Showing papers on "Functionally graded material published in 2002"
TL;DR: In this article, the equilibrium and stability equations of a rectangular plate made of functionally graded material under thermal loads are derived, based on the classical plate theory, when it is assumed that the material properties vary as a power form of thicknesscoordinate variable z and when the variational method is used, the system of fundamental differential equations is established.
Abstract: Equilibrium and stability equations of a rectangular plate made of functionally graded material under thermal loads are derived, based on the classical plate theory. When it is assumed that the material properties vary as a power form of thicknesscoordinate variable z and when the variational method is used, the system of fundamental differential equations isestablished. Thederived equilibrium and stability equationsforfunctionally graded plates areidenticalwith theequationsforhomogeneousplates. Bucklinganalysisoffunctionally graded platesunderfour typesofthermalloadsiscarriedoutresultinginclosed-formsolutions.Thebucklingloadsarereducedtothecritical buckling temperature relationsfor functionally graded plates with linearcomposition of constituent materials and homogeneous plates. The results are validated with the reduction of the buckling relations for functionally graded plates to those of isotropic homogeneous plates given in the literature.
381 citations
TL;DR: In this paper, a general analysis of one-dimensional steady-state thermal stresses in a hollow thick cylinder made of functionally graded material is developed, where the temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions along the inside and outside surfaces.
361 citations
TL;DR: In this article, equilibrium and stability equations of a rectangular plate made of functionally graded material (FGM) under thermal loads are derived, based on the higher order shear deformation plate theory.
Abstract: Equilibrium and stability equations of a rectangular plate made of functionally graded material (FGM) under thermal loads are derived, based on the higher order shear deformation plate theory. Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations is established. The derived equilibrium and stability equations for functionally graded plates (FGPs) are identical to the equations for laminated composite plates. A buckling analysis of a functionally graded plate under four types of thermal loads is carried out and results in closed-form solutions. The critical buckling temperature relations are reduced to the respective relations for functionally graded plates with a linear composition of constituent materials and homogeneous plates. The results are compared with the critical buckling temperatures obtained for functionally graded plates based on classical plate theory given in...
317 citations
TL;DR: In this paper, a finite element computation of fracture parameters in functionally graded material (FGM) assemblages of arbitrary geometry with stationary cracks is addressed, where the elastic moduli are smooth functions of spatial co-ordinates which are integrated into the element stiffness matrix.
Abstract: This paper is directed towards finite element computation of fracture parameters in functionally graded material (FGM) assemblages of arbitrary geometry with stationary cracks. Graded finite elements are developed where the elastic moduli are smooth functions of spatial co-ordinates which are integrated into the element stiffness matrix. In particular, stress intensity factors for mode I and mixed-mode two-dimensional problems are evaluated and compared through three different approaches tailored for FGMs: path-independent J*k-integral, modified crack-closure integral method, and displacement correlation technique. The accuracy of these methods is discussed based on comparison with available theoretical, experimental or numerical solutions. Copyright © 2001 John Wiley & Sons, Ltd.
310 citations
TL;DR: In this article, a new interaction energy integral method for the computation of mixed-mode stress intensity factors at the tips of arbitrarily oriented cracks in functionally graded materials is described, where the auxiliary stress and displacement fields are chosen to be the asymptotic near-tip fields for a homogeneous material having the same elastic constants as those found at the crack tip in the functionally graded material.
250 citations
TL;DR: In this article, the equilibrium and stability equations of rectangular functionally graded plates (FGPs) are determined using the variational approach, where the material properties vary with the power product form of thickness coordinate variable z.
Abstract: In the present article, equilibrium and stability equations of rectangular functionally graded plates (FGPs) are determined using the variational approach. Derivation of equations are based on the classical plate theory. It is assumed that the material properties vary with the power product form of thickness coordinate variable z. Equilibrium and stability equations for FGPs are the same as the equations for homogeneous plates. The equilibrium and stability equations are employed to study the buckling behaviour of functionally graded plates with all edges simply supported and subjected to in-plane loading conditions. By equating power law index to zero, predicted relation is reduced to the buckling equation of homogeneous plates which is available in the literature.
248 citations
TL;DR: In this article, the buckling analysis of radially loaded solid circular plate made of functionally graded material is presented, where the edge is either simply supported or clamped and the plate is assumed to be geometrically perfect and the equilibrium and stability equations, derived through variational formulation, are used to determine the prebuckling forces and critical buckling loads.
179 citations
TL;DR: In this article, a finite element methodology is developed for fracture analysis of orthotropic functionally graded materials (FGMs) where cracks are arbitrarily oriented with respect to the principal axes of material orthotropy.
