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1.
FengYangde WangYuesheng ZhangZimao CuiJunzhi 《Acta Mechanica Solida Sinica》2003,16(3):189-196
A 2D time domain boundary element method (BEM) is developed to solve the transient scattering of plane waves by a unilaterally frictionally constrained inclusion. Coulomb friction is assumed along the contact interface. The incident wave is assumed strong enough so that localized slip and separation take place along the interface. The present problem is in effect a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (slip, separation and stick regions). In order to determine the unknown intervals, an iterative technique is developed. As an example, we consider the scattering of a circular cylinder embeddedin an infinite solid. 相似文献
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Summary Transient response of a sub-interface crack in a bi-material is studied with emphasis on the dynamic interaction between the crack and the interface, by combining the traditional time-domain displacement boundary element method (BEM) and the non-hypersingular traction BEM. Computations are performed for an unbounded bi-material with a crack subjected to impact tensile loading on its faces or incident impact waves and a bounded rectangular bi-material plate under remote impact tensile loading. Numerical results of the dynamic stress intensity factors (DSIFs) and dynamic interface tractions are presented for various material combinations and crack locations. It is shown that pronounced increases in DSIFs and the interface tractions may be caused in some cases because of the dynamic interaction between the crack and the interface.This work was initialized during the second author's stay at Institute of Mechanics, TU Darmstadt, Germany under the support of the Alexander von Humboldt Foundation. Discussion on the BEM formulation with Dr. Seelig is gratefully acknowledged. The first two authors are also grateful for the partial support by the China National Natural Science Foundation under Grant No. 10025211 and the NJTU Scientific Paper Fund (PD195). 相似文献
4.
The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the
dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems:
one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the
scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and
stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the
second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations.
Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction
of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous
function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the
end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material
parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic
effects cannot be ignored.
This work was supported by the National Natural Science Foundation of China (No.19772064) and by the project of CAS KJ 951-1-20 相似文献
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W.-J. Feng R.-J. Hao J.-X. Liu S.-M. Duan 《Archive of Applied Mechanics (Ingenieur Archiv)》2005,74(10):649-663
Summary In this paper, the scattering of SH waves by a magneto-electro-elastic cylindrical inclusion partially debonded from its surrounding magneto-electro-elastic material is investigated by using the wavefunction expansion method and a singular integral equation technique. The debonding regions are modeled as multiple arc-shaped interface cracks with non-contacting faces. The magneto-electric impermeable boundary conditions are adopted. By expressing the scattered fields as wavefunction expansions with unknown coefficients, the mixed boundary-value problem is firstly reduced to a set of simultaneous dual-series equations. Then, dislocation density functions are introduced as unknowns to transform these dual-series equations to Cauchy singular integral equations of the first type,which can be numerically solved easily. The solution is valid for arbitrary number and size of the arc-shaped interface cracks. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond. The effects of incident direction, crack configuration and various material parameters on the dynamic stress intensity factors are discussed. The solution of this problem is expected to have applications in the investigation of dynamic fracture properties of magneto-electro-elastic materials with cracks.The work was supported by the National Natural Science Fund of China (Project No. 19772029) and the Research Fund for Doctors of Hebei Province, China (Project No. B2001213). 相似文献
7.
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
8.
Scattering of elastic waves in an elastic matrix containing an inclusion with interfaces 总被引:1,自引:0,他引:1
Based on the theory of elastic dynamics, the scattering of elastic waves and dynamic stress concentration in fiber-reinforced
composite with interfaces are studied. Analytical expressions of elastic waves in different medium areas are presented and
an analytic method of solving this problem is established. The mode coefficients are determined by means of the continuous
conditions of displacement and stress on the boundary of the interfaces. The influence of material properties and structural
size on the dynamic stress concentration factors near the interfaces is analyzed. It indicates that they have a great influence
on the dynamic properties of fiber-reinforced composite. As examples, numerical results of dynamic stress concentration factors
near the interfaces are presented and discussed. This paper provides reliable theoretical evidence for the study of dynamic
properties in fiber-reinforced composite.
Project supported by the National Natural Science Foundation of China (No. 19972018). 相似文献
9.
