共查询到20条相似文献,搜索用时 31 毫秒
1.
The interaction of a general plane P wave and an elastic cylindrical inclusion of infinite length partially debonded from
its surrounding viscoelastic matrix of infinite extension is investigated. The debonded region is modeled as an arc-shaped
interface crack between inclusion and matrix with non-contacting faces. With wave functions expansion and singular integral
equation technique, the interaction problem is reduced to a set of simultaneous singular integral equations of crack dislocation
density function. By analysis of the fundamental solution of the singular integral equation, it is found that dynamic stress
field at the crack tip is oscillatory singular, which is related to the frequency of incident wave. The singular integral
equations are solved numerically, and the crack open displacement and dynamic stress intensity factor are evaluated for various
incident angles and frequencies.
The project supported by the National Natural Science Foundation of China (19872002) and Climbing Foundation of Northern Jiaotong
University 相似文献
2.
王银邦 《应用数学和力学(英文版)》2001,22(1):10-16
IntroductionWhentheboundaryintegralequationmethodisappliedtocrackanalysis,onlynumericalsolutionscanbeobtained ,suchas:thetypicalworksofSnyderandCruse[1],Crouch[2 ],Blandfordetal.[3],Portelaetal.[4 ],Bui[5 ],Weaver[6 ]andWANGetal.[7- 9].Itisverydifficulttoapplytheboundar… 相似文献
3.
O. M. Khai 《Mechanics of Solids》2008,43(6):910-918
We consider a three-dimensional problem on the interaction of harmonic waves with a thin rigid movable inclusion in an infinite elastic body. The problem is reduced to solving a system of two-dimensional boundary integral equations of Helmholtz potential type for the stress jump functions on the opposite surfaces of the inclusion. We propose a boundary element method for solving the integral equations on the basis of the regularization of their weakly singular kernels. Using the asymptotic relations between the amplitude-frequency characteristics of the wave farzone field and the obtained boundary stress jump functions, we determine the amplitudes of the shear plane wave scattering by a circular disk-shaped inclusion for various directions of the wave incident on the inclusion and for a broad range of wave numbers. 相似文献
4.
如果把通常裂纹问题中奇异积分方程中的右端项由应力改为合力,此时积分方程的核也要由奇异核改为对数型奇异核。文中对于反乎面剪切裂纹和刚性线问题和带裂纹圆轴扭转问题,推导出了这种带对数核的积分方程。 相似文献
5.
6.
The present paper deals with the problem of load transfer from elastic inclusions to an infinite elastic orthotropic plane with cuts located on one of the principal orthotropy directions. The constitutive system of equations of this problem is derived under the assumption that the inclusions are in a uniaxial stress state. The obtained system consists of a singular integro-differential equation and a singular integral equation for the jumps of the tangential stresses acting on the inclusion shores and for the derivative of the the cut opening function. The behavior of solutions of the system of constitutive equations at the endpoints of the inclusions and cuts is studied, and the solution of this system is constructed by the numerical-analytic discrete singularity method. 相似文献
7.
Y. A. Bogan 《Journal of Elasticity》2011,103(2):269-280
By definition, the principal problem of the two-dimensional theory of elasticity consists in solving the equation for the
Airy’s stress function in a region with its first order derivatives assigned at a boundary. In this paper, an indirect formulation
of this problem based on integral equations with weakly singular kernels is proposed. In a bounded region with a Lyapunov
boundary it is reduced to the solution of weakly singular integral equations. Differential properties of its solution are
investigated. 相似文献
8.
IntroductionUptonow ,thetechnicalliteratureonseparatecracks,voids,inclusionsandtheinteractionsbetweencracksandinclusionshavebeenquiteextensive.However,thecontactproblemsofcrack_inclusiondonotseemtobeaswidelystudied .Thispapercanberegardedasthefurtherrese… 相似文献
9.
