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1.
Numerical solutions of singular integral equations are discussed in the analysis of a planar rectangular interfacial crack in three-dimensional bimaterials subjected to tension. The problem is formulated as a system of singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental density functions are chosen to express singular behavior along the crack front of the interface crack exactly. The calculation shows that the present method gives smooth variations of stress intensity factors along the crack front for various aspect ratios. The present method gives rapidly converging numerical results and highly satisfied boundary conditions throughout the crack boundary. The stress intensity factors are given with varying the material combination and aspect ratio of the crack. It is found that the stress intensity factors KI and KII are determined by the bimaterial constant ε alone, independent of elastic modulus ratio and Poisson’s ratio. 相似文献
2.
N.-A. Noda K. Kobayashi T. Oohashi 《Archive of Applied Mechanics (Ingenieur Archiv)》2001,71(1):43-52
Summary In this study, the interaction between two semi-elliptical co-planar surface cracks is considered when Poisson's ratio ν
= 0.3. The problem is formulated as a system of singular integral equations, based on the idea of the body force method. In
the numerical calculation, the unknown density of body force density is approximated by the product of a fundamental density
function and a polynomial. The results show that the present method yields smooth variations of stress intensity factors along
the crack front very accurately, for various geometrical conditions. When the size of crack 1 is larger than the size of crack
2, the maximum stress intensity factor appears at a certain point, β1=177∘, of crack 1. Along the outside of crack 1, that is at β1=0∼90∘, the interaction can be negligible even if the two cracks are very close. The interaction can be negligible when the two
cracks are spaced in such a manner that their two closest points are separated by a distance exceeding the small crack's major
diameter. The variations of stress intensity factor of a semi-elliptical crack are tabulated and charted.
Received 30 August 1999; accepted for publication 22 February 2000 相似文献
3.
Summary The paper deals with numerical solutions of singular integral equations in stress concentration problems for longitudinal
shear loading. The body force method is used to formulate the problem as a system of singular integral equations with Cauchy-type
singularities, where unknown functions are densities of body forces distributed in the longitudinal direction of an infinite
body. First, four kinds of fundamental density functions are introduced to satisfy completely the boundary conditions for
an elliptical boundary in the range 0≤φ
k
≤2π. To explain the idea of the fundamental densities, four kinds of equivalent auxiliary body force densities are defined
in the range 0≤φ
k
≤π/2, and necessary conditions that the densities must satisfy are described. Then, four kinds of fundamental density functions
are explained as sample functions to satisfy the necessary conditions. Next, the unknown functions of the body force densities
are approximated by a linear combination of the fundamental density functions and weight functions, which are unknown. Calculations
are carried out for several arrangements of elliptical holes. It is found that the present method yields rapidly converging
numerical results. The body force densities and stress distributions along the boundaries are shown in figures to demonstrate
the accuracy of the present solutions.
Received 26 May 1998; accepted for publication 27 November 1998 相似文献
4.
Summary This paper deals with interaction problems of elliptical and ellipsoidal inclusions under bending, using singular integral
equations of the body force method. The problems are formulated as a system of singular integral equations with Cauchy-type
or logarithmic-type singularities, where unknown functions are densities of body forces distributed in the x,y and r,θ,z directions in infinite bodies having the same elastic constants as those of the matrix and inclusions. In order to satisfy
the boundary conditions along the elliptical and the ellipsoidal boundaries, the unknown functions are approximated by a linear
combination of fundamental density functions and polynomials. The present method is found to yield the exact solutions for
a single elliptical or spherical inclusion under a bending stress field. It yields rapidly converging numerical results for
interface stresses in the interaction of inclusions.
Received 9 September 1999; accepted for publication 15 January 2000 相似文献
5.
Summary This paper deals with the stress concentration problem of an ellipsoidal inclusion of revolution in a semi-infinite body under biaxial tension. The problem is formulated as a system of singular integral equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r- and z-directions in semi-infinite bodies having the same elastic constants as the ones of the matrix and inclusion. In order to satisfy the boundary conditions along the ellipsoidal boundary, four fundamental density functions proposed in [24, 25] are used. The body-force densities are approximated by a linear combination of fundamental density functions and polynomials. The present method is found to yield rapidly converging numerical results for stress distribution along the boundaries even when the inclusion is very close to the free boundary. The effect of the free surface on the stress concentration factor is discussed with varying the distance from the surface, the shape ratio and the elastic modulus ratio. The present results are compared with the ones of an ellipsoidal cavity in a semi-infinite body.accepted for publication 11 November 2003 相似文献
6.
Summary The problem of an interface edge crack between two bonded quarter-planes of dissimilar piezoelectric materials is considered
under the conditions of anti-plane shear and in-plane electric loading. The crack surfaces are assumed to be impermeable to
the electric field. An integral transform technique is employed to reduce the problem under consideration to dual integral
equations. By solving the resulting dual integral equations, the intensity factors of the stress and the electric displacement
and the energy release rate as well as the crack sliding displacement and the electric voltage across the crack surfaces are
obtained in explicit form for the case of concentrated forces and free charges at the crack surfaces and at the boundary.