An experimental study on turbulent coherent structures near a sheared air-water interface 总被引:3,自引:0,他引:3
The turbulence structures near a sheared air-water interface were experimentally investigated with the hydrogen bubble visualization
technique. Surface shear was imposed by an airflow over the water flow which was kept free from surface waves. Results show
that the wind shear has the main influence on coherent structures under air-water interfaces. Low- and high- speed streaks
form in the region close to the interface as a result of the imposed shear stress. When a certain airflow velocity is reached,
“turbulent spots” appear randomly at low-speed streaks with some characteristics of hairpin vortices. At even higher shear
rates, the flow near the interface is dominated primarily by intermittent bursting events. The coherent structures observed
near sheared air-water interfaces show qualitative similarities with those occurring in near-wall turbulence. However, a few
distinctive phenomena were also observed, including the fluctuating thickness of the instantaneous boundary layer and vertical
vortices in bursting processes, which appear to be associated with the characteristics of air-water interfaces.
The project supported by the National Natural Science Foundation of China (Grant No.19672070) 相似文献
10.
A theoretical solution of cylindrically isotropic cylindrical tube for axisymmetric plane strain dynamic thermoelastic problem 总被引:2,自引:0,他引:2
A dynamic thermoelastic solution of a cylindrically isotropic cylindrical tube or solid cylinder with axisymmetric plane deformations
is developed. Since there exist thermal boundary conditions and tractions on the two surfaces of a cylindrical tube, the problem
under consideration is with inhomogeneous boundary conditions. Therefore we introduce a special function to transform the
inhomogeneous boundary conditions to homogeneous ones for an unknown function. Then by using the method of separation of variables,
the unknown function can be expressed as the multiplication series of Bessel functions and unknown time functions. Thirdly,
by virtue of the orthogonal properties of Bessel functions, the equations about these unknown time functions are derived and
the solutions are obtained. Finally, the displacement is obtained by adding the two parts mentioned above. By means of the
present method, integral transform can be avoided. It is suitable for arbitrary thermal loads and mechanical loads. Numerical
results are also presented for thermal shocked, cylindrically isotropic cylindrical tube and solid cylinder.
Project supported by the National Natural Science Foundation of China (No. 10172075 and No. 10002016). 相似文献
11.
R. Kumar 《Theoretical and Applied Fracture Mechanics》2009,52(3):131-139
The present paper concentrates on the study of reflection and refraction characteristics of plane waves at an imperfectly bonded interface of two orthotropic generalized thermoelastic rotating half-spaces with different elastic and thermal properties. In this type of problem of orthotropic thermoelastic rotating medium, there are three types of plane waves quasi longitudinal (QL-) wave, quasi thermal (T-mode) wave and quasi transverse (QT-) wave, whose velocities depend on the angle of incidence, imperfection and rotation. The amplitude ratios of reflected waves to that of incident one in each case have been derived. Some special cases of boundaries, i.e. normal stiffness, transverse stiffness, thermal contact conductance, slip boundary and welded contact boundary have been deduced from an imperfect one. Effect of rotation on the amplitude ratios of different reflected and refracted waves with respect to incident QL-wave at different boundaries have been studied graphically. It is observed that thermal properties, imperfect boundary and rotation have significant effect on the propagation of waves. 相似文献
12.
Investigated in this paper are the effects of strain gradients on the stress distribution near an interface. The quasi axis-symmetry
interface problem is solved by using the couple stress theory and the perturbation method. The results show that a boundary
layer exists near an interface or a fixed boundary, where the shear stress perpendicular to the interface is significantly
different from that obtained from the classical elasticity theory.
Supported by the National Natural Science Foundation of China (No. 19891180). 相似文献
13.
The scattering of Love waves by an interface crack between a piezoelectric layer and an elastic substrate is investigated
by using the integral transform and singular integral equation techniques. The dynamic stress intensity factors of the left
and the right crack tips are determined. It is found from numerical calculation that the dynamic response of the system depends
significantly on the crack configuration, the material combination and the propagating direction of the incident wave. It
is expected that specifying an appropriate material combination may retard the growth of the crack for a certain crack configuration.
Project supported by the National Natural Science Foundation of China (No. 19891180), the Fundamental Research Foundation
of Tsinghua University (JZ 2000.007) and the Fund of the Education Ministry of China. 相似文献
14.
This paper presents a method for analytical solving the plane elasticity and thermoelasticity problems for planes and half-planes
which exhibit inhomogeneous material properties in one of the planar directions (in the case of half-plane, the inhomogeneity
direction is assumed to be perpendicular to the boundary.) With the aid of direct integration of equilibrium equations, the
original problems are reduced to the set of governing, harmonic equations with corresponding conditions. In the transform
domain of the integral Fourier-transform, the governing equations are reduced to an integral equation which is solved by simple
iteration technique. The rapid convergence of the iterative procedure is established to perform the numerical calculation.
