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1.
The antiplane stress analysis of two anisotropic finite wedges with arbitrary radii and apex angles that are bonded together along a common edge is investigated. The wedge radial boundaries can be subjected to displacement-displacement boundary condi- tions, and the circular boundary of the wedge is free from any traction. The new finite complex transforms are employed to solve the problem. These finite complex transforms have complex analogies to both kinds of standard finite Mellin transforms. The traction free condition on the crack faces is expressed as a singular integral equation by using the exact analytical method. The explicit terms for the strength of singularity are extracted, showing the dependence of the order of the stress singularity on the wedge angle, material constants, and boundary conditions. A numerical method is used for solving the resul- tant singular integral equations. The displacement boundary condition may be a general term of the Taylor series expansion for the displacement prescribed on the radial edge of the wedge. Thus, the analysis of every kind of displacement boundary conditions can be obtained by the achieved results from the foregoing general displacement boundary condition. The obtained stress intensity factors (SIFs) at the crack tips are plotted and compared with those obtained by the finite element analysis (FEA). 相似文献
2.
A.R. Shahani 《Journal of Elasticity》1999,56(1):17-32
The antiplane deformation of an anisotropic wedge with finite radius is considered in this paper within the classical linear
theory of elasticity. The traction-free condition is imposed on the circular segment of the wedge. Three different cases of
boundary conditions on the radial edges are considered, which are: traction-displacement, displacement-displacement and traction-traction.
The solution to the governing differential equation of the problem is accomplished in the complex plane by relating the displacement
field to a complex function. Several complex transformations are defined on this complex function and its first and second
derivatives to formulate the problem in each of the three cases of the problem corresponding to the radial boundary conditions,
separately. These transformations are then related to integral transforms which are complex analogies to the standard finite
Mellin transforms of the first and second kinds. Closed form expressions are obtained for the displacement and stress fields
in the entire domain. In all cases, explicit expressions for the strength of singularity are derived. These expressions show
the dependence of the order of stress singularity on the wedge angle and material constants. In the displacement-displacement
case, depending upon the applied displacement, a new type of stress singularity has been observed at the wedge apex.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
3.
The non-zero traction condition is introduced in piezoelectric crack problems with the unknown Coulombic traction acting on
the crack surfaces. An analytical solution under this condition is obtained by means of the generalized Stroh formalism and
by accounting for the permittivity of medium inside the crack gap. As the crack in such materials can be thought of as a low-capacitance
medium carrying a potential drop, the Coulombic traction always pulls the two opposite surfaces of the crack together. It
is proved that under relatively larger mechanical loading and relatively smaller electrical field, the Coulombic traction
may be negligible and the previous investigations under the traction-free crack condition may be accepted in a tolerant way,
otherwise the Coulombic traction may lead to some erroneous results with over 10% relative errors. It is also shown that,
unlike the traction-free crack condition, the applied electric field does change the Mode I stress intensity factor (SIF)
for a central crack in an infinite plane piezoelectric material, and in this way may significantly influence piezoelectric
fracture. It is also concluded that the variable tendencies of the normalized SIF and the ERR against the applied electric
field depend on the mechanical loading levels. This load-dependence feature may lead to a transformation of the normalized
SIF and the ERR from an even functional dependence to an odd functional dependence on the applied electric field. 相似文献
4.
《International Journal of Solids and Structures》2005,42(11-12):3093-3113
The antiplane shear deformation of a bi-material wedge with finite radius is studied in this paper. Depending upon the boundary condition prescribed on the circular segment of the wedge, traction or displacement, two problems are analyzed. In each problem two different cases of boundary conditions on the radial edges of the composite wedge are considered. The radial boundary data are: traction–displacement and traction–traction. The solution of governing differential equations is accomplished by means of finite Mellin transforms. The closed form solutions are obtained for displacement and stress fields in the entire domain. The geometric singularities of stress fields are observed to be dependent on material property, in general. However, in the special case of equal apex angles in the traction–traction problem, this dependency ceases to exist and the geometric singularity shows dependency only upon the apex angle. A result which is in agreement with that cited in the literature for bi-material wedges with infinite radii. In part II of the paper, Antiplane shear deformation of bi-material circular media containing an interfacial edge crack is considered. As a special case of bi-material wedges studied in part I of the paper, explicit expressions are derived for the stress intensity factor at the tip of an edge crack lying at the interface of the bi-material media. It is seen that in general, the stress intensity factor is a function of material property. However, in special cases of traction–traction problem, i.e., similar materials and also equal apex angles, the stress intensity factor becomes independent of material property and the result coincides with the results in the literature. 相似文献
5.
