a functionally graded material (FGM) on thermoelastic instability (TEI). An optimal FGM volume that exhibits the highest critical speed was found to exist. Beyond the optimal FGM volume, the critical speed is much lower than that of a homogeneous steel layer. For all FGM volumes, the performance against TEI is dominant for the same nonhomogeneous parameter, which determines the compositional shape of the material property grading in the FGM. In addition, the thermal conductivity of the frictional material and the modulus of elasticity of the FGM were found to have the most significant impact on an increase in the critical speed.

Stability Analysis of FGM Layered Shells in the Surrounding Medium

In this study, the stability analysis of three-layered shells containing a functionally graded material layer in the surrounding medium and subjected to the uniform lateral pressure is investigated. The surrounding elastic medium is modeled as a Pasternak foundation. The dimensionless critical lateral pressures of three-layered functionally graded material shells with and without elastic foundations are obtained. Effects of compositional profiles and elastic foundation on the dimensionless critical lateral pressures have been studied.

Use of Functionally Graded Material Layers in a Two-Layered Pressure Vessel

This work explores the possibilities of using functionally graded material (FGM) layers to reduce normal and shear stress gradients due to internal pressure and thermal loadings at the interface of a two-layered wall pressure vessel. The two walls are made of an internal thin metallic layer (titanium used as a liner to avoid a chemical/physical reaction between the gas and the external layer) and an external thick layer (carbon fiber used as a structural restraint). Two main geometrical elements are investigated: a cylindrical shell and a spherical panel. The shell analysis has been made by referring to mixed layerwise theories, which lead to a three-dimensional description of the stress/strain fields in the thickness shell direction; results related to the first order shear deformation theory are given for comparison purposes. It has been concluded that it is convenient to use FGM layers to reduce shear and normal stress gradients at the interfaces. Furthermore, the FGM layers lead to benefits as far as buckling load is concerned; lower values of in-plane shear and longitudinal compressive stresses are, in fact, obtained with respect to a pure two-layered wall.

Energy Conversion Efficiency of a Novel Hybrid Solar System for Photovoltaic, Thermoelectric, and Heat Utilization

A novel hybrid solar system has been designed to utilize photovoltaic (PV) cells, thermoelectric (TE) modules, and hot water (HW) through a multilayered building envelope. Water pipelines are cast within a functionally graded material layer to serve as a heat sink, allowing heat to be easily transferred into flowing water through an aluminum-rich surface, while remaining insulated by a polymer rich bottom. The theoretical energy conversion efficiency limit of the system has been investigated for documenting the potential of this hybrid solar panel design. Given the material properties of each layer, the actual energy conversion efficiency depends on the solar irradiation, ambient temperature, and water flow temperature. Compared to the traditional solar panel, this design can achieve better overall efficiencies with higher electrical power output and thermal energy utilization. Based on theoretical conversion efficiency limits, the PV/TE/HW system is superior to PV/HW and traditional PV systems with 30% higher output electrical power. However, the advantages of the PV/TE/HW system are not significant from experimental data due to the low efficiency of the bulk TE material. Thus, QW/QD TE materials are highly recommended to enhance the overall efficiency of the PV/TE/HW design. This design is general and open to new PV and TE materials with emerging nanotechnology for higher efficiencies.

Refined and Advanced Models for Multilayered Plates and Shells Embedding Functionally Graded Material Layers

The present work investigates the static response problem of multilayered plates and shells embedding functionally graded material (FGM) layers. Carrera's unified formulation (CUF) is employed to obtain several hierarchical refined and advanced two-dimensional models for plates and shells. The refined models are based on the principle of virtual displacements. The advanced models, based on Reissner's mixed variational theorem, permit the transverse shear and normal stresses to be “a priori” modelled. Refined and advanced models are developed in both equivalent single layer and layer wise multilayer approaches. CUF is also employed to describe the continuous variation of elastic properties in the thickness direction for the embedded FGM layers. The numerical results, which are restricted to simply supported plates/shells loaded by a harmonic distribution of transverse pressure, show that the use of refined and advanced models, based on CUF, is mandatory with respect to the classical theories that are widely employed for isotropic and one-layered structures. Furthermore, advanced models lead to a quasi-3D description of the bending problem for FGM plates and shells. New benchmarks are considered in order to investigate the possible benefits of introducing FGM layers into common multilayered structures. It has been concluded that significant benefits can be obtained by employing opportune values for -hFGM parameters, where is the exponent of the thickness law for the FGM elastic properties and hFGM is the thickness of the embedded FGM layers.