166 citations
TL;DR: In this paper, the nonlinear equilibrium and linear stability equations are derived using variational formulations for thermal buckling of solid circular plates under uniform temperature rise, gradient through the thickness, and linear temperature variation along the radius.
Abstract: Thermal buckling of circular plates made of functionally graded material is discussed. The nonlinear equilibrium and linear stability equations are derived using variational formulations. The thermal buckling of solid circular plates under uniform temperature rise, gradient through the thickness, and linear temperature variation along the radius are considered, and the buckling temperatures are derived. The buckling temperatures are derived for simply supported and clamped edges. The results are verified with known results in the literature.
143 citations
TL;DR: In this paper, the authors examined the possibility of the gradual particle size distributions in the functionally graded material (FGM) fabricated by centrifugal solid-particle method and found that the larger particles are located in the outer part of the tube.
128 citations
TL;DR: In this paper, an analytical-numerical method is presented for analysing characteristics of waves in a cylinder composed of functionally graded material (FGM), where the FGM cylinder is divided into a number of annular elements with three-nodal lines in the wall thickness.
Abstract: An analytical-numerical method is presented for analysing characteristics of waves in a cylinder composed of functionally graded material (FGM). In this method, the FGM cylinder is divided into a number of annular elements with three-nodal-lines in the wall thickness. The elemental material properties are assumed to vary linearly in the thickness direction so as to better model the spatial variation of material properties of FGM. The Hamilton principle is used to develop the dispersion equations for the cylinder, and the frequency and the group velocity are established in terms of the Rayleigh quotient. The method is applied to analyse several FGM cylinders, and its efficiency is demonstrated. Numerical results demonstrate that the ratio of radius to thickness has a stronger influence on the frequency spectra in the circumferential wave than on that in the axial wave, that negative group velocity presents at a range of smaller wave numbers and that the range varies as the wave normal and the ratio of radius to thickness of FGM cylinders. Copyright © 2001 John Wiley & Sons, Ltd.
TL;DR: In this article, a functionally graded bioactive coating was obtained by coating titanium oxide (TiO 2 ) powders of known particle size as the first layer, which was sintered at 900 °C for a few minutes.
TL;DR: In this paper, a generic static and dynamic finite element formulation is derived for the modeling and control of piezoelectric shell laminates under coupled displacement, temperature and electric potential fields.
Abstract: A generic static and dynamic finite element formulation is derived for the modelling and control of piezoelectric shell laminates under coupled displacement, temperature and electric potential fields. The base shell is of functionally graded material (FGM) type, which consists of combined ceramic–metal materials with different mixing ratios of the ceramic and metal constituents. A multi-input–multi-output (MIMO) system is applied to provide active feedback control of the laminated shell using self-monitoring sensors and self-controlling actuators through a close loop. Numerical studies clearly show the influence of the positional configurations of sensor/actuator pairs on the effectiveness of static and dynamic control for the shell laminates. The effects of the constituent volume fractions on the static and dynamic responses of the shell laminate are also elucidated. Copyright © 2002 John Wiley & Sons, Ltd.
TL;DR: In this paper, a Green's function approach based on the laminate theory is adopted for solving the two-dimensional unsteady temperature field (r, z) and the associated thermal stresses in an infinite hollow circular cylinder made of a functionally graded material (FGM) with radial-directionally dependent properties.
Abstract: A Green's function approach based on the laminate theory is adopted for solving the two-dimensional unsteady temperature field (r, z) and the associated thermal stresses in an infinite hollow circular cylinder made of a functionally graded material (FGM) with radial-directionally dependent properties. The unsteady heat conduction equation is formulated as an eigenvalue problem by making use of the eigenfunction expansion theory and the laminate theory. The eigenvalues and the corresponding eigenfunctions obtained by solving an eigenvalue problem for each layer constitute the Green's function solution for analyzing the unsteady temperature. The associated thermoelastic field is analyzed by making use of the thermoclastic displacement potential function and Michell's function. Numerical results are carried out and shown in figures.
TL;DR: In this article, a functionally graded material strip containing an embedded or a surface crack perpendicular to its boundaries is considered, and the problem is reduced to an integral equation and is solved numerically.
Abstract: Functionally Graded Materials (FGMs) have been developed as super-resistant materials for propulsion systems and airframe of space-planes in order to decrease thermal stresses and to increase the effect of protection from heat. It has been experimentally observed that surface cracking in FGMs is the most common failure mode of a metal-ceramic FGM when it is subjected to a thermal shock. Therefore, it is very important to consider the thermally induced fracture behaviors of FGMs. In this paper, a functionally graded material strip containing an embedded or a surface crack perpendicular to its boundaries is considered. The graded region is treated as a large number of single layers, with each layer being homogeneous material. The problem is reduced to an integral equation and is solved numerically. Unlike most of the existing researches, which considered only certain assumed material distributions, the method developed in this paper can be used to investigate functionally graded materials with arbitrarily varied material properties.