D. I. Bardzokas M.L. Filshtinsky 《Archive of Applied Mechanics (Ingenieur Archiv)》2004,74(3-4):165-178
Summary The anti-plane mixed boundary problem of electroelasticity for vibrations of an infinite piezoceramic cylinder with a thin
rigid inclusion is considered. Using the developed integral representation of the solution, the boundary problem is reduced
to a system of singular integro-differential equations of the second kind with resolvent kernels. Calculations yeild the amplitude-frequency
characteristics of the piecewise homogeneous cylinder. The behaviour of electroelastic fields, both within the cylinder and
on its boundary, is given. 相似文献
10.
L. A. Filshtinskii Yu. D. Kovalev E. S. Ventsel 《International Journal of Solids and Structures》2002,39(26):6385-6402
A novel procedure for solving three-dimensional problems for elastic layer weakened by through-thickness tunnel cracks has been developed and is presented in this paper. This procedure reduces the given boundary value problem to an infinite system of one-dimensional singular integral equations and is based on a system of homogeneous solutions for a layer. Integral representations of single- and double-layer potentials are used for metaharmonic and harmonic functions entering in the singular integral equations. These representations provide a continuous extendibility of the stress vector while allowing a jump in the displacement vector in the transition through the cut.Expanding the potential and biharmonic solutions in the Fourier series over the thickness coordinate yields the integral representations of the displacement vector and stress tensor. The problem of reducing a denumerable set of the integral equations of the given boundary value problem to one-to-one correspondence with the set of unknown densities appearing in the Fourier’s coefficient representations has been settled efficiently. Numerical investigations show a rapid convergence of the proposed reduction procedure as applied to the solution of the infinite system of one-dimensional integral equations. Numerical examples illustrate the proposed method and demonstrate its advantages. 相似文献
11.
Variation of the stress intensity factor along the front of a 3-D rectangular crack subjected to mixed-mode load 总被引:3,自引:0,他引:3
Summary The singular integral equation method is applied to the calculation of the stress intensity factor at the front of a rectangular
crack subjected to mixed-mode load. The stress field induced by a body force doublet is used as a fundamental solution. The
problem is formulated as a system of integral equations with r
−3-singularities. In solving the integral equations, unknown functions of body-force densities are approximated by the product
of polynomial and fundamental densities. The fundamental densities are chosen to express two-dimensional cracks in an infinite
body for the limiting cases of the aspect ratio of the rectangle. The present method yields rapidly converging numerical results
and satisfies boundary conditions all over the crack boundary. A smooth distribution of the stress intensity factor along
the crack front is presented for various crack shapes and different Poisson's ratio.
Received 5 March 2002; accepted for publication 2 July 2002 相似文献
12.
The interaction problem between a circular inclusion and a symmetrically branched crack embedded in an infinite elastic medium is solved. The branched crack is modeled as three straight cracks which intersect at a common point and each crack is treated as a continuous contribution of edge dislocations. Green's functions are used to reduce the problem into a system of singular equations consisting of the distributions of Burger's dislocation vectors as unknown functions through the superposition technique. The resulting integral equations are solved numerically by the method of Gauss-Chebychev quadrature. The proposed integral equation approach is first verified for two limiting cases against the literature. More effort is paid on the effect of inclusion on both the Mode I and Mode lI stress intensity factors at the branch tips. The effect of inclusion on the branching path is also investigated. 相似文献
13.
The interaction of plane harmonic waves with a thin elastic inclusion in the form of a strip in an infinite body (matrix)
under plane strain conditions is studied. It is assumed that the bending and shear displacements of the inclusion coincide
with the displacements of its midplane. The displacements in the midplane are found from the theory of plates. The priblem-solving
method represents the displacements as discontinuous solutions of the Lamé equations and finds the unknown discontinuities
solving singular integral equations by the numerical collocation method. Approximate formulas for the stress intensity factors
at the ends of the inclusion are derived 相似文献
14.