This paper studies a numerical solution of multiple crack problem in a finite plate using coupled integral equations. After using the principle of superposition, the multiple crack problem in a finite plate can be converted into two problems: (a) the multiple crack problem in an infinite plate and (b) a usual boundary value problem for the finite plate. For the former problem, the Fredholm integral equation is used. For the latter problem, a BIE based on complex variable is suggested in which a Cauchy singular kernel exists. For the proposed BIE, after using the inverse matrix technique, the dependence of the traction at a domain point from the boundary tractions is formulated indirectly. This is a particular advantage of the present study. Several numerical examples are provided and the computed results for stress intensity factor and T-stress at crack tips are given. 相似文献
6.
Qun Li Andreas Ricoeur Meinhard Kuna 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(6):685-700
The axisymmetric problem of a penny-shaped crack embedded in an infinite three-dimensional (3D) piezoelectric body is considered.
A general formulation of Coulomb traction on the crack surfaces can be obtained based on thermodynamical considerations of
electromechanical systems. Three-dimensional electroelastic solutions are derived by the classical complex potential theory
when Coulomb traction is taken into account and the poling direction of piezoelectric body is perpendicular to the crack surfaces.
Numerical results show that the magnitude of Coulomb tractions can be large, especially when a large electric field in connection
with a small mechanical load is applied. Unlike the traditional traction-free crack model, Coulomb tractions induced by an
applied electric field influence the Mode I stress intensity factor for a penny-shaped crack in 3D piezoelectric body. Moreover,
compared to the current model, the traditional traction-free crack model always overestimates the effect of the applied electric
load on the field intensity factors and energy release rates, which has consequences for 3D piezoelectric fracture mechanics. 相似文献
7.
This paper presents the effects of elastic mismatch and crack-tip position on the stress intensity factors of a long crack penetrating a circular inhomogeneity. The analysis relies on closed-form solutions, derived using complex variable techniques, for the stresses and displacements produced by dislocations positioned inside and outside the inhomogeneity. Dislocation distributions are introduced to express the traction boundary condition along the crack surfaces as a system of singular integral equations, whose solution is obtained through a numerical procedure. It is shown that if the elastic mismatch is interpreted correctly, then the stress intensity factors of this micromechanical model are very good approximations to those computed using a Monte Carlo finite element model of a long crack in a polycrystalline plate with compliant grain boundaries. 相似文献
8.
The numerical solutions to the singular integral equations obtained by the fracture mechanical analyses of a cracked wedge under three different conditions are considered. The three considered conditions are: (i) a radial crack on a wedge with a non-finite radius under the traction-traction boundary condition, (ii) a radial crack on a wedge with a finite radius under the traction-traction boundary condition, and (iii) a radial crack on a finite radius wedge under the traction-displacement boundary condition. According to the boundary conditions, the extracted singular integral equations have different forms. Numerical methods are used to solve the obtained coupled singular integral equations, where the Gauss-Legendre and the Gauss-Chebyshev polynomials are used to approximate the responses of the singular integral equations. The results are presented in figures and compared with those obtained by the analytical response. The results show that the obtained Gauss-Chebyshev polynomial response is closer to the analytical response. 相似文献
9.
Chih-Hao Chen Chein-Lee Wang 《International Journal of Solids and Structures》2009,46(11-12):2444-2452
In this study, the problem of an isotropic sector subjected to anti-plane shear loadings is investigated. The loadings were applied to the arc of the sector, and the radial edges of the sector were under traction-free or fixed conditions. Depending on these conditions, three problems, namely, free–free, fixed–free, and fixed–fixed edges were studied. A procedure using the finite Mellin transform combined with the Laplace transform was proposed for solving these problems. Explicit closed form solutions for the displacement and stress fields throughout the sector were obtained. The stress intensity factor (SIF) for each problem was analyzed using the obtained stress fields. It was determined that the SIF disappeared under the special condition of a fixed–fixed edge. Other special cases having anti-symmetric conditions were deduced from the derived solutions, and the results of these verified those cited in the literature as well as those obtained using finite element analysis (FEA). 相似文献
10.
相对于有限元法,边界单元法在求解断裂问题上有着独特的优势,现有的边界单元法中主要有子区域法和双边界积分方程法.采用一种改进的双边界积分方程法求解二维、三维断裂问题的应力强度因子,对非裂纹边界采用传统的位移边界积分方程,只需对裂纹面中的一面采用面力边界积分方程,并以裂纹间断位移为未知量直接用于计算应力强度因子.采用一种高阶奇异积分的直接法计算面力边界积分方程中的超强奇异积分;对于裂纹尖端单元,提供了三种不同形式的间断位移插值函数,采用两点公式计算应力强度因子.给出了多个具体的算例,与现存的精确解或参考解对比,可得到高精度的计算结果. 相似文献
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13.
