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1.
V. S. Kirilyuk 《International Applied Mechanics》2005,41(3):302-308
The stress-concentration problem for an elastic orthotropic medium containing an ellipsoidal cavity is solved. The stress state in the elastic space is represented as a superposition of the principal state and the perturbed state due to the cavity. The equivalent-inclusion method, the triple Fourier transform in spatial variables, and the Fourier-transformed Green function for an infinite medium are used. Double integrals over a finite domain are evaluated using the Gaussian quadrature formulas. The results for particular cases are compared with those obtained by other authors. The influence of the geometry of the cavity and the elastic properties of the material on stress concentration is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 93–100, March 2005. 相似文献
2.
V. S. Kirilyuk 《International Applied Mechanics》2003,39(6):704-712
The interaction of an elastic ellipsoidal inclusion with an elliptic crack in an infinite elastic medium under triaxial loading is analyzed. The stress state in the elastic space is represented as a superposition of the principal state and perturbed states, which are due to the presence and interaction of the inclusion and the crack. The analytical solution of the problem is found using the method of equivalent inclusion, the potential of an inhomogeneous ellipsoid, and a system of harmonic functions for an elliptic crack. The effect of triaxial loading on the stress intensity factors is analyzed 相似文献
3.
V. S. Kirilyuk 《International Applied Mechanics》2005,41(4):358-366
The static-equilibrium problem for an elastic orthotropic space with an elliptical crack is solved. The stress state of the space is represented as a superposition of the principal and perturbed states. To solve the problem, Willis’s approach is used. It is based on the Fourier transform in spatial variables, the Fourier-transformed Green function for anisotropic material, and Cauchy’s residue theorem. The contour integrals appearing during solution are evaluated using Gaussian quadratures. The results for particular cases are compared with those obtained by other authors. The influence of anisotropy on the stress intensity factors is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 20–29, April 2005. 相似文献
4.
V. S. Kirilyuk 《International Applied Mechanics》2005,41(8):895-903
The static-equilibrium problem for an elastic orthotropic space with an elliptic crack is solved. The stress state of the
space is represented as a superposition of the principal and perturbed states. To solve the problem, Willis' approach is used.
It is based on the Fourier transform in spatial variables, the Fourier-transformed Green function for anisotropic material,
and Cauchy's residue theorem. The contour integrals appearing during solution are evaluated using Gaussian quadratures. The
results for particular cases are compared with those obtained by other authors. The influence of anisotropy on the stress
intensity factors is studied
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 8, pp. 72–81, August 2005. 相似文献
5.
A stress–strain problem is solved for an infinite elastic magnetically soft medium with an ellipsoidal inclusion in an external magnetic field. The main characteristics of the stress–strain state and induced magnetic fields in the medium and the inclusion are determined and their distribution over the surface of the inclusion is analyzed 相似文献
6.
The stress state of an elastic orthotropic medium with an arbitrarily oriented triaxial ellipsoidal inclusion is analyzed.
A solution is obtained using the triple Fourier transform and the Fourier-transformed Green’s function for an infinite anisotropic
medium. The high efficiency of the approach is demonstrated by solving the problem for a transversely isotropic material with
a spheroidal cavity for which the exact solution is known. A numerical analysis is conducted to study the stress distribution
over the surface of the inclusion with different orientations in the orthotropic space. It is revealed that in some cases
the orientation of the inclusion has a strong effect on the stress concentration
__________
Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 55–61, April 2007. 相似文献
7.
This paper is a study into the interaction of two triaxial ellipsoidal cavities whose surfaces are under different pressures with an elliptic crack in an infinite elastic medium. The stress state in the elastic space is represented by a superposition of perturbed states due to the presence and interaction of the cavities and the crack. The exact solution of the problem is constructed by using a modified method of equivalent inclusion, the potential of an inhomogeneous ellipsoid, and a system of harmonic functions for the elliptic crack. A numerical analysis is carried out to find how the geometry of the cavities and the crack, the distance between them, and the pressure on their surfaces affect the stress intensity factors 相似文献
8.
9.
IntroductionWiththedevelopmentofparticleandfiberreinforcedcomposites,theinclusion_crackinteractionproblemisbecominganimportantfieldbeingstudied .Andasamodel,itisalsousedtostudytheeffectsofmaterialdefectsonthestrengthandfractureofengineeringstructure.TheinterationbetweencircularinclusionandcrackwasstudiedinRefs.[1 -6 ] ;InRefs.[7-1 2 ] ,theinterationbetweenlineinclusionandcrackswasdiscussed ;TheinterationbetweenellipticalinclusionandcrackwasstudiedinRefs.[1 3,1 4] .However,withthedevelopmento… 相似文献
10.
