Dynamics of a Mode III Crack Impacted by Elastic Wave in Half Space with a Removable Rigid Cylindrical Inclusion

2006 ◽  
Vol 324-325 ◽  
pp. 679-682 ◽  
Author(s):  
Zai Lin Yang ◽  
Dian Kui Liu ◽  
Xiao Lang Lv
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Complex Function ◽  
Elastic Half Space ◽  
Cylindrical Inclusion ◽  
Sh Wave ◽  
Mode Iii ◽  
Scattering Wave ◽  
Moving Coordinate

Scattering of SH wave by a crack is studied in elastic half space with a removable rigid cylindrical inclusion by Green’s function, complex function and moving coordinate method. In half space, firstly the scattering wave function of removable rigid cylindrical inclusion is constructed; next a suitable Green’s function is solved for present problem, then using crack-division to make a crack. Thus the solution of problem can be obtained. Numerical examples are provided and discussed.

Scattering of SH Wave by an Interacting Mode III Crack and a Circular Cavity in Half Space

2007 ◽  
Vol 348-349 ◽  
pp. 861-864 ◽  
Author(s):  
Zai Lin Yang ◽  
Zhi Gang Chen ◽  
Dian Kui Liu
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Complex Function ◽  
Dynamic Stress Intensity Factor ◽  
Arbitrary Point ◽  
Circular Cavity ◽  
Sh Wave ◽  
Mode Iii

Scattering of SH wave by an elastic half space with a circular cavity and a crack in any position and direction is studied with Green’s function, complex function and multi-polar coordinate method. 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 impacted by an out-plane harmonic line source loading at an arbitrary point in half space. Then a crack in any position and direction is constructed by means of crack-division in half space. Finally the displacement field and stress field are established in the case of coexistence of circular cavity and crack, and the expression of dynamic stress intensity factor (DSIF) at the tip of crack is given. According to numerical examples, the influences of different parameters on DSIF are discussed.

Interaction of SH-Wave on Multiple Linear Cracks near Shallow-Embedded Structure

2011 ◽  
Vol 488-489 ◽  
pp. 440-443
Author(s):  
Zai Lin Yang ◽  
Hua Nan Xu ◽  
Mei Juan Xu ◽  
Bai Tao Sun
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Complex Function ◽  
Surface Displacement ◽  
Elastic Half Space ◽  
Polar Coordinates ◽  
Multiple Cracks ◽  
Sh Wave ◽  
Lining Structure

The surface displacement of a circular lining structure and multiple cracks in an elastic half space by incident SH-wave is studied in this paper based on the methods of Green's function, complex function and multi-polar coordinates. Firstly, we construct a suitable Green’s function which indicates a fundamental solution to the displacement field for an elastic half space possessing a circular lining structure and cracks while bearing out-plane harmonic line loads at arbitrary point. Then using the method of crack-division, a crack is created. Thus expressions of displacement and stress field are established at the existence of the structure and the cracks. Finally, the interaction of inclusion and two cracks is chosen as numerical examples and the influences of different parameters on the surface displacement are discussed.

The Dynamic Response of Circular Lining Structure and Multiple Cracks in Half Space under Impact Loading

2009 ◽  
Vol 417-418 ◽  
pp. 713-716
Author(s):  
Zai Lin Yang ◽  
Mei Juan Xu ◽  
Bai Tao Sun
Keyword(s):  
Dynamic Response ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Impact Loading ◽  
Complex Function ◽  
Polar Coordinates ◽  
Multiple Cracks ◽  
Sh Wave ◽  
Lining Structure

The dynamic response of a circular lining structure and multiple cracks in an elastic half space while bearing impact loading is studied in this paper. This problem can be seen as the problem of defending of blast. The methods of Green's function, complex function and multi-polar coordinates are used here. First, the scattering wave which satisfies the condition of stress free on the ground surface of half-space containing a shallow-embedded circular lining structure impacted by incident SH-wave is constructed based on the symmetry of SH-wave scattering and the method of multi-polar coordinates system. Then a crack or multiple cracks in any position and direction can be constructed by Green's function and means of crack-division in half space. Finally the displacement field and stress field are established in the case of coexistence of circular lining structure and cracks, and the expression of dynamic stress intensity factor (DSIF) at the tip of crack is given. The interaction of inclusion and two cracks is chosen as numerical examples finally. According to nu-merical examples, the influences of different parameters on DSIF are discussed.

