Frictionless contact of a functionally graded magneto-electro-elastic layered half-plane under a conducting punch

This paper investigates the two-dimensional frictionless contact problem of a functionally graded magneto-electro-elastic materials (FGMEEMs) layered half-plane under a rigid flat or a cylindrical punch. It is assumed that the punch is a perfect electro-magnetic conductor with a constant electric potential and a constant magnetic potential. The magneto-electro-elastic (MEE) properties of the FGMEEM layer vary exponentially along the thickness direction. Using the Fourier transform technique, the contact problem can be reduced to Cauchy singular integral equations, which are then solved numerically to determine the normal contact stress, electric displacement and magnetic induction on the contact surface. Numerical results show that the gradient index, punch geometry and magneto-electro-mechanical loads have a significant effect on the contact behavior of FGMEEMs.     

The axisymmetric torsional contact problem of a functionally graded piezoelectric coated half-space

In this article, we study the axisymmetric tor-sional contact problem of a half-space coated with func-tionally graded piezoelectric material (FGPM) and subjected to a rigid circular punch. It is found that, along the thick-ness direction, the electromechanical properties of FGPMs change exponentially. We apply the Hankel integral trans-form technique and reduce the problem to a singular integral equation, and then numerically determine the unknown con-tact stress and electric displacement at the contact surface. The results show that the surface contact stress, surface azimuthal displacement, surface electric displacement, and inner electromechanical field are obviously dependent on the gradient index of the FGPM coating. It is found that we can adjust the gradient index of the FGPM coating to modify the distributions of the electric displacement and contact stress.     

A finite crack in a semi-infinite strip of a graded piezoelectric material under electric loading

In this paper, the mixed-mode crack problem for a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under in-plane electric loading. The problem is formulated in terms of a system of singular integral equations. The stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.     

Functionally graded piezoelectric strip with a penny-shaped crack under electromechanical loadings

In this paper, the mixed-mode penny-shaped crack problem for a functionally graded piezoelectric material (FGPM) strip is considered. It is assumed that the electroelastic properties of the strip vary continuously along the thickness of the strip, and that the strip is under in-plane electromechanical loadings. The problem is formulated in terms of a system of singular integral equations. The stress and electric displacement intensity factors are presented for various values of dimensionless parameters representing the crack size, the crack location, and the material nonhomogeneity.     

SCATTERING OF THE HARMONIC STRESS WAVE BY CRACKS IN FUNCTIONALLY GRADED PIEZOELECTRIC MATERIALS

The present paper considers the scattering of the time harmonic stress wave by a single crack and two collinear cracks in functionally graded piezoelectric material （FGPM）. It is assumed that the properties of the FGPM vary continuously as an exponential function. By using the Fourier transform and defining the jumps of displacements and electric potential components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement and electric potential components across the crack surface are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the influences of material properties on the dynamic stress and the electric displacement intensity factors.     

Frictional moving contact problem between a conducting rigid cylindrical punch and a functionally graded piezoelectric layered half plane

Meccanica - In this study, a frictional moving contact problem between an electrically conducting rigid cylindrical punch and a functionally graded piezoelectric material (FGPM) layer bonded to a...     

功能梯度压电带中裂纹对SH波的散射

研究功能梯度压电带中裂纹对SH波的散射问题,为了便于分析,材料性质假定为指数模型,并假设裂纹面上的边界条件为电渗透型的.根据压电理论得到压电体的状态方程,利用Fourier积分变换,问题转化为对偶积分方程的求解.用Copson方法求解积分方程.求得了裂纹尖端动应力强度因子、电位移强度因子的解析表达式,最后数值结果显示了标准动应力强度因子与入射波数、材料参数、带宽、波数以及入射角之间的关系.     

A moving mode-III crack in functionally graded piezoelectric material: permeable problem

In this paper a moving mode-III crack in functionally graded piezoelectric materials (FGPM) is studied. The crack surfaces are assumed to be permeable. The governing equations for FGPM are solved by means of Fourier cosine transform. The mathematical formulation for the permeable crack condition is derived as a set of dual integral equations, which, in turn, are reduced to a Fredholm integral equation of the second kind. The results obtained indicate that the stress intensity factor of moving crack in FGPM depends only on the mechanical loading. The gradient parameter of the FGPM and the moving velocity of the crack do have significant influence on the dynamic stress intensity factor.     