TL;DR: In this paper, a generic finite element formulation is developed for the static and dynamic control of FGM shells with piezoelectric sensor and actuator layers, where the properties of the FGM shell are graded in the thickness direction according to a volume fraction power-law distribution.
Abstract: In this paper, a generic finite element formulation is developed for the static and dynamic control of FGM (functionally graded material) shells with piezoelectric sensor and actuator layers. The properties of the FGM shell are graded in the thickness direction according to a volume fraction power-law distribution. The proposed finite element model is based on variational principle and linear piezoelectricity theory. A constant displacement and velocity feedback control algorithm coupling the direct and inverse piezoelectric effects is applied in a closed-loop system to provide feedback control of the integrated FGM shell structure. Both static and dynamic control of FGM shells are simulated to demonstrate the effectiveness of the proposed active control scheme within a framework of finite element discretization and piezoelectric integration.
TL;DR: In this article, a self-consistent constitutive framework is proposed to describe the behavior of a generic three-layered system containing a functionally graded material (FGM) layer subjected to thermal loading.
Abstract: In this work, a self-consistent constitutive framework is proposed to describe the behaviour of a generic three-layered system containing a functionally graded material (FGM) layer subjected to thermal loading. Analytical and semi-analytical solutions are obtained to describe the thermo-elastic and thermo-elastoplastic behaviour of a three-layered system consisting of a metallic and a ceramic layer joined together by an FGM layer of arbitrary composition profile. Solutions for the stress distributions in a generic FGM system subjected to arbitrary temperature transient conditions are presented. The homogenisation of the local elastoplastic FGM behaviour in terms of the properties of its individual phases is performed using a self-consistent approach. In this work, power-law strain hardening behaviour is assumed for the FGM metallic phase. The stress distributions within the FGM systems are compared with accurate numerical solutions obtained from finite element analyses and good agreement is found throughout. Solutions are also given for the critical temperature transients required for the onset of plastic deformation within the three-layered systems.
TL;DR: In this article, a computational method is presented to investigate SH waves in functionally graded material (FGM) plates, in which the material properties are assumed as a quadratic function in the thickness direction, and a general solution for the equation of motion governing the QLE has been derived.
TL;DR: In this article, functionally graded material is modeled in several different ways, including fiber phases and particle phases, and four different dynamic input loads are applied to the detailed micro-structure to examine its effect.
Abstract: In this investigation, functionally graded material is modeled in several different ways. Five models are presented, two of which simulate fiber phases and three simulate particle phases. For fibers, there is a model in which the detailed micro-structure is simulated and one in which the material is represented by layers such that the volume fraction of the fibers in each layer changes. For the particles, a model with layers is employed and two models with continuously changing material parameters are presented. Four different dynamic input loads are applied to the detailed micro-structure to examine its effect. The finite element method is employed to determine the effective stress. Then one of the dynamic loads which simulates a step function is applied to all models. It is observed that there are no significant differences in the effective stresses at particular points within the time domain. The amplitude of the wave for each model is quite similar. The phase of the wave shifts as time increases. Thus, in the space domain, differences are observed in the effective stress at a particular time. As may be expected, the stresses are rather high within the fibers in the detailed micro-structural model. It is concluded that a continuously changing material model is a good candidate for carrying out dynamic analyses of functionally graded material.
TL;DR: In this paper, the singular behavior of a propagating crack in a functionally graded material (FGM) with spatially varying elastic properties under plane elastic deformation was investigated in terms of Fourier transforms and the solution of the resulting singular integral equations by using Chebyshev polynomials.
TL;DR: In this article, a laminated piezoelectric bimorph actuator with a graded compositional distribution of PZT and Pt was fabricated, and its deflection characteristics were evaluated.
TL;DR: In this paper, the eigenfunctions of Green's function for the transient temperature distribution of a plate made of functionally graded materials (FGMs) were derived from the continuity conditions of the temperature and the heat flux at interfaces.