The derived results can be taken as fundamental solutions which can be superposed to model more realistic problems.
Received 10 November 2000; accepted for publication 28 March 2001 相似文献
7.
陈光祖 《应用数学和力学(英文版)》1987,8(12):1191-1199
Expressing the total potential energy of the system of a cracked body П by Williams’ infinite series solution of stress and displacement components containing coefficients An(n = 1,2,...), we obtain a set of simultaneous linear equations of unknown coefficients An by using the principle of minimum potential energy. When the set of equations is solved, the stress intensity factor K1 can be easily determined. It is equal to √2πaA1 Take a sample plate as an example. A single-edgc-cracked plate under tension, with the ratio of crack length to the width of the plate being 0.5 and the ratio of half plate height to the width of the plate being 2.0 and 2. 5, has been calculated. Only 20 - 30 coefficients are taken, and the errors in stress intensity factors are within 5%. 相似文献
8.
X.-F. Li 《Archive of Applied Mechanics (Ingenieur Archiv)》2003,72(10):745-758
Summary The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform
electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral
equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and
the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results
are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results
reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors
depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results
reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied
stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack
in a piezoelectric strip.
Received 14 August 2001; accepted for publication 24 September 2002
The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported
by the National Natural Science Foundation of China under Grant 70272043. 相似文献
9.
A theoretical treatment of the scattering of anti-plane shear (SH) waves is provided by a single crack in an unbounded transversely
isotropic electro-magneto-elastic medium. Based on the differential equations of equilibrium, electric displacement and magnetic
induction intensity differential equations, the governing equations for SH waves were obtained. By means of a linear transform,
the governing equations were reduced to one Helmholtz and two Laplace equations. The Cauchy singular integral equations were
gained by making use of Fourier transform and adopting electro-magneto impermeable boundary conditions. The closed form expression
for the resulting stress intensity factor at the crack was achieved by solving the appropriate singular integral equations
using Chebyshev polynomial. Typical examples are provided to show the loading frequency upon the local stress fields around
the crack tips. The study reveals the importance of the electro-magneto-mechanical coupling terms upon the resulting dynamic
stress intensity factor.
Contributed by SHEN Ya-peng
Foundation item: the National Natural Science Foundation of China (10132010, 50135030)
Biographies: DU Jian-ke (1970∼) 相似文献
10.
利用双材料位移基本解和Somigliana公式,将三维体内含垂直于双材料界面混合型裂纹问题归结为求解一组超奇异积分方程。使用主部分析法,通过对裂纹前沿应力奇性的分析,得到用裂纹面位移间断表示的应力强度因子的计算公式,进而利用超奇异积分方程未知解的理论分析结果和有限部积分理论,给出了超奇异积分方程的数值求解方法。最后,对典型算例的应力强度因子做了计算,并讨论了应力强度因子数值结果的收敛性及其随各参数变化的规律。 相似文献
11.
Summary This paper presents an M-integral analysis for the microcracked anisotropic composite materials. By using an elementary solution derived for a single
finite crack subjected to a concentrated force on crack faces, the problem of strong interacting, arbitrarily oriented and
located microcracks in an anisotropic composite materials is reduced to a system of Fredholm integral equations. The crack-tip
fracture parameters, such as the stress intensity factors, are evaluated from a numerical solution of the system of integral
equations. Its dependence on the coordinate system, calculation, and physical interpretation of the M-integral are discussed in the interaction problem. Finally, a numerical example of the damage evaluation by the M-integral analysis is given.
Received 24 September 1999; accepted for publication 8 February 2000 相似文献
12.
《International Journal of Solids and Structures》2002,39(17):4437-4455
For any plane crack in an infinite isotropic elastic body subjected to some constant loading, Bueckner–Rice's weight function theory gives the variation of the stress intensity factors due to a small coplanar perturbation of the crack front. This variation involves the initial SIF, some geometry independent quantities and an integral extended over the front, the “fundamental kernel” of which is linked to the weight functions and thus depends on the geometry considered. The aim of this paper is to determine this fundamental kernel for the tunnel-crack. The component of this kernel linked to purely tensile loadings has been obtained by Leblond et al. [Int. J. Solids Struct. 33 (1996) 1995]; hence only shear loadings are considered here. The method consists in applying Bueckner–Rice's formula to some point-force loadings and special perturbations of the crack front which preserve the crack shape while modifying its size and orientation. This procedure yields integrodifferential equations on the components of the fundamental kernel. A Fourier transform in the direction of the crack front then yields ordinary differential equations, that are solved numerically prior to final Fourier inversion. 相似文献
13.
三维有限体平片裂纹的超奇异积分方程与边界元法 总被引:1,自引:2,他引:1
利用Somigliana公式及有限部积分的概念,导出了含任意平片裂纹三维有限体问题的超奇异积分方程组,并联合使用有限部积分与边界元法,建立了数值求解方法.在裂纹前沿附近单元,采用与理论分析一致的平方根位移模型,以提高数值结果的精度.最后计算了若干典型例子的应力强度因子. 相似文献
14.