Dynamic Analysis for Circular Inclusion Near Interfacial Crack Impacted by SH-Wave in Half Space

2012 ◽  
Vol 28 (1) ◽  
pp. 143-151 ◽  
Author(s):  
H. Qi ◽  
J. Yang ◽  
Y. Shi ◽  
J. Y. Tian
Keyword(s):  
Free Boundary ◽  
Dynamic Analysis ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Interfacial Crack ◽  
Circular Inclusion ◽  
Wave Number ◽  
Complex Method ◽  
Sh Wave

ABSTRACTComplex method and Green's function method are used here to investigate the dynamic analysis for circular inclusion near interfacial crack impacted by SH-wave in bi-material half-space. Firstly, the displacement expression of the scattering wave was constructed which satisfied the free boundary conditions, then Green's function could be constructed, which was an essential solution to the displacement field for an elastic right-angle space with a circular inclusion impacted by out-plane harmonic line source loading at vertical surface. Secondly, crack was made out with “crack-division” technique. Meanwhile, the bi-material media was divided into two parts along the bi-material interface based on the idea of interface “conjunction”, and then the vertical surfaces of the two right-angle spaces were loaded with undetermined anti-plane forces in order to satisfy displacement continuity and stress continuity conditions at linking section. So a series of algebraic equations for determining the unknown forces could be set up through continuity conditions and the Green's function. Finally, some examples and results for dynamic stress concentration factor of the circular elastic inclusion were given. Numerical results show that they are influenced by interfacial crack, the incident wave number and the free boundary in some degree.

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.

The Scattering Field of SH-Wave in Half-Space With a Semi-Cylindrical Hill and a Horizontal Circular Tunnel

2005 ◽  
Author(s):  
Guoqing Wang ◽  
Liming Dai ◽  
Diankui Liu
Keyword(s):  
Wave Function ◽  
Half Space ◽  
Stress Condition ◽  
Complex Function ◽  
Sh Wave ◽  
Coordinate Method ◽  
Linear Algebraic Equations ◽  
Scattering Field ◽  
Moving Coordinate ◽  
The Hill

The scattering field of SH-wave in a half-space with a semi-cylindrical hill and a subsurface horizontal hole is studied in the present research by utilizing a complex function and the moving-coordinate method. Based on the concept of ‘conjunction,’ the domain considered is divided into two subdomains. The first subdomain is a cylindrical one which includes the surface of the hill, while the rest is the second subdomain. In the cylindrical subdomain, a standing wave function is constructed which automatically satisfies the zero-stress condition at the hill surface and arbitrary-stress condition at the other part of the circular subdomain. For the second subdomain, which contains a semi-cylindrical canyon and a subsurface hole, a scattering wave function is assumed, which satisfies the zero-stress condition on the horizontal surface. By employing the moving-coordinate method, the solutions of the mathematical model established for the SH-wave can be obtained with the satisfaction of the continuous conditions of stress and displacement across the junction interface together with the zero-stress condition at the surface of the tunnel. The solutions such obtained consist of a series of infinite linear algebraic equations, which can be solved numerically with consideration of the first finite terms corresponding to the frequencies of the wave. For demonstrating the application of the model developed, the displacements of the horizontal and semi-cylindrical hill surfaces are quantified with different properties of wave and geometry parameters.

Impact of point source on fissured poroelastic medium: Green’s function approach

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Shishir Gupta ◽  
Soumik Das ◽  
Rachaita Dutta
Keyword(s):  
Point Source ◽  
Green’S Function ◽  
Half Space ◽  
Porous Layer ◽  
Green's Function ◽  
Anisotropic Fluid ◽  
Complex Frequency ◽  
Sh Wave ◽  
Content Type ◽  
Porous Half Space

Purpose The purpose of this paper is to investigate the mathematical model comprising a heterogeneous fluid-saturated fissured porous layer overlying a non-homogeneous anisotropic fluid-saturated porous half-space without fissures. The influence of point source on horizontally polarized shear-wave (SH-wave) propagation has been studied intensely. Design/methodology/approach Techniques of Green’s function and Fourier transform are applied to acquire displacement components, and with the help of boundary conditions, complex frequency equation has been constructed. Findings Complex frequency relation leads to two distinct equations featuring dispersion and attenuation properties of SH-wave in a heterogeneous fissured porous medium. Using MATHEMATICA software, dispersion and damping curves are sketched to disclose the effects of heterogeneity parameters associated with both media, parameters related to rigidity and density of single porous half-space, attenuation coefficient, wave velocity, total porosity, volume fraction of fissures and anisotropy. The fact of obtaining classical Love wave equation by introducing several particular conditions establishes the validation of the considered model. Originality/value To the best of the authors’ knowledge, effect of point source on SH-wave propagating in porous layer containing macro as well as micro porosity is not analysed so far, although theory of fissured poroelasticity itself has vast applications in real life and impact of point source not only enhances the importance of fissured porous materials but also opens a new area for future research.

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