梯度材料中矩形裂纹的对偶边界元方法分析 总被引:2,自引:0,他引:2
采用对偶边界元方法分析了梯度材料中的矩形裂纹. 该方法基于层状材料基本解,以非裂纹边界的位移和面力以及裂纹面的间断位移作为未知量. 位移边界积分方程的源点配置在非裂纹边界上,面力边界积分方程的源点配置在裂纹面上. 发展了边界积分方程中不同类型奇异积分的数值方法. 借助层状材料基本解,采用分层方法逼近梯度材料夹层沿厚度方向力学参数的变化. 与均匀介质中矩形裂纹的数值解对比,建议方法可以获得高精度的计算结果. 最后,分析了梯度材料中均匀张应力作用下矩形裂纹的应力强度因子,讨论了梯度材料非均匀参数、夹层厚度和裂纹与夹层之间相对位置对应力强度因子的影响. 相似文献
14.
王银邦 《应用数学和力学(英文版)》2004,25(2):152-157
The interaction between an elastic rectangular inclusion and a kinked crack inan infinite elastic body was considered by using boundary element method. The new complexboundary integral equations were derived. By introducing a complex unknown function H(t)related to the interface displacement density and traction and applying integration by parts,the traction continuous condition was satisfied automatically. Only one complex boundaryintegral equation was obtained on interface and involves only singularity of order l/ r. Toverify the validity and effectiveness of the present boundary element method, some typicalexamples were calculated. The obtained results show that the crack stress intensity factorsdecrease as the shear modulus of inclusion increases. Thus, the crack propagation is easiernear a softer inclusion and the harder inclusion is helpful for crack arrest. 相似文献
15.
采用Green函数法研究界面上含圆孔边界径向有限长度裂纹的两半无限压电材料对SH波的散射和裂纹尖端动应力强度因子问题.首先构造出具有半圆型凹陷半空间的位移Green函数和电场Green函数,然后采用裂纹"切割"方法构造孔边裂纹,并根据契合思想和界面上的连接条件建立起求解问题的定解积分方程.最后作为算例,给出了孔边界面裂纹尖端动应力强度因子的计算结果图并进行了讨论. 相似文献
16.
This paper provides the solution to the problem of dissimilar, homogeneous semi-infinite strips bonded through a functionally graded interlayer and weakened by an embedded or edge interfacial crack. The bonded system is assumed to be under antiplane deformation, subjected to either traction-free or clamped boundary conditions along its bounding planes. Based on the Fourier integral transform, the problem is formulated in terms of a singular integral equation which has a simple Cauchy kernel for the embedded crack and a generalized Cauchy kernel for the edge crack. In the numerical results, the effects of geometric and material parameters of the bonded system on the crack-tip stress intensity factors are presented in order to quantify the interfacial fracture behavior in the presence of the graded interlayer. 相似文献
17.
In this paper, the basic presentation in antiplane shear and inplane electric field of piezoelectric materials is refreshed.
In order that the functions used in the formulation can be distinguished by their usage, four analytic functions, or four
complex potentials, are introduced. A multiple crack problem for piezoelectric materials is studied. After taking the traction
or the electric displacement on the crack face as unknown functions, one can naturally obtain a Fredholm integral equation
for the multiple crack problem. It is found that the Fredholm integral equation approach is effective for solving the multiple
crack problem. Finally, numerical examples are given. 相似文献
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19.
Jaroon Rungamornrat Mark E. Mear 《International Journal of Solids and Structures》2008,45(5):1283-1301
Singularity-reduced integral relations are developed for displacement discontinuities in three-dimensional, anisotropic linearly elastic media. An isolated displacement discontinuity is considered first, and a systematic procedure is followed to develop relations for the displacement and stress fields induced by the discontinuity. The singularity-reduced relation for the stress is particularly important since it is in a form which allows a weakly-singular, weak-form traction integral equation to be readily established. The integral relations obtained for a general displacement discontinuity are then specialized to an isolated crack and to dislocations; the relations for dislocations are introduced to emphasize their direct connection to corresponding results for cracks and to allow earlier independent findings for these two types of discontinuities to be put into proper context. Next, the singularity-reduced integral equations obtained for an isolated crack are extended to allow treatment of cracks in a finite domain, and a pair of weakly-singular, weak-form displacement and traction integral equations is established. These integral equations can be combined to obtain a final formulation which is in a symmetric form, and in this way they serve as the basis for a weakly-singular, symmetric Galerkin boundary element method suitable for analysis of cracks in anisotropic media. 相似文献
20.
Mohammad R. Torshizian Mohammad H. Kargarnovin Cyrus Nasirai 《Mechanics Research Communications》2011,38(3):164-169
In this paper, a two dimensional functionally graded material (2D-FGM) under an anti-plane load with an internal crack is considered. The crack is oriented in an arbitrary direction. The material properties are assumed to vary exponentially in two planar directions. The problem is analyzed and solved by two different methods namely Fourier integral transforms with singular integral equation technique, and then by the finite element method. The effects of crack orientation, material non-homogeneity, and other parameters on the value of stress intensity factor (SIF) are studied. Finally, the obtained results for Mode III stress intensity factor of different methods are compared. 相似文献