From Functionally Graded Materials Research Articles

Modified model for instability analysis of symmetric FGM double-sided nano-bridge: Corrections due to surface layer, finite conductivity and size effect

Finite conductivity, size dependency and surface layer are known as crucial factors that affect the electromechanical response and pull-in instability of micro/nano-electromechanical systems (MEMS/NEMS). However, these effects are yet ignored on modeling the instability of MEMS/NEMS fabricated from functionally graded materials (FGMs). Herein, a modified continuum model is developed to incorporate these effects on the dynamic behavior and electromechanical instability of double-sided FGM NEMS bridge. Using Gurtin–Murdoch model in conjunction with nonlocal Eringen elasticity, the governing equations of the nano-bridges is derived considering the surface layer and size dependency. The Coulomb and Casimir forces are incorporated in the governing equation considering the corrections due to the finite conductivity of FGM (relative permittivity and plasma frequency). The validity of the proposed method is elucidated by comparing the results obtained from the present study with the results reported in the literature. The stability analysis of the nanostructure is conducted by plotting time history and phase portraits. The effects of various parameters including finite conductivity, nonlocal parameter, surface stresses and material characteristics on the dynamic pull-in behavior of the nano-bridges are studied. The obtained results imply a significant impact of the abovementioned corrections on the instability threshold and pull-in parameters of the FGM nanobridge.

Vibration characteristics of stepped beams made of FGM using differential transformation method

The present paper is given to investigate free vibration analysis of stepped beams produced from functionally graded materials (FGMs). The differential transformation method is employed to solve the governing differential equations of the beams to obtain their natural frequencies and mode shapes. The power law distribution is used and modified for describing material compositions across the thickness of the stepped beams made of FGM. Two main types of the stepped FGM beams in which their material compositions can be described by the modified power law distribution are selected to investigate the free vibration behaviour. The significant parametric studies such as step ratio, step location, boundary conditions and material volume fraction are also covered in this paper.

Vibration response of stepped FGM beams with elastically end constraints using differential transformation method

In this paper, free vibration response of stepped beams made from functionally graded materials (FGMs) is investigated. The beams are supported by various types of elastically end constraints. The differential transformation method (DTM) is employed to solve the governing differential equations of such beams in order to obtain natural frequencies and mode shapes. The power law distribution is used and modified to describe material compositions across the thickness of the beams made of FGMs. Two main types of the stepped FGM beams in which their material compositions can be described by using the modified power law distribution are selected to investigate their vibration behaviour. The significant parametric studies such as step ratio, step location, boundary conditions, spring constants and material volume fraction are taken into investigation.

A three-dimensional boundary element stress and bending analysis of transversely/longitudinally graded plates with circular cutouts under biaxial loading

Abstract In the present paper, a full three-dimensional graded boundary element model adequate for elastostatic response investigation of heterogeneous plates fabricated from functionally graded materials (FGMs) with circular cutouts is presented. The local volume fractions of the constituent materials vary continuously in the transverse or longitudinal direction according to an exponential law. In contrast to all of the available works, influence of the bending-extension coupling due to asymmetric transverse distribution of the material properties is considered under a biaxial loading. The available works have used the plane stress assumption. A numerical implementation of Somigliana identity for three-dimensional elasticity of the isotropic heterogeneous plates is represented implicitly. On the basis of the constitutive and governing equations of the FGM plate and the weighted residual technique, an effective computational formulation is developed for the heterogeneous isotropic solid models. Verification is accomplished through comparisons made with results of ANSYS software for homogeneous models. Influence of the location of the cutout, effects of the distance from the boundary, and effects of the load ratio have also been studied and discussed in detail.

Vibration Characteristics of Ring-Stiffened Functionally Graded Circular Cylindrical Shells

The vibration characteristics of ring stiffened cylindrical shells are analyzed. These shells are assumed to be structured from functionally graded materials (FGM) and are stiffened with isotropic rings. The problem is formulated by coupling the expressions for strain and kinetic energies of a circular cylindrical shell with those for rings. The Lagrangian function is framed by taking difference of strain and kinetic energies. The Rayleigh-Ritz approach is employed to obtain shell dynamical equations. The axial model dependence is approximated by characteristic beam functions that satisfy the boundary conditions. The validity and efficiency of the present technique are verified by comparisons of present results with the previous ones determined by other researchers.

Design of new generation femoral prostheses using functionally graded materials: A finite element analysis

This study aimed to develop a three-dimensional finite element model of a functionally graded femoral prosthesis. The model consisted of a femoral prosthesis created from functionally graded materials (FGMs), cement, and femur. The hip prosthesis was composed of FGMs made of titanium alloy, chrome-cobalt, and hydroxyapatite at volume fraction gradient exponents of 0, 1, and 5, respectively. The stress was measured on the femoral prosthesis, cement, and femur. Stress on the neck of the femoral prosthesis was not sensitive to the properties of the constituent material. However, stress on the stem and cement decreased proportionally as the volume fraction gradient exponent of the FGM increased. Meanwhile, stress became uniform on the cement mantle layer. In addition, stress on the femur in the proximal part increased and a high surface area of the femoral part was involved in absorbing the stress. As such, the stress-shielding area decreased. The results obtained in this study are significant in the design and longevity of new prosthetic devices because FGMs offer the potential to achieve stress distribution that more closely resembles that of the natural bone in the femur.

Buckling of FGM cylindrical shells subjected to pure bending load

In this paper, buckling behaviors of composite cylindrical shells made from functionally graded materials (FGMs) subjected to pure bending load were investigated. The material properties were assumed to be graded along the thickness. The non-uniform bending force on the shell section was considered in the buckling government equation of FGM cylindrical shells based on the Donnell shallow shell theory. The prebuckling deformation of the FGM cylindrical shells was neglected and the buckling mode was assumed to occur non-uniformly in local district along the shell circumferential direction. The eigenvalue method was used to obtain the buckling critical condition. The theoretical results were in excellent agreement with those of ABAQUS code. Results show that the inhomogenity of the materials is significant for buckling of FGM cylindrical shells.

Active Vibration Control of an FGM Rectangular Plate using Fuzzy Logic Controllers

In this paper, active vibration control of a simply supported rectangular plate made from functionally graded materials (FGM) with fuzzy logic control (FLC) is investigated and compared to the results obtained with the application of PID control. According to the importance of vibration reduction of plates as a major element of industrial and aerospace structures many researches in this field have been done. Application of smart materials specially, piezoelectric patches as actuators and sensors can effectively reduce plate vibrations. Firstly differential equation of motion for a rectangular plate made of functionally graded material equipped with piezoelectric patches is derived using a local function to consider the effects of piezoelectric mass and stiffness. Classical plate theory is used to derive the equation of motion. Double Fourier series is used to obtain the first nine natural frequencies and mode shapes of plate. Modal analysis is applied to obtain the system responses imposed to an initial condition and a comparison is made between the application of PID control and FLC to dampen the plate vibration. The results of both methods are shown through numerical results and graphical illustrations. The research shows FLC has more capability to dampen the vibration of the smart plate compared to PID control.