Scattering of SH Wave by a Semi-Circle Inclusion Embedded in Bi-Material Half Space Surface

2020 ◽  
Vol 36 (4) ◽  
pp. 497-506 ◽  
Author(s):  
Paeksan Jang ◽  
Yongguk Ri ◽  
Songchol Ri ◽  
Cholho Pang ◽  
Changson Ok
Keyword(s):  
Half Space ◽  
Dynamic Stress ◽  
Incidence Angle ◽  
Addition Theorem ◽  
Sh Wave ◽  
Displacement Fields ◽  
Green Function Method ◽  
Dynamic Stress Concentration Factor ◽  
Region Matching ◽  
Matching Technique

ABSTRACTInvestigation of SH wave scattering by inclusions in bi-material half space is an important issue in engineering. The purpose of this work is to study the dynamic response of a semi-circle inclusion embedded in bi-material half space surface by SH wave. Graf's addition theorem, Green function method and region-matching technique are used to determine the displacement fields in the bi-material half space and the inclusion. The distributions of dynamic stress concentration factor (DSCF) around the semi-circle inclusion are depicted graphically considering different material parameters. The results show that the frequency and the incidence angle of SH wave, the rigidities of the inclusion and bi-material half space, and the distance from the inclusion to the interface have a great effect on the distribution of DSCF around the inclusion.

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.

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.

Dynamic Response of Shallow Buried Tunnel Subjected to SH Wave

2010 ◽  
Vol 163-167 ◽  
pp. 4265-4268
Author(s):  
Zhi Gang Chen
Keyword(s):  
Stress Concentration ◽  
Half Space ◽  
Dynamic Stress ◽  
Complex Function ◽  
Least Square ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Scattering Wave

The dynamic stress concentration on quadratic and U-shaped cavities in half space, which are similar to the cross-section of the tunnels, is solved in this paper impacted by SH-wave. The analytical solution for the cavity in elastic half space is gained by the complex function method. In the complex plane, the scattering wave which satisfies the zero-stress condition at the horizontal surface can be constructed, the problem can be inverted into a set of algebraic equations to solve coefficients of the constructed scattering wave by least square method. For the earthquake-resistance researches, the numerical examples of the dynamic stress concentration around the quadratic and U-shaped cavities impacted by SH-wave are given. The influences of the dynamic stress concentration by the incident wave number and angle, the depth and shape of the cavity are discussed. It is showed that the interaction among the wave, the surface and the shallow buried tunnels should be cared in half space. In this situation, the dynamic stress concentration around the tunnel is greater obvious than the whole space.

Dynamic stress concentration of a cylindrical cavity in vertical exponentially inhomogeneous half space under SH wave

Meccanica ◽  
2019 ◽  
Vol 54 (15) ◽  
pp. 2411-2420
Author(s):  
Guanxixi Jiang ◽  
Zailin Yang ◽  
Cheng Sun ◽  
Xinzhu Li ◽  
Yong Yang
Keyword(s):  
Stress Concentration ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Dynamic Stress Concentration ◽  
Sh Wave

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 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 Dynamic Stress around a Cylindrical Nano-Inclusion with an Interface in a Right-Angle Plane under SH-Wave

2020 ◽  
Vol 2020 ◽  
pp. 1-10 ◽  
Author(s):  
Hongmei Wu ◽  
Zhiying Ou
Keyword(s):  
Dynamic Stress ◽  
Surface Effect ◽  
Scattering Problem ◽  
Surface Elasticity ◽  
Sh Wave ◽  
Complex Variable Function ◽  
Dynamic Stress Concentration Factor ◽  
Variable Function ◽  
Elastic Substrates ◽  
The Right

Based on the surface elasticity theory, the scattering of shear wave (SH-wave) by a cylindrical nano-inclusion with an interface in a right-angle plane is studied using the method of complex variable function. The dynamic stress concentration factor along the interface of inclusion by the SH-wave and scattering cross section are derived and numerically evaluated. The surface effect, the incident wave’s frequency, the shear modulus, and the distances from the center of nano-inclusion to the right-angle boundaries show the different degrees effects on the DSCF. Our results can aid in analyzing the mechanical properties of nonuniform nanocomposites. The proposed method can better solve the scattering problem of the holes/inclusions on noninfinite elastic substrates.

Scttering of SH-Waves by Interface Semicircular Debonded Cylindrical Lining and Linear Cracks Originating at Edge of Lining

2011 ◽  
Vol 399-401 ◽  
pp. 2149-2154
Author(s):  
Jing Fu Nan ◽  
Hui Qi ◽  
Chun Xiang Zhao
Keyword(s):  
Half Space ◽  
Dynamic Stress ◽  
Elastic Half Space ◽  
Lower Half ◽  
Sh Wave ◽  
Two Phase ◽  
Sh Waves ◽  
Complex Functions ◽  
The Green Function ◽  
Elastic Lining

The Green function and other complex functions were employed to study the problem of scatteing of SH wave by a interface semicircular debonded elastic lining of two-phase mediums and interface linear cracks originating at edge of lining. We divided the whole model into upper elastic half space with the semi-circular canyon and lower elastic half space with semi-circular lining hill.In lower half space. Semicircular debonded elastic lining is constructed by satisfing the continuous condition of displacement and stress on interface when upper half part and lower half part are conjoined,and linear cracks is constructed by using the method of crack incision, upper half part and lower half part are conjoined by method of “conjunction”.In the end some examples and results of dynamic stress intensify factor are given with discussions.

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