Authors: Hong Liang Li, Hong Li, Yong Yang

Abstract: In mechanical engineering, circular hole is used widely in structure design. When the
structure is overloaded or the load is changed regularly, cracks emerge and spread. Based on the
former study of dynamic stress concentration problem of SH wave by a crack originating at a
circular hole edge, in this paper, the method of Green’s function is used to investigate the problem
of dynamic stress intensity problem of double linear cracks near a circular hole impacted by
incident SH-wave. The train of thought for this problem is that: Firstly, a Green’s function is
constructed for the problem, which is a fundamental solution of displacement field for an elastic
space possessing a circular hole and a linear crack while bearing out-of-plane harmonic line source
force at any point; Secondly, in terms of the solution of SH-wave’s scattering by an elastic space
with a circular hole and a linear crack, anti-plane stresses which are the same in quantity but
opposite in direction to those mentioned before, are loaded at the region where the second crack is
in existent actually, we called this process “crack-division”; Finally, the expressions of the
dynamic stress intensity factor(DSIF) of the cracks are given when the circular hole and double
linear crack exist at the same time. Then, by using the expressions, an example was provided to
show the effect of circular hole and cracks on the dynamic stress intensity factor of the cracks.

105

Authors: Bai Tao Sun, Pei Lei Yan, Zai Lin Yang

Abstract: Based on Green’s function, complex function and multi-polar coordinate system, the far
field solution of SH wave scattered by an elastic half space with a circular cavity and a crack at an
arbitrary position and orientation is investigated. First, a suitable Green’s function is constructed,
which is the fundamental solution of the displacement field for a half space with a circular cavity
subjected to an out-plane time-harmonic line force at an arbitrary position in half space. Second, by
means of crack-division technique, a crack with any location and orientation can be constructed in
the region of the half space. The displacement field and stress field are established in the situation
of coexistence of circular cavity and crack. At last expressions of far field, such as displacement
mode of scattering wave are deduced. Some examples and numerical results are illustrated. The
influences of the combination of different media parameters on solutions of far field are discussed.

157

Authors: Xue Yi Zhang, Guang Ping Zou, Hong Liang Li

Abstract: Sacttering of SH-wave of combined deffectiveness which included single circular cavity and double linear cracks in elastic medium was investigated in detail. Analytic solution of this problem was obtained by Green’s Function method and idea of crack-division at actual position of crack at two times. There were two key steps of this method. First step was to employ a special Green’s Function which was a fundamental solution of displacement field for an elastic space with a cavity in it subjected to out-of-plane harmonic line source force at any point at first. The sceond step was crack-division which was artificially to produce a crack by apllying opposite shear stress caused by incident SH-wave. Distribution of dynamic stress concentration factor (DSCF) at edge of cavity was studied by numerical analysis. Distribution Curves of DSCF of three models were plotted by numerical method in polar coordinate system. Three models were one circular cavity and without crack, one circular cavity and single crack and single circular cavity double cracks. The results were compared and discussed in different incident angle of SH-wave.Conclusion was that the interaction among SH-wave, single cavity and double crack was obvious. Dynamic stress concentration factor varied with angle and distance between cavity and crack.

825

Authors: Zai Lin Yang, Hua Nan Xu, Mei Juan Xu, Bai Tao Sun

Abstract: In this paper, we study the problems of scattering of out-of-plane line source load by half-space shallow-embedded circular lining structure and a crack in the field of linearly elastic dynamic mechanics. This is an essential solution to the displacement field for the elastic space possessing shallow-embedded circular lining structure and a crack while bearing out-of-plane harmonic line source load at arbitrary point. The wave function of scattering of shallow-embedded circular lining structure impacted by incident steady SH-wave is constructed based on the symmetry of SH-wave scattering and the method of multi-polar coordinates system. Then a crack is made out using the method of “crack-division”. Thus expressions of displacement and stress are established when shallow-embedded circular lining structure and a crack are both in existent. Finally, with two different dimensionless parameters, numerical results of scattering of out-of-plane line source load by half-space shallow-embedded circular lining structure and a crack are obtained and numerical examples are provided to show the influence of wave number ratio, shear modulus ratio, thickness ratio and the ratio of distance between the center of the different cavity and ground surface and the radius of the circular lining structure upon the dynamic stress concentration factor(DSCF) and dynamic stress intensity factor(DSIF) at crack tip.

329

Authors: Dong Ni Chen, Hui Qi, Yong Shi

Abstract: The scattering of SH-wave caused by the subsurface circular cavities in an elastic half-space covered with an elastic layer was discussed, which was based on the complex function method ,wave functions expansion method and big circular arc postulation method in which the circular boundary of large radius was used to approximate straight boundary of surface elastic layer. By the theory of *Helmholtz*, the general solution of the *Biot**’s* wave function was achieved. Utilizing the complex series expansion technology and the boundary conditions, we could transform the present problem into the problem in which we needed to solve the infinite linear algebraic equations with unknown coefficients in wave functions. Finally, the dynamic stress concentration factors around the circular cavities were discussed in numerical examples.

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