Some dynamic problems for elastic materials with functional inhomogeneities: anti-plane deformations
The paper considers two dynamical problems for an isotropic elastic media with spatially varying functional inhomogeneity, the propagation of surface anti-plane shear SH waves, and the stress deformation state of an anti-plane vibrating medium with a semi-infinite crack. These problems are considered for five different types of inhomogeneity. It is shown that the propagation of surface anti-plane shear waves is possible in all these cases. The existence conditions and the speed of propagation of surface waves have been found. In the section devoted to the investigation of the stress deformation state of a vibrating medium with a semi-infinite crack, Fourier transforms along with the Wiener Hopf technique are employed to solve the equations of motion. The asymptotic expression for the stress near the crack tip is analyzed, which leads to a closed form solution of the dynamic stress intensity factor (DSIF). Here also the problem is considered for five different functional inhomogeneities. From the formulae for DSIF thus obtained one can see that the inhomogeneity can have both a quantitative and qualitative impact on the character of the stress distribution near the crack.Received: 25 July 2002, Accepted: 3 April 2003, Published online: 27 June 2003PACS:
83.20.Lr, 83.50.Tq, 83.50.Vr, 46.30.Nz 相似文献
11.
V. S. Kirilyuk 《International Applied Mechanics》2004,40(12):1371-1377
The static-equilibrium problem for an elastic orthotropic space with a circular (penny-shaped) crack is solved. The stress state of an elastic medium is represented as a superposition of the principal and perturbed states. To solve the problem, Willis approach is used, which is based on the triple Fourier transform in spatial variables, the Fourier-transformed Greens function for an anisotropic material, and Cauchys residue theorem. The contour integrals obtained are evaluated using Gauss quadrature formulas. The results for particular cases are compared with those obtained by other authors. The influence of anisotropy on the stress intensity factors is studied.__________Translated from Prikladnaya Mekhanika, Vol. 40, No. 12, pp. 76–83, December 2004. 相似文献
12.
Stress–Strain State of a Ferromagnetic with a Paraboloidal Inclusion in a Homogeneous Magnetic Field
The stress–strain state of an infinite elastic soft ferromagnetic medium with an elliptic paraboloidal inclusion is analyzed. The material of the inclusion is a soft ferromagnetic too. The medium is in a magnetic field directed along the minor axis of the elliptic section of the paraboloid by a plane perpendicular to its axis. The main characteristics of the stress–strain state and induced magnetic fields in the medium and inclusion are determined. The features of the stress distribution over the inclusion boundary are studied 相似文献
13.
Koffi Espoir Koumi Lv Zhao Julien Leroux Thibaut Chaise Daniel Nelias 《International Journal of Solids and Structures》2014
Many materials contain inhomogeneities or inclusions that may greatly affect their mechanical properties. Such inhomogeneities are for example encountered in the case of composite materials or materials containing precipitates. This paper presents an analysis of contact pressure and subsurface stress field for contact problems in the presence of anisotropic elastic inhomogeneities of ellipsoidal shape. Accounting for any orientation and material properties of the inhomogeneities are the major novelties of this work. The semi-analytical method proposed to solve the contact problem is based on Eshelby’s formalism and uses 2D and 3D Fast Fourier Transforms to speed up the computation. The time and memory necessary are greatly reduced in comparison with the classical finite element method. The model can be seen as an enrichment technique where the enrichment fields from the heterogeneous solution are superimposed to the homogeneous problem. The definition of complex geometries made by combination of inclusions can easily be achieved. A parametric analysis on the effect of elastic properties and geometrical features of the inhomogeneity (size, depth and orientation) is proposed. The model allows to obtain the contact pressure distribution – disturbed by the presence of inhomogeneities – as well as subsurface and matrix/inhomogeneity interface stresses. It is shown that the presence of an inclusion below the contact surface affects significantly the contact pressure and subsurfaces stress distributions when located at a depth lower than 0.7 times the contact radius. The anisotropy directions and material data are also key elements that strongly affect the elastic contact solution. In the case of normal contact between a spherical indenter and an elastic half space containing a single inhomogeneity whose center is located straight below the contact center, the normal stress at the inhomogeneity/matrix interface is mostly compressive. Finally when the axes of the ellipsoidal inclusion do not coincide with the contact problem axes, the pressure distribution is not symmetrical. 相似文献
14.