The authors gratefully acknowledge the financial support of this research by the National Science Council (Republic of China)
under Grant NSC 95-2221-E-002-048-MY2.
The co-author, Yu Tokovyy, gratefully acknowledges the particular financial support of this research by the grant of the President
of Ukraine for young scientists (No GP/F13/0094). 相似文献
15.
Michael Renardy 《Theoretical and Computational Fluid Dynamics》1995,7(6):457-461
Proofs of instability are given for two problems in fluid dynamics. These problems are of a transonic nature and the instability results from real eigenvalues which cross and bifurcate into the complex plane. The first problem concerns the stability of linear shear flow in shallow water, and the second problem concerns shear flow in non-Newtonian fluids.This research was supported by the Office of Naval Research under Grant N00014-92-J-1664 and by the National Science Foundation under Grant DMS-9306635. 相似文献
16.
A method of interface inversion in inhomogeneous media 总被引:1,自引:0,他引:1
First, an approximate solution of time domain interface scattering field is derived by extending the classical Born approximation
in the problem of interface scattering. In accordance with the solution form, a projection density compensation (PDC) inversion
method is developed according to the projection slice theorem, which is valid for the cases of inhomogeneous media and wave
mode transformation. Finally, in the model of layered media, the calculation algorithm and the simulation inversion comparison
results of point defect, crack, and crack on an interface, as well as the experiment method and results in the condition of
acoustic wave, are given.
The project supported by the National Natural Science Foundation of China (No.19232031) and Chinese Education Commission Science
Foundation 相似文献
17.
The present work concerns with the investigation of the interior transmission problem, which is naturally associated to the
inverse elastic scattering problem of determining the support of an isotropic homogeneous penetrable body from a knowledge
of the time harmonic incident plane waves and the far-field patterns of the corresponding scattered wave-fields. Our approach
combines a boundary integral formulation of the problem and a compact perturbation argument to establish the discreteness
of the set of transmission eigenvalues and the well-posedness of the interior transmission problem under the most general
assumptions on the elastic parameters of the underlying media.
相似文献
18.
T. C. T. Ting 《Rheologica Acta》1973,12(2):150-154
Summary The problem of a rigid punch pressed against and moved on the surface of an elastic or viscoelastic layer is studied. It is shown that the governing equations reduce to the same integral equation for the elastic contact problem. Two particular motions of the punch are considered. In the first case the punch moves at a constant speed along a straight line on the surface of a viscoelastic layer. In the second case the punch moves at a constant speed along a circular path. Finally, the special case of a punch moving on a layer of a standard linear viscoelastic solid is studied. The equation is identical to a punch of modified shape pressed on an elastic layer.The work presented here was supported by the National Science Foundation under Grant GK 35163 with the University of Illinois.With 1 figure 相似文献
19.
William W. Feng 《International Journal of Solids and Structures》1975,11(4):437-448
The nonaxisymmetric contact problem between an inflated membrane and a rigid indentor is considered. The membrane is assumed to be an initially thin plane sheet. The shape and the boundary of the contact region and the configuration of the deformed membrane under both inflation and indentation are found by employing the minimum potential energy principle subjected to an inequality constraint condition. A slack variable that converts the inequality constraint to an equality constraint condition is introduced. The coordinate functions that describe the deformed configurations of the membrane are assumed to be represented by a series of geometric admissible functions with unknown coefficients. The unknown coefficients that minimize the total potential energy are determined by Fletcher and Powell's[1] iterative descent method for finding the minimum of a function of multivariables. 相似文献
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Rajneesh Kumar Manjeet Singh 《应用数学和力学(英文版)》2007,28(5):627-641
A problem concerned with the reflection and refraction of thermoelastic plane waves at an imperfect interface between two generalized thermally conducting cubic crystal solid half-spaces of different elastic and thermal properties with two relaxation times has been investigated. The generalized thermoelastic theory with two relaxation times developed by Green and Lindsay has been used to study the problem. The expressions for the reflection and refraction coefficients which are the ratios of the amplitudes of reflected and refracted waves to the amplitude of incident waves are obtained for an imperfect boundary and deduced for normal stiffness, transverse stiffness, thermal contact conductance, slip and welded boundaries. Amplitude ratios of different reflected and refracted waves for different boundaries with angle of emergence have been compared graphically for different incident waves. It is observed that the amplitude ratios of reflected and refracted waves are affected by the stiffness and thermal properties of the media. 相似文献