共查询到12条相似文献,搜索用时 55 毫秒
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本文研究了含非完整界面的功能梯度压电复合材料的Ⅲ型裂纹问题.此裂纹垂直于非完整界面,采用弹簧型力电耦合界面模型模拟非完整界面.界面两侧材料的性质,如弹性模量、压电常数和介电常数均假定呈指数函数形式且沿着裂纹方向变化.运用积分变换法将裂纹面条件转换为奇异积分方程,并使用Gauss-Chebyshev方法对其进行数值求解.根据算例结果讨论了一些退化问题并分析了裂纹尖端强度因子与材料的非均匀系数和非完整界面参数的关系. 相似文献
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《International Journal of Solids and Structures》2006,43(3-4):658-674
In this paper, we consider the plane problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half-space, when the two bodies are pressed together. The graded layer is modeled as a nonhomogeneous medium with an isotropic stress–strain law and over a certain segment of its top surface is subjected to normal tractions while the rest of this surface is free of tractions. Since the contact between the two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact area. Using integral transforms, the plane elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact half-length. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact half-length that satisfies the global equilibrium condition. The main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact. 相似文献
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M. Rhimi S. El-Borgi W. Ben Saïd F. Ben Jemaa 《International Journal of Solids and Structures》2009,46(20):3633-3642
In this paper, we consider the axisymmetric problem of a frictionless receding contact between an elastic functionally graded layer and a homogeneous half-space, when the two bodies are pressed together. The graded layer is modeled as a nonhomogeneous medium with an isotropic stress–strain law and is subjected over a part of its top surface to normal tractions while the rest of it is free of tractions. Since the contact between the two bodies is assumed to be frictionless, then only compressive normal tractions can be transmitted in the contact area. Using Hankel transform, the axisymmetric elasticity equations are converted analytically into a singular integral equation in which the unknowns are the contact pressure and the receding contact radius. The global equilibrium condition of the layer is supplemented to solve the problem. The singular integral equation is solved numerically using orthogonal Chebychev polynomials and an iterative scheme is employed to obtain the correct receding contact length that satisfies the global equilibrium condition. The main objective of the paper is to study the effect of the material nonhomogeneity parameter and the thickness of the graded layer on the contact pressure and on the length of the receding contact. 相似文献
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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. 相似文献
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《International Journal of Solids and Structures》2014,51(25-26):4462-4476
This paper investigates the plane problem of a frictional receding contact formed between an elastic functionally graded layer and a homogeneous half space, when they are pressed against each other. The graded layer is assumed to be an isotropic nonhomogeneous medium with an exponentially varying shear modulus and a constant Poisson’s ratio. A segment of the top surface of the graded layer is subject to both normal and tangential traction while rest of the surface is devoid of traction. The entire contact zone thus formed between the layer and the homogeneous medium can transmit both normal and tangential traction. It is assumed that the contact region is under sliding contact conditions with the Coulomb’s law used to relate the tangential traction to the normal component. Employing Fourier integral transforms and applying the necessary boundary conditions, the plane elasticity equations are reduced to a singular integral equation in which the unknowns are the contact pressure and the receding contact lengths. Ensuring mechanical equilibrium is an indispensable requirement warranted by the physics of the problem and therefore the global force and moment equilibrium conditions for the layer are supplemented to solve the problem. The Gauss–Chebyshev quadrature-collocation method is adopted to convert the singular integral equation to a set of overdetermined algebraic equations. This system is solved using a least squares method coupled with a novel iterative procedure to ensure that the force and moment equilibrium conditions are satisfied simultaneously. The main objective of this paper is to study the effect of friction coefficient and nonhomogeneity factor on the contact pressure distribution and the size of the contact region. 相似文献
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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. 相似文献
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《International Journal of Solids and Structures》2007,44(16):5272-5288
The concept of functionally graded material (FGM) is actively explored in coating design for the purpose of eliminating the mismatch of material properties at the coating/substrate interface, typical for conventional coatings, which can lead to cracking, debonding and eventual functional failure of the coating. In this paper, an FGM coating/substrate system of finite thickness subjected to transverse loading is analysed within the context of three-dimensional elasticity theory. The Young’s modulus of the coating is assumed to vary exponentially through the thickness, and the Poisson’s ratio is assumed to be constant. A comparative study of FGM versus homogeneous coating is conducted, and the dependence of stress and displacement fields in the coating substrate/system on the type of coating, geometry and loading is examined and discussed. 相似文献
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Jian Chen 《Archive of Applied Mechanics (Ingenieur Archiv)》2006,75(2-3):138-152
The static and dynamic anti-plane problem for a functionally graded coating–substrate structure containing a periodic array
of parallel cracks, which are perpendicular to the boundary, is considered. Integral-transform techniques are employed to
reduce the problem to the solution of an integral equation with hypersingular kernels. Numerical results are presented to
show the influence of geometry, material properties and material gradient parameter on the fracture behavior. 相似文献
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研究Winker地基模型上功能梯度材料涂层在一刚性圆柱形冲头作用下的摩擦接触问题。功能梯度材料涂层表面作用有法线向和切线向集中作用力。假设材料非均匀参数呈指数形式变化,泊松比为常量,利用Fourier积分变换技术将求解模型的接触问题转化为奇异积分方程组,再利用切比雪夫多项式对所得奇异积分方程组进行数值求解。最后,给出了功能梯度材料非均匀参数、摩擦系数、Winker地基模型刚度系数及冲头曲率半径对接触应力分布和接触区宽度的影响情况。 相似文献
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Considering the dielectric effects inside a crack, the problem of an electrically dielectric crack in a functionally graded piezoelectric layer is addressed in this paper. The energetically consistent crack-face boundary conditions are utilized to analyze the effects of a dielectric of crack interior. Applying the Fourier transform technique, the boundary-value problem is reduced to solving three coupling singular equations. Then a system of non-linear algebraic equations is obtained and the field intensity factors along with the energy release rate are given. Numerical results show the differences of the electric displacement inside a crack, the stress and electric displacement intensity factors and the energy release rate using the permeable, impermeable, semi-permeable and energetically consistent boundary conditions respectively. The effects of the material non-homogeneity, the applied electric field and the discharge field of crack interior on the electrostatic traction acting on the crack faces and the energy release rate are further studied through the energetically consistent boundary conditions. 相似文献
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Stanis?aw J. Matysiak Roman Kulchytsky-ZhyhailoDariusz M. Perkowski 《Mechanics Research Communications》2011,38(4):320-325
This paper is concerned with the axisymmetric elastostatic problem related to the rotation of a rigid punch which is bonded to the surface of a nonhomogeneous half-space. The half-space is composed of an isotropic homogeneous coating in the form of layer, which is attached to the functionally graded half-space. The shear modulus of the FGM is assumed to vary in the direction of axis Oz normal to the boundary as μ1(z) = μ0(1 + αz)β, where μ0, α, β are positive constants. The punch undergoes rotation due to the action of the internal loads. By using Hankel's integral transforms, the mixed boundary value problem is reduced to dual integral equations, and next, to a Fredholm's integral equation of the second kind, which is solved numerically for the case of β = 2. The final results show the effect of non-homogeneity on the shear stresses and an unknown moment of punch rotation. 相似文献