Xiaoqing Jin Zhanjiang Wang Qinghua Zhou Leon M. Keer Qian Wang 《Journal of Elasticity》2014,114(1):1-18
Stress analysis of an elliptical inhomogeneity in an infinite isotropic elastic plane is a classical elasticity problem, which is usually solved by means of the complex variable formulation. In this work, we demonstrate that an alternative method of solution for such a problem, via the equivalent inclusion method, may be more convenient and straightforward without recourse to complex potentials or curvilinear coordinates. The explicit analytical solution can be derived through simple algebraic manipulation, although the longitudinal eigenstrain component should be handled with care in the case of plane strain. Since the exterior Eshelby tensor for an elliptical inclusion is available in closed-form, the present study provides a full field stress solution expressed in Cartesian coordinates. Furthermore, the in-plane stress components are represented in terms of Dundurs’ parameters. The solution methodology and the convenient formulae of the stress concentration may be of practical use to the engineers in developing benchmarks for design evaluation. 相似文献
15.
The interaction of a plane harmonic longitudinal wave with a thin circular elastic inclusion is considered. The wave front
is assumed to be parallel to the inclusion plane. Since the inclusion is thin, the matrix-inclusion interface conditions (perfect
bonding) are formulated on the mid-plane of the inclusion. The bending displacements of the inclusion are determined from
the bending equation for a thin plate. The problem is solved using discontinuous Lamé solutions for harmonic vibrations. Therefore,
the problem can be reduced to the Fredholm equation of the second kind for a function associated with the discontinuity of
normal stresses on the inclusion. The equation obtained is solved by the method of mechanical quadratures using Gaussian quadrature
formulas. Approximate formulas for the stress intensity factors are derived. Results from a numerical analysis of the dependence
of the SIFs on the dimensionless wave number and the stiffness of the inclusion are presented
__________
Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 16–21, May 2008. 相似文献
16.
Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated. The solution of dynamic stress concentration factor is given using the Green's function and the method of complex variable functions. First, the space is divided into upper and lower parts along the interface. In the lower half space, a suitable Green's function for the problem is constructed. It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at the horizontal surface. Thus, the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces. Also, the expressions of displacement and stress fields are obtained in this situation. Finally, examples and results of dynamic stress concentration factor are given. Influences of the cylindrical inclusion and the difference parameters of the two mediators are discussed. 相似文献
17.
Scattering of SH wave from an interface cylindrical elastic inclusion with a semicircular disconnected curve is investigated.The solution of dynamic stress concentration factor is given using the Gteen's function and the method of complex variable functions.First,the space is divided into upper and lower parts along the interface.In the lower half space,a suitable Green's function for the problem is constructed.It is an essential solution of the displacement field for an elastic half space with a semi-cylindrical hill of cylindrical elastic inclusion while bearing out-plane harmonic line source load at the horizontal surface.Thus,the semicircular disconnected curve can be constructed when the two parts are bonded and continuous on the interface loading the undetermined anti-plane forces on the horizontal surfaces.Also,the expressions of displacement and stress fields are obtained in this situation.Finally,examples and results of dynamic stress concentration factor are given.Influences of the cylindrical inclusion and the difierence parameters of the two mediators are discussed. 相似文献
18.
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
19.
Interaction of plane nonstationary waves with a thin elastic inclusion under smooth contact conditions 总被引:1,自引:0,他引:1
We solve the problem of determining the stress state near a thin elastic inclusion in the form of a strip of finite width
in an unbounded elastic body (matrix) with plane nonstationary waves propagating through it and with the forces exerted by
the ambient medium taken into account. We assume that the matrix is in the plane strain state, and the smooth contact conditions
are realized on both sides of the inclusion. The method for solving this problem consists in using the integral Laplace transform
with respect to time and in representing the stress and displacement images in terms of the discontinuous solution of Lamé
equations in the case of plane strain. As a result, the initial problem is reduced to a system of singular integral equations
for the transforms of the unknown stress and displacement jumps. To invert the Laplace transform, we use a numerical method
based on replacing the Mellin integral by the Fourier series. As a result, we obtain approximate formulas for calculating
the stress intensity factors (SIF) for the inclusion, which are used to study the SIF time-dependence and its influence on
the values of the inclusion rigidity. We also studied the possibility of considering the inclusions of higher rigidity as
absolutely rigid inclusions. 相似文献
20.
I. P. Dobrovolskii 《Mechanics of Solids》2007,42(1):50-56
For a weakly contrasting anisotropic inhomogeneity in a linearly elastic homogeneous space or half-space, using the perturbation method, we obtain an approximate solution and estimate its accuracy. In the case of inhomogeneity of arbitrary contrast, we reduce the problem to a system of integral equations. In the general case, it is easy to compose the procedure for solving this problem approximately. In the special case of a homogeneous anisotropic ellipsoidal inhomogeneity in space, the strain state inside the inhomogeneity turns out to be homogeneous, and we thus obtain the exact solution of the problem. 相似文献