Static analysis for functionally graded piezoelectric actuators or sensors under a combined electro-thermal load

Based on the theory of piezoelasticity, a functionally graded piezoelectric sandwich cantilever under an applied electric field and/or a heat load is studied. All materials may be arbitrary functional gradients in the thickness direction. The static solution for the mentioned problems is presented by the Airy stress function method. As a special case, assuming that the material composition varies continuously in the direction of the thickness according to a power law distribution, a comprehensive parametric study is conducted to show the influence of electromechanical coupling (EMC), functionally graded index, temperature change and thickness ratio on the bending behavior of actuators or sensors. The distribution of electric field or normal stress in present FGPM actuators is continuous along the thickness, which overcomes the problem in traditional layered actuators. The solution facilitates the design optimization for different piezoelectric actuators and has another potential application for material parameter identification.     

Electromechanical impact of an impermeable parallel crack in a functionally graded piezoelectric strip

The dynamic fracture problem for a functionally graded piezoelectric material (FGPM) strip containing a crack parallel to the free boundaries is considered in this study. It is assumed that the electroelastic properties of the strip vary continuously along the thickness direction of the strip, and that the strip is under the in-plane mechanical and electric impact. Integral transform techniques and dislocation density functions are employed to reduce the problem to the solutions of a system of singular integral equations. The dynamic stress and electric displacement intensity factors versus time are presented for various values of dimensionless parameters representing the crack size, the crack location, the material nonhomogeneity and the loading combination.     

A penny-shaped interface crack between a functionally graded piezoelectric layer and a homogeneous piezoelectric layer

The problem of a penny-shaped interface crack between a functionally graded piezoelectric layer and a homogeneous piezoelectric layer is investigated. The surfaces of the composite structure are subjected to both mechanical and electrical loads. The crack surfaces are assumed to be electrically impermeable. Integral transform method is employed to reduce the problem to a Fredholm integral equation of the second kind. The stress intensity factor, electric displacement intensity factor and energy release rate are derived, some typical numerical results are plotted graphically. The effects of electrical loads, material nonhomogeneity and crack configuration on the fracture behaviors of the cracked composite structure are analyzed in detail.     

Mode III fracture problem of a cracked FGPM surface layer bonded to a cracked FGPM substrate

This work deals with the mode III fracture problem of a cracked functionally graded piezoelectric surface layer bonded to a cracked functionally graded piezoelectric substrate. The cracks are normal to the interface and the electro-elastic material properties are assumed to be varied along the crack direction. Potential and flux types of boundary condition are assigned on the edge of the surface layer. The problem under the assumptions of impermeable and permeable cracks can be formulated to the standard singular integral equations, which are solved by using the Gauss–Chebyshev technique. The effects of the boundary conditions, the material properties and crack interaction on the stress and electric displacement intensity factors are discussed.     

Electromechanical impact of a crack in a functionally graded piezoelectric medium

The Mode-I transient response of a functionally graded piezoelectric medium is solved for a through crack under the in-plane mechanical and electric impact. Integral transforms and dislocation density functions are employed to reduce the problem to singular integral equations. Numerical results display the effects of the loading combination parameter λ and the material parameter βa on the dynamic stress intensity factor and electric displacement intensity factor. The energy density factor criterion is applied to obtain the maximum of the minimum energy density factor and the direction of crack initiation.     

Basic solutions of multiple parallel symmetric mode-III cracks in functionally graded piezoelectric/piezomagnetic material plane

The Schmidt method is adopted to investigate the fracture problem of multiple parallel symmetric and permeable finite length mode-III cracks in a functionally graded piezoelectric/piezomagnetic material plane. This problem is formulated into dual integral equations, in which the unknown variables are the displacement jumps across the crack surfaces. In order to obtain the dual integral equations, the displacement jumps across the crack surfaces are directly expanded as a series of Jacobi polynomials. The results show that the stress, the electric displacement, and the magnetic flux intensity factors of cracks depend on the crack length, the functionally graded parameter, and the distance among the multiple parallel cracks. The crack shielding effect is also obviously presented in a functionally graded piezoelectric/piezomagnetic material plane with mul- tiple parallel symmetric mode-III cracks.     

Closed-form solutions of the frictional sliding contact problem for a magneto-electro-elastic half-plane indented by a rigid conducting punch

This paper focuses on the study of a frictional sliding contact problem between a homogeneous magneto-electro-elastic material (MEEM) and a perfectly conducting rigid flat punch subjected to magneto-electro-mechanical loads. The problem is formulated under plane strain conditions. Using Fourier transform, the resulting plane magneto-electro-elasticity equations are converted analytically into three coupled singular integral equations in which the main unknowns are the normal contact stress, the electric displacement and the magnetic induction. An analytical closed-form solution is obtained for the normal contact stress, electric displacement and magnetic induction distributions. The main objective of this paper is to study the effect of the friction coefficient and the elastic, electric and magnetic coefficients on the surface contact pressure, electric displacement and magnetic induction distributions for the case of flat stamp profile.     

