Sharif Digital Repository

In this paper, the vibration of a constant thickness circular plate made of functionally graded material (FGM) is controlled by implementing two piezoelectric layers as a sensor and an actuator. Assuming that the material properties of FGM plate vary only in the thickness direction according to the power law manner, the governing differential equations are derived based on the Reissner-Mindlin plate theory (RMPT). Moreover, in a parallel work another set of differential equations are also derived using classical plate theory (CPT). Then for two different kinds of plate boundary conditions these coupled differential equations are solved using separation of variable technique and obtained... 

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. The temperature distribution is assumed to be a function of radius, with general thermal and mechanical boundary conditions along the inside and outside surfaces. The material properties, except Poisson's ratio, are assumed to depend on variable the r and they are expressed as power functions of r. The direct method is used to solve the heat conduction and Navier equations. © 2002 Elsevier Science Ltd. All rights reserved  

The effect of axial deformation of shell particles on the dynamic instability (flutter) of cantilevered cylindrical shells made of functionally graded materials (FGM) under an end axial follower force is addressed. To this end, at first, results for free vibration of FGM cylindrical shells were verified with previous outcomes and they were in very good agreement. Then, the effect of axial deformation of the shell, acting like a reducing linearly-distributed follower load, on the critical circumferential mode number and the flutter load of FGM shells was accounted for. Finally, the effect of axial deformation of the shell particles on the critical circumferential mode number and the flutter... 

The performance of perturbation method in nonlinear analyses of plates subjected to mechanical, thermal, and thermo-mechanical loadings is investigated. To this end, cylindrical bending of FG plates with clamped and simply-supported edges is considered. The governing equations of Mindlin's first-order shear deformation theory with von Kármán's geometric nonlinearity are solved using one- and two-parameter perturbation methods and the results are compared with the results of an analytical solution. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. It is shown that the... 

The performance of perturbation method in nonlinear analyses of plates subjected to mechanical, thermal, and thermo-mechanical loadings is investigated. To this end, cylindrical bending of FG plates with clamped and simply-supported edges is considered. The governing equations of Mindlin's first-order shear deformation theory with von Kármán's geometric nonlinearity are solved using one- and two-parameter perturbation methods and the results are compared with the results of an analytical solution. The material properties are assumed to vary continuously through the thickness of the plate according to a power-law distribution of the volume fraction of the constituents. It is shown that the... 

The experimental observations indicate that the mechanical behavior of micro and nano scale structures is size-dependent. In this study, employing the modified couple stress theory the size-dependent strain energy release rate of notched Euler-Bernoulli beams made of functionally graded material (FGM) is formulated. The normalized energy release rate for the problem of three-point bending in notched FG beams is obtained using the procedure established by Kienzler and Herrmann [Kienzler R, Herrmann G, An elementary theory of defective beams. Acta Mech 1986; 62:37-46]. It is assumed that the material properties vary continuously along the beam thickness according to a power law distribution.... 

In this study, nonlinear bending of functionally graded (FG) circular sector plates with simply supported radial edges subjected to transverse mechanical loading has been investigated. Based on the first-order shear deformation plate theory with von Karman strain-displacement relations, the nonlinear equilibrium equations of sector plates are obtained. Introducing a stress function and a potential function, the governing equations which are five non-linear coupled equations with total order of ten are reformulated into three uncoupled ones including one linear edge-zone equation and two nonlinear interior equations with total order of ten. The uncoupling makes it possible to present... 

Functionally graded material shafts are the main part of many modern rotary machines such as turbines and electric motors. The purpose of this study is to present an analytical solution of the elastic-plastic deformation of functionally graded material hollow rotor under a high centrifugal effect and finally determine the maximum allowed angular velocity of a hollow functionally graded material rotating shaft. Introducing non-dimensional parameters, the equilibrium equation has been analytically solved. The results for variable material properties are compared with the homogeneous rotor and the case in which Young’s modulus is the only variable while density and yield stress are considered... 

In this article, vibration of viscoelastic axially functionally graded (AFG) moving Rayleigh and Euler-Bernoulli (EB) beams are investigated and compared, aiming at a performance improvement of translating systems. Additionally, a detailed study is performed to elucidate the influence of various factors, such as the rotary inertia factor and axial gradation of material on the stability borders of the system. The material properties of the beam are distributed linearly or exponentially in the longitudinal direction. The Galerkin procedure and eigenvalue analysis are adopted to acquire the natural frequencies, dynamic configuration, and instability thresholds of the system. Furthermore, an... 