Abstract: Green's function approach is adopted for analyzing the deflection and the transient temperature distribution of a plate made of functionally graded materials (FGMs). The governing equations for the deflection and the transient temperature are formulated into eigenvalue problems by using the eigenfunction expansion theory. Green's functions for solving the deflection and the transient temperature are obtained by using the Galerkin method and the laminate theory, respectively. The eigenfunctions of Green's function for the deflection are approximated in terms of a series of admissible functions that satisfy the homogeneous boundary conditions of the plate. The eigenfunctions of Green's function for the temperature are determined from the continuity conditions of the temperature and the heat flux at interfaces.
TL;DR: In this article, a flat-shell element is presented for the active control of functionally graded material (FGM) shells through integrated piezoelectric sensor/actuator layers.
Abstract: A flat-shell element is presented for the active control of functionally graded material (FGM) shells through integrated piezoelectric sensor/actuator layers. The finite element formulation based on first-order shear deformation theory (FSDT) can be applied to shells ranging from relatively thin to moderately thick dimensions. A constant gain displacement and velocity feedback control algorithm coupling the direct and inverse piezoelectric effects is applied to provide active control of the integrated FGM shell in a self-monitoring and self-controlling system. Frequency response characteristics of the FGM shell containing the piezoelectric sensors/actuators are analyzed in the frequency domain. The effects of constituent volume fraction and the influence of feedback control gain values on the dynamic responses of the FGM shell system are examined in detail.
TL;DR: In this paper, the authors present experimental measurements of the through-thickness distribution of residual stress in a ceramic-metallic functionally graded material (FGM) and further present an error analysis and optimization of the residual stress measurement technique.
Abstract: This paper presents experimental measurements of the through-thickness distribution of residual stress in a ceramic-metallic functionally graded material (FGM). It further presents an error analysis and optimization of the residual stress measurement technique, Measurements are made in a seven-layered plate with a base of commercially pure titanium and successive layers containing an increasing proportion of titanium-boride, reaching 85% titanium-boride in the final layer. The compliance method is employed to determine residual stress, where a slot is introduced using wire electric-discharge machining and strain release is measured as a function of increasing slot depth. Strain release measurements are used with a back-calculation scheme, based on finite element simulation, to provide residual stresses in the FGM. The analysis is complicated by the variation of material properties in the FGM, but tractable due to the flexibility of the finite element method. The Monte Carlo approach is used for error analysis and a method is described for optimization of the functional form assumed for the residual stresses. The magnitude and variation of the resulting residual stress distributions and several aspects of the error analyses are discussed.
TL;DR: In this article, transient heat conduction in a strip of a functionally graded material (FGM) with continuous and piecewise differentiable properties was studied, where a multi-layered material model was used to obtain the Laplace transforms of temperatures at the interfaces between the layers.
TL;DR: In this article, a two-phase isotropic composite under time-dependent thermomechanical loadings is considered and a control-like problem and a structural optimization problem are formulated using a common framework.
TL;DR: In this article, a numerical method is proposed for analyzing transient waves in cylindrical shells of a functionally graded material (FGM) excited by impact point loads, where the FGM shell is divided into layer elements with three nodal lines along the wall thickness.
TL;DR: In this article, the authors used crack tip measurements to examine continuum models for FGMs by treating the material as isotropic and nonhomogeneous at macroscales, where cracks are located on the compliant and the stiff sides of the beams are separately examined by mapping cracks using optical interferometry.
Abstract: Particulate functionally graded materials (FGM) made of glass-filled epoxy with edge cracks parallel to the direction of the elastic gradient and subjected to pure bending have been studied. Crack tip measurements are used to examine continuum models for FGMs by treating the material as isotropic and nonhomogeneous at macroscales. Situations where cracks are located on the compliant and the stiff sides of the beams are separately examined by mapping crack tip deformations using optical interferometry. Comparative experiments on homogeneous compositions corresponding to identical elastic properties of the crack tip region in the FGM are also undertaken. A methodology for extracting fracture parameters in FGMs based on locally homogeneous material descriptions is advanced. Companion finite element models are used to aid the development of fringe analysis procedures and to provide a direct comparison to the optical measurements. Stress intensity factors in FGMs are compared to each other and to their homogeneous counterparts. Optical measurements near quasi-statically growing cracks in FGMs have been undertaken, and crack growth resistance behavior is explained using crack initiation toughness variation as a function of filler volume fraction in homogeneous sheets.
TL;DR: In this paper, a crack in a viscoelastic strip of a functionally graded material (FGM) is studied under tensile loading conditions, where the extensional relaxation modulus is assumed as E=E0exp(βy/h)f(t), where h is a scale length and f(t) is a nondimensional function of time t.
TL;DR: In this paper, a numerical procedure to determine an optimal material layout of a functionally graded material (FGM) within the context of a transient phenomenon is presented, in which the physical problem considered here is transient heat conduction.