Thermoelastic contact mechanics for a flat punch sliding over a graded coating/substrate system with frictional heat generation

The problem of thermoelastic contact mechanics for the coating/substrate system with functionally graded properties is investigated, where the rigid flat punch is assumed to slide over the surface of the coating involving frictional heat generation. With the coefficient of friction being constant, the inertia effects are neglected and the solution is obtained within the framework of steady-state plane thermoelasticity. The graded material exists as a nonhomogeneous interlayer between dissimilar, homogeneous phases of the coating/substrate system or as a nonhomogeneous coating deposited on the substrate. The material nonhomogeneity is represented by spatially varying thermoelastic moduli expressed in terms of exponential functions. The Fourier integral transform method is employed and the formulation of the current thermoelastic contact problem is reduced to a Cauchy-type singular integral equation of the second kind for the unknown contact pressure. Numerical results include the distributions of the contact pressure and the in-plane component of the surface stress under the prescribed thermoelastic environment for various combinations of geometric, loading, and material parameters of the coated medium. Moreover, in order to quantify and characterize the singular behavior of contact pressure distributions at the edges of the flat punch, the stress intensity factors are defined and evaluated in terms of the solution to the governing integral equation.     

Mode III eccentric crack in a functionally graded piezoelectric strip

This paper studies the internal crack problem located within one functionally graded piezoelectric strip. One crack is normal to the edge of the strip and the material properties vary along the direction of crack length. Three different boundary conditions and both impermeable and permeable cases are discussed. The problem can be reduced to a system of singular integral equations and solved by using the Gauss–Chebyshev formulas. The results show that the edge boundary conditions and the nonhomogeneous parameter significantly control the magnitudes of stress and electric displacement intensity factors.     

Transient thermal response of functionally graded piezoelectric laminates with an infinite row of parallel cracks normal to the bimaterial interface

In this paper, the problem of a functionally graded piezoelectric material strip(FGPM strip)containing an infinite row of parallel cracks perpendicular to the interface between the FGPM strip and a homogeneous layer is analyzed under transient thermal loading condition. The crack faces are supposed to be completely insulated. Material properties are assumed to be exponentially dependent on the distance from the interface. Using the Fourier transforms, the electro-thermoelastic problem is reduced to a singular integral equation, which is solved numerically. The stress intensity factors are computed and presented as a function of the normalized time, the nonhomogeneous and geometric parameters.     

Dynamic stress intensity factors of multiple cracks in a functionally graded orthotropic half-plane

In the present paper dynamic stress intensity factor and strain energy density factor of multiple cracks in the functionally graded orthotropic half-plane under time-harmonic loading are investigated. By utilizing the Fourier transformation technique the stress fields are obtained for a functionally graded orthotropic half-plane containing a Volterra screw dislocation. The variations of the material properties are assumed to be exponential forms which the equilibrium has an analytical solution. The dislocation solution is utilized to formulate integral equation for the half-plane weakened by multiple smooth cracks under anti-plane deformation. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically to obtain the dislocation density on the faces of the cracks. The dislocation densities are employed to determined stress intensity factor and strain energy density factors (SEDFs) for multiple smooth cracks under anti-plane deformation. Numerical examples are provided to show the effects of material properties and the crack configuration on the dynamic stress intensity factors and SEDFs of the functionally graded orthotropic half-plane with multiple curved cracks.     

Stresses distributions in a rotating functionally graded piezoelectric hollow cylinder

An analytic solution to the axisymmetric problem of a long, radially polarized, hollow cylinder composed of functionally graded piezoelectric material (FGPM) rotating about its axis at a constant angular velocity is presented. For the case that electric, thermal and mechanical properties of the material obey different power laws in the thickness direction, distributions for radial displacement, stresses and electric potential in the FGPM hollow cylinder are determined by using the theory of electrothermoelasticity. Some useful discussions and numerical examples are presented to show the significant influence of material nonhomogeneity, and adopting suitable graded indexes and applying suitable geometric size and rotating velocity ω may optimize the rotating FGPM hollow cylindrical structures. This will be of particular importance in modern engineering application.