In this paper, the general theoretical analysis of two-dimensional steady-state thermal stresses for a hollow thick cylinder made of functionally graded material is developed. The temperature distribution is assumed to be a function of radial and circumferential directions with general thermal and mechanical boundary conditions on the inside and outside surfaces. The material properties, except Poisson's ratio, are assumed to depend on the variable r and they are expressed as power functions of r. The separation of variables and complex Fourier series are used to solve the heat conduction and Navier equations  

The cast-decant-cast is a new method for the preparation of the functionally graded components that has been developed in recent years. The functionally graded cylindrical shape component with a radial gradient, e.g. the first alloy (A390) with high wear resistance on the surface of the piece and toughness and the second alloy (A356) of low machining costs in the core of the piece can be produced via this melt process. The effect of the second alloy superheat at temperatures of 750, 820 and 860 °C as well as the effect of the first alloy solidified layer at 25, 35 and 45 s decanting time on achieving the perfect interface between the two alloys was investigated. The characterization of the... 

This study presents the bending analysis of functionally graded conical panels under transverse compression with various boundary conditions. Equations was derived using first order shear deformation theory (FSDT) and solved using generalized differential quadrature (GDQ) method. Using this method results in the capability of studying any combinations of boundary conditions on four edges of the panel. Results are compared and validated with the results available in the literature. Effect of boundary conditions, volume fractions, panel length, semi-vertex angle and subtended angle on deflection of the panel was investigated  

Eshelby's theories on the nature of the disturbance strains due to polynomial eigenstrains inside an isotropic ellipsoidal inclusion, and the form of homogenizing eigenstrains corresponding to remote polynomial loadings in the equivalent inclusion method (EIM) are not valid for spherically anisotropic inclusions and inhomogeneities. Materials with spherically anisotropic behavior are frequently encountered in nature, for example, some graphite particles or polyethylene spherulites. Moreover, multi-inclusions/inhomogeneities/ inhomogeneous inclusions have abundant engineering and scientific applications and their exact theoretical treatment would be of great value. The present work is devoted... 

Aseptic loosening is one of the main reasons for the revision of a total knee replacement (TKR). The design of the key component of a TKR, the femoral component, is particularly problematic because its failure can be the result of different causes. This makes the development of new biomaterials for use in the femoral component a challenging task. This paper focuses on the engineering design aspects in order to understand the limitationsof current materials and design deficiencies. The paper describes the introduction of a new biomaterial for a femoral component and justifies the recommendation to use multi-functional materials as a possible solution to aseptic loosening. The potential... 

The sliding frictional contact problem for a laterally graded half-plane has been considered. Two finite element (FE) models, in macro and micro scales have been developed to investigate the effective parameters in contact mechanics of laterally graded materials loaded by flat and triangular rigid stamps. In macro scale model, the laterally graded half-plane is discretized by piecewise homogeneous layers for which the material properties are specified at the centroids by Mori-Tanaka method. In micro scale model, functionally graded material (FGM) structure has been modeled as ideal solid quadrant particles which are spatially distributed in a homogeneous matrix. Boundary conditions and... 

A size-dependent functionally graded Euler-Bernoulli beam model is developed based on the strain gradient theory, a non-classical theory capable of capturing the size-effect in micro-scaled structures. The governing equation and both classical and non-classical boundary conditions are obtained using variational approach. To develop the new model, the previously used simplifying assumption which considered the length scale parameter to be constant through the thickness is avoided in this work. As a consequence, equivalent length scale parameters are introduced for functionally graded microbeams as functions of the constituents' length scale parameters. Moreover, a generally valid closed-form... 

In the present paper, buckling behavior of a rectangular Functionally Graded Plate (FGP) under combined shear and direct loading is considered. The total potential energy is derived for a FGP in stability condition. Derivation of totalpotential function is based on the classical plate theory. Also, in-plane flexibility is considered in shear buckling analysis. It is assumed that the non-homogeneous mechanical properties of the plate graded through thickness and are described with a power function of the thickness variable. The critical buckling shear loads in conjunction with in-plane direct loads have been obtained for different ratios and power law indices of functionally graded materials... 

Two new displacement potential functions are introduced for the general solution of a three-dimensional piezoelasticity problem for functionally graded transversely isotropic piezoelectric solids. The material properties vary continuously along the axis of symmetry of the medium. The four coupled equilibrium equations in terms of displacements and electric potential are reduced to two decoupled sixth- and second-order linear partial differential equations for the potential functions. The obtained results are verified with two limiting cases: (i) a functionally graded transversely isotropic medium, and (ii) a homogeneous transversely isotropic piezoelectric solid. The simplified relations... 

In this paper, pull-in behavior of cantilever micro/nano-beams made of functionally graded materials (FGM) with small-scale effects under electrostatic force is investigated. Consistent couple stress theory is employed to study the influence of small-scale on pull-in behavior. According to this theory, the couple tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients. The material properties except Poisson’s ratio obey the power law distribution in the thickness direction. The approximate analytical solutions for the pull-in voltage and pull-in displacement of the microbeams are derived using the Rayleigh–Ritz method. Comparison between the results of the...