Scattering of Sh-Wave by Cylindrical Inclusion Near Interface in Bi-Material Half-Space

2011 ◽  
Vol 27 (1) ◽  
pp. 37-45 ◽  
Author(s):  
H. Qi ◽  
J. Yang ◽  
Y. Shi
Keyword(s):  
Stress Concentration ◽  
Half Space ◽  
Green's Function ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Dynamic Stress ◽  
Cylindrical Inclusion ◽  
Dynamic Stress Concentration ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor

ABSTRACTGreen's function and complex function methods are used here to investigate the problem of the scattering of SH-wave by a cylindrical inclusion near interface in bi-material half-space. Firstly, Green's function was constructed which was an essential solution of displacement field for an elastic right-angle space possessing a cylindrical inclusion while bearing out-of-plane harmonic line source load at any point of its vertical boundary. Secondly, the bi-material media was divided into two parts along the vertical interface using the idea of interface “conjunction”, then undetermined anti-plane forces were loaded at the linking sections respectively to satisfy continuity conditions, and a series of Fredholm integral equations of first kind for determining the unknown forces could be set up through continuity conditions on surface. Finally, some examples for dynamic stress concentration factor of the cylindrical elastic inclusion are given. Numerical results show that dynamic stress concentration factor is influenced by interfaces, free boundary and combination of different media parameters.

Dynamic Stress Concentration of Circular Cavity and Double Linear Cracks in Elastic Medium

2009 ◽  
Vol 419-420 ◽  
pp. 825-828
Author(s):  
Xue Yi Zhang ◽  
Guang Ping Zou ◽  
Hong Liang Li
Keyword(s):  
Stress Concentration ◽  
Elastic Medium ◽  
Green's Function ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Dynamic Stress ◽  
Dynamic Stress Concentration ◽  
Circular Cavity ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor

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.

Dynamic Response of Multiple Holes in Half Space Saturated Soil to the Effect of the P Waves

2013 ◽  
Vol 639-640 ◽  
pp. 648-651
Author(s):  
You Ping Liu
Keyword(s):  
Stress Concentration ◽  
Dynamic Response ◽  
Half Space ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Dynamic Stress ◽  
Saturated Soil ◽  
Dynamic Stress Concentration ◽  
Dynamic Stress Concentration Factor ◽  
Peak Value

According to the Biot wave theory and the complex function combined with multi coordinate method, seismic wave dynamic response of underground holes in the half space saturated soil is studied. Given P wave on two circular holes of the dynamic stress concentration factor of the numerical results, the distribution situations of the dynamic stress concentration factors are discussed with the variation of the hole spacing, incidence angle and the dimensionless wave number. The results show that, the effect of the underground hole spacing to the interaction effects of the holes is obvious. When the hole spacing reaches up to 6 times the radius of the hole, the peak value of the dynamic stress concentration factor decreases obviously, and the peripheral distribution of offset is weakened. With increasing of the incident angle, the hole peripheral stress concentration coefficient showed the trend of first increasing then decreasing, distribution also occurs at certain angle deflection. In low frequency waves, the hole stress peak value will influence mutually more, while in the high frequency input, interaction between holes will reduce.

Dynamic Analysis for a Subsurface Elastic Cylindrical Inclusion with a Semi- Cylindrical Hill Impacted by SH-Wave

2011 ◽  
Vol 199-200 ◽  
pp. 945-948
Author(s):  
Xiao Lang Lv ◽  
Dian Kui Liu
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Dynamic Stress ◽  
Scattered Wave ◽  
Cylindrical Inclusion ◽  
Dynamic Stress Concentration ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor ◽  
Variable Function

An analytic method is developed for dynamic stress concentration of a subsurface elastic cylindrical inclusion below a semi-cylindrical hill under SH-wave. And the dynamic stress concentration factor (DSCF) is given by complex variable function. During the solution, a standing wave and scattered wave displacement functions are constructed in different parts respectively. All of these displacement functions should satisfy the boundary conditions of each part. Employed to the boundary conditions around the elastic cylindrical inclusion, a series of infinite algebraic equations about the problem can be obtained. The calculating results of DSCF around the elastic cylindrical inclusion are plotted to show the effects of some parameters on DSCF.

scholarly journals A Series Solution for 2D Scattering of Cylindrical SH-Waves by Surrounding Loose Rock Zone of Underground Tunnel Lining

2021 ◽  
Vol 9 ◽  
Author(s):  
Liguo Jin ◽  
Hongyang Sun ◽  
Shengnian Wang ◽  
Zhenghua Zhou
Keyword(s):  
Stress Concentration ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Series Solution ◽  
Dynamic Stress ◽  
Tunnel Lining ◽  
Dynamic Stress Concentration ◽  
Sh Wave ◽  
Wave Source ◽  
Loose Rock

This paper presents a closed-form series solution of cylindrical SH-wave scattering by the surrounding loose rock zone of underground tunnel lining in a uniform half-space based on the wave function expansion method and the mirror image method. The correctness of the series solution is verified through residual convergence and comparison with the published results. The influence of the frequency of the incident cylindrical SH-wave, the distance between the wave source and the lining, the lining buried depth, and the properties of the surrounding loose rock zone on the dynamic stress concentration of the tunnel lining is investigated. The results show that the incident wave with high frequency always makes the dynamic stress concentration of the tunnel lining obvious. With the increase of the distance between the wave source and the tunnel lining, the stress around the tunnel lining decreases, but the dynamic stress concentration factor around the tunnel lining does not decrease significantly but occasionally increases. The ground surface has a great influence on the stress concentration of the tunnel lining. The amplitude of the stress concentration factor of tunnel lining is highly related to the shear wave velocity of the surrounding loose rock zone. When the property of the surrounding rock (shear wave velocity) changes more, the amplitude of the stress concentration factor is larger, that is, the stress concentration is more significant.

Scattering of SH Wave by a Cylindrical Inclusion and a Semi-Cylindrical Hollow Near Vertical Interface Crack in the Bi-Material Half Space

2016 ◽  
Vol 33 (5) ◽  
pp. 619-629 ◽  
Author(s):  
H. Qi ◽  
X.-M. Zhang ◽  
H.-Y. Cheng ◽  
M. Xiang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Stress Concentration ◽  
Half Space ◽  
Function Method ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Cylindrical Inclusion ◽  
Sh Wave ◽  
Dynamic Stress Concentration Factor

AbstractWith the aid of the Green's function method and complex function method, the scattering problem of SH-wave by a cylindrical inclusion and a semi-cylindrical hollow in the bi-material half space is considered to obtain the steady state response. Firstly, by the means of the image method, the essential solution of displacement field as well as Green's function is constructed which satisfies the stress free on the horizontal boundary in a right-angle space including a cylindrical inclusion and a semi-cylindrical hollow and bearing a harmonic out-plane line source force at any point on the vertical boundary. Secondly, the bi-material half space is divided into two parts along the vertical interface, and the first kind of Fredholm integral equations containing undetermined anti-plane forces at the linking section is established by “the conjunction method” and “the crack-division method”, the integral equations are reduced to the algebraic equations consisting of finite items by effective truncation. Finally, dynamic stress concentration factor around the edge of cylindrical inclusion and dynamic stress intensity factor at crack tip are calculated, and the influences of effect of interface and different combination of material parameters, etc. on dynamic stress concentration factor and dynamic stress intensity factor are discussed.

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