《International Journal of Solids and Structures》2005,42(18-19):5010-5020
A new integral equation formulation of two-dimensional infinite isotropic medium (matrix) with various inclusions and cracks is presented in this paper. The proposed integral formulation only contains the unknown displacements on the inclusion–matrix interfaces and the discontinuous displacements over the cracks. In order to solve the inclusion–crack problems, the displacement integral equation is used when the source points are acting on the inclusion–matrix interfaces, whilst the stress integral equation is adopted when the source points are being on the crack surfaces. Thus, the resulting system of equations can be formulated so that the displacements on the inclusion–matrix interfaces and the discontinuous displacements over the cracks can be obtained. Based on one point formulation, the stress intensity factors at the crack tips can be achieved. Numerical results from the present method are in excellent agreement with those from the conventional boundary element method. 相似文献
15.
16.
Summary In this paper, the curved-crack problem for an infinite plate containing an elastic inclusion is considered. A fundamental
solution is proposed, which corresponds to the stress field caused by a point dislocation in an infinite plate containing
an elastic inclusion. By placing the distributed dislocation along the prospective site of the crack, and by using the resultant
force function as the right-hand term in the equation, a weaker singular integral equation is obtainable. The equation is
solved numerically, and the stress intensity factors at the crack tips are evaluated. Interaction between the curved crack
and the elastic inclusion is analyzed.
Received 8 October 1996; accepted for publication 27 March 1997 相似文献
17.
V. V. Mikhas’kiv I. O. Butrak I. P. Laushnik 《Journal of Applied Mechanics and Technical Physics》2013,54(3):465-471
The propagation of harmonic elastic wave in an infinite three-dimensional matrix containing an interacting low-rigidity disk-shaped inclusion and a crack. The problem is reduced to a system of boundary integral equations for functions that characterize jumps of displacements on the inclusion and crack. The unknown functions are determined by numerical solution of the system of boundary integral equations. For the symmetric problem, graphs are given of the dynamic stress intensity factors in the vicinity of the circular inclusion and the crack on the wavenumber for different distances between them and different compliance parameters of the inclusion. 相似文献
18.
V. Makaryan M. Sutton D. Hasanyan X. Deng 《International Journal of Solids and Structures》2011,48(7-8):1210-1218
We consider boundary value problem in which an elastic layer containing a finite length crack is under compressive loading. The crack is parallel to the layer surfaces and the contact between crack surfaces are either frictionless or with adhesive friction or Coulomb friction.Based on fourier integral transformation techniques the solution of the formulated problems is reduced to the solution of a singular integral equation, then, using Chebyshev’s orthogonal polynomials, to an infinite system of linear algebraic equations. The regularity of these equations is established. The expressions for stress and displacement components in the elastic layer are presented. Based on the developed analytical algorithm, extensive numerical investigations have been conducted.The results of these investigations are illustrated graphically, exposing some novel qualitative and quantitative knowledge about the stress field in the cracked layer and their dependence on geometric and applied loading parameters. It can be seen from this study that the crack tip stress field has a mode II type singularity. 相似文献
19.
20.
《International Journal of Solids and Structures》2003,40(19):5037-5049
Green’s functions of a point dislocation as well as a concentrated force for the plane problem of an infinite plane containing an arbitrarily shaped hole under stress, displacement, and mixed boundary conditions are stated. The Green’s functions are obtained in closed forms by using the complex stress function method along with the rational mapping function technique, which makes it possible to deal with relatively arbitrary configurations. The stress functions for these problems consist of two parts: a principal part containing singular and multi-valued terms, and a complementary part containing only holomorphic terms. These Green’s functions can be derived without carrying out any integration. The applications of the Green’s functions are demonstrated in studying the interaction of debonding and cracking from an inclusion with a line crack in an infinite plane subjected to remote uniform tension. The Green’s functions should have many other potential applications such as in boundary element method analysis. The boundary integral equations can be simplified by using the Green’s functions as the kernels. 相似文献