The Interaction of a Cylindrical Elastic Inclusion with Semicircular Disconnected Curve and Linear Cracks in an Homogeneous Medium by SH-Waves

2007 ◽  
Vol 348-349 ◽  
pp. 357-360
Author(s):  
Qi Hui ◽  
Jia Xi Zhao
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Function Method ◽  
Dynamic Stress ◽  
Elastic Inclusion ◽  
Complex Function ◽  
Dynamic Stress Intensity Factor ◽  
Homogeneous Medium ◽  
Sh