Sharif Digital Repository

In this paper, flutter of functionally graded material (FGM) cylindrical shells under distributed axial follower forces is addressed. The first-order shear deformation theory is used to model the shell, and the material properties are assumed to be graded in the thickness direction according to a power law distribution using the properties of two base material phases. The solution is obtained by using the extended Galerkin's method, which accounts for the natural boundary conditions that are not satisfied by the assumed displacement functions. The effect of changing the concentrated (Beck's) follower force into the uniform (Leipholz's) and linear (Hauger's) distributed follower loads on the... 

Flutter of cantilevered, functionally graded cylindrical shells under an end axial follower force is addressed. The material properties are assumed to be graded along the thickness direction according to a simple power law. Using the Hamilton principle, the governing equations of motion are derived based on the first-order shear deformation theory. The stability analysis is carried out using the extended Galerkin method and minimum flutter loads and corresponding circumferential mode numbers are obtained for different volume fractions, length-to-radius, and thicknesses-to-radius ratios. Two different configurations are considered for the FGM: one in which the metal phase is the outer layer... 

The properties of Functionally Graded Materials (FGM) are characterized by gradual variation of volume fraction of their constituents or phases over the thickness direction. They are normally ceramic in one side and metal in the other side. This kind of material has been employed as thermal barrier and also as coatings in many applications including turbine blades. Thermal stress behavior of FGMs is normally studied by simulating the material as a composite laminate where the properties ofeach layer are found by averaging the properties and volume fraction of FGM constituents through the thickness of the layer. However, it should be mentioned that the grains of FGM constituents are usually... 

A finite element formulation is derived for the structural analysis of functionally graded hollow cylinders. The power-law distribution model is used for the composition of the constituent material in the thickness direction. According to property variation in FG cylinders, it is difficult to analyze them using the conventional element formulation. In order to facilitate the process of modeling and analyzing the FG cylinders, the finite element formulation is based on a newly designed cylindrical element. The new cylindrical element allows for property variations along the thickness, which results in considerable reduction of the required elements and eliminates the need to mesh the cross... 

Rings are widely used in mechanical equipment, and their fitness may undergo some damage under severe vibration. In these structures, functionally graded rings can be used to optimize the resistance, energy consumption, and fitness. Due to their complexity, the finite-element analysis may be implemented using special elements. Enhancement of accuracy and minimization of time consumption play an important role in the analysis of these rings. In this study, a new cylindrical superelement for the FGM rings is designed and implemented to facilitate the vibration analysis of the rings. The power-law distribution is used for the modeling of the FGM rings in the thickness direction. Natural... 

In this research, electrically characteristics of a graphene nanoplatelet (GPL)-reinforced composite (GPLRC) microdisk are explored using generalized differential quadrature method. Also, the current microstructure is coupled with a piezoelectric actuator (PIAC). The extended form of Halpin–Tsai micromechanics is used to acquire the elasticity of the structure, whereas the variation of thermal expansion, Poisson’s ratio, and density through the thickness direction is determined by the rule of mixtures. Hamilton’s principle is implemented to establish governing equations and associated boundary conditions of the GPLRC microdisk joint with PIAC. The compatibility conditions are satisfied by... 

Deformation modeling of an infinite plate of functionally graded materials (FGMs) loaded by normal force to the plate surface is studied. The material properties of FGM plate 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. The governing equations are based on stress-strain relation and the equilibrium force equation. Keeping generality, FGM plate has been assumed as a multilayer with linear material property in each layer while arbitrary exponential material property through the thickness. A plate made of Aluminum and Alumina is considered as an example to illustrate the effects of the... 

This paper presents free vibration analysis of functionally graded material (FGM) beams with different boundary conditions, using RKPM (Reproducing Kernel Particle Method), which is a meshless method. System of equations of motion is derived by using Lagrange's method under the assumption of Euler-Bernoulli beam theory. Boundary conditions of beam are taken into account by using Lagrange multipliers. It is assumed that material properties of the beam vary continuously in the thickness direction according to the power-law form. RKPM is applied to obtain eigenvalue equation of vibration and natural frequencies are obtained. It should be noted that for special cases where the beam is uniform,... 

The electroelastic response of functionally graded piezoelectric cantilever beams which includes the effect of body force is presented in this paper. The material properties such as elastic compliance, piezoelectric and dielectric impermeability are assumed to be graded with different indices in the thickness direction according to exponential distributions. Systems of fourth order inhomogeneous partial differential equations (PDEs) which are satisfied by the stress and induction functions and involve the body force terms are derived. Spectral forms for electrical and mechanical variables in the x-axis are employed to convert the partial differential governing equations and the associated... 

Based on classical plate theory (CLPT), free vibration analysis of a circular plate composed of functionally graded material (FGM) with its upper and lower surfaces bounded by two piezoelectric layers was performed. Assuming that the material properties vary in a power law manner within the thickness of the plate the governing differential equations are derived. The distribution of electric potential along the thickness direction in piezoelectric layers is considered to vary quadratically such that the Maxwell static electricity equation is satisfied. Then these equations are solved analytically for two different boundary conditions, namely clamped and simply supported edges. The validity of... 

In this study, buckling and vibrational characteristics of a nanoshell reinforced with graphene nanoplatelets under uniform axial load are investigated. The material properties of the piece-wise graphene-reinforced composites (GPLRCs) are assumed to be graded in the thickness direction of a nanoshell and are estimated using a nanomechanical model. The effects of the small scale are analyzed based on nonlocal stress–strain gradient theory (NSGT). The governing equations and boundary conditions (BCs) are developed using Hamilton’s principle and are solved with assistance of the generalized differential quadrature method. The novelty of the current study is the consideration of GPLRC and size... 

In this research, electrically characteristics of a graphene nanoplatelet (GPL)-reinforced composite (GPLRC) microdisk are explored using generalized differential quadrature method. Also, the current microstructure is coupled with a piezoelectric actuator (PIAC). The extended form of Halpin–Tsai micromechanics is used to acquire the elasticity of the structure, whereas the variation of thermal expansion, Poisson’s ratio, and density through the thickness direction is determined by the rule of mixtures. Hamilton’s principle is implemented to establish governing equations and associated boundary conditions of the GPLRC microdisk joint with PIAC. The compatibility conditions are satisfied by... 

The dynamic behavior of a functionally graded (FG) simply supported Euler-Bernoulli beam subjected to a moving oscillator has been investigated in this paper. The Young's modulus and the mass density of the FG beam vary continuously in the thickness direction according to the power-law model. The system of equations of motion is derived by using Hamilton's principle. By employing Petrov-Galerkin method, the system of fourth-order partial differential equations of motion has been reduced to a system of second-order ordinary differential equations. The resulting equations are solved using Runge-Kutta numerical scheme. In this study, the effect of the various parameters such as power-law... 

An internal crack located within a functionally graded material (FGM) strip bonded with two dissimilar half-planes and under an anti-plane load is considered. The crack is oriented in an arbitrary direction. The material properties of strip are assumed to vary exponentially in the thickness direction and two half-planes are assumed to be isotropic. Governing differential equations are derived and to reduce the difficulty of the problem dealing with solution of a system of singular integral equations Fourier integral transform is employed. Semi closed form solution for the stress distribution in the medium is obtained and mode III stress intensity factor (SIF), at the crack tip is calculated...