《International Journal of Solids and Structures》2003,40(24):6577-6592
In this paper, numerical solutions of singular integral equations are discussed in the analysis of axi-symmetric interface cracks under torsion and tension. The problems of a ring-shaped interface crack are formulated in terms of a system of singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental densities are chosen to express a two-dimensional interface crack exactly. The accuracy of the present analysis is verified by comparing the present results with the results obtained by other researchers for the limiting cases of the geometries. The calculation shows that the present method gives rapidly converging numerical results for those problems as well as for ordinary crack problems in homogeneous material. The stress intensity factors of a ring-shaped interface crack are shown in tables and charts with varying the material combinations and also geometrical conditions. 相似文献
15.
Using the boundary integral equation method, the problem of stationary heat conduction and thermoelasticity for a semi-infinite
body with a crack parallel to its boundary is solved. Temperature or heat flow on the crack is prescribed. The body boundary
is heat-insulated or is at zero temperature. The dependence of the stress intensity factor on the depth of occurrence of a
circular crack at a constant temperature or under a constant heat flow is studied. In contrast to mechanical loading, thermal
loading shows less SIF values than in an infinite body
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 46–54, April 2007. 相似文献
16.
Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts 总被引:1,自引:0,他引:1
Summary The dynamic response of an interface crack between two dissimilar piezoelectric layers subjected to mechanical and electrical
impacts is investigated under the boundary condition of electrical insulation on the crack surface by using the integral transform
and the Cauchy singular integral equation methods. The dynamic stress intensity factors, the dynamic electrical displacement
intensity factor, and the dynamic energy release rate (DERR) are determined. The numerical calculation of the mode-I plane
problem indicates that the DERR is more liable to be the token of the crack growth when an electrical load is applied. The
dynamic response shows a significant dependence on the loading mode, the material combination parameters as well as the crack
configuration. Under a given loading mode and a specified crack configuration, the DERR of an interface crack between piezoelectric
media may be decreased or increased by adjusting the material combination parameters. It is also found that the intrinsic
mechanical-electrical coupling plays a more significant role in the dynamic fracture response of in-plane problems than that
in anti-plane problems.
Received 4 September 2001; accepted for publication 23 July 2002
The work was supported by the National Natural Science Foundation under Grant Number 19891180, the Fundamental Research Foundation
of Tsinghua University, and the Education Ministry of China. 相似文献
17.
Ralf Müller Petia Dineva Tsviatko Rangelov Dietmar Gross 《Archive of Applied Mechanics (Ingenieur Archiv)》2012,82(1):97-110
The anti-plane dynamic problem of a functionally graded piezoelectric plane containing a hole–crack system is treated by a
non-hypersingular traction-based boundary integral equation method. The material parameters vary exponentially in the same
manner in an arbitrary direction. The system is loaded by an incident SH-type wave, and impermeable boundary conditions are
assumed. Using a frequency-dependent fundamental solution of the wave equation, the boundary value problem is transformed
into a system of integro-differential equations along the boundary of the hole and on the crack line. Its numerical solution
yields the dynamic stress intensity factors and stress concentration factors. A parametric study reveals their dependence
on the hole–crack scenario and its geometry, characteristics of the dynamic load and magnitude and direction of material inhomogeneity. 相似文献
18.
Summary In a hybrid laminate containing an interfacial crack between piezoelectric and orthotropic layers, the dynamic field intensity
factors and energy release rates are obtained for electro-mechanical impact loading. The analysis is performed within the
framework of linear piezoelectricity. By using integral transform techniques, the problem is reduced to the solution of a
Fredholm integral equation of the second kind, which is obtained from one pair of dual integral equations. Numerical results
for the dynamic stress intensity factor show the influence of the geometry and electric field.
Received 29 June 2001; accepted for publication 3 December 2001 相似文献
19.
《International Journal of Solids and Structures》2007,44(14-15):4770-4783
Using the hypersingular integral equation method based on body force method, a planar crack in a three-dimensional transversely isotropic piezoelectric solid under mechanical and electrical loads is analyzed. This crack problem is reduced to solve a set of hypersingular integral equations. Compare with the crack problems in elastic isotropic materials, it is shown that for the impermeable crack, the intensity factors for piezoelectric materials can be obtained from those for elastic isotropic materials. Based on the exact analytical solution of the singular stresses and electrical displacements near the crack front, the numerical method of the hypersingular integral equation is proposed by the finite-part integral method and boundary element method, which the square root models of the displacement and electric potential discontinuities in elements near the crack front are applied. Finally, the numerical solutions of the stress and electric field intensity factors of some examples are given. 相似文献
20.
Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes 总被引:3,自引:0,他引:3
Summary In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through
a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular
integral equations. Numerical results illustrate the effect of the loading combination parameter λ, material property distribution
and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of
the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of
applied electric impact.
Received 4 December 2001; accepted for publication 9 July 2002
This work is supported by the National Natural Science Foundation of China through Grant No. 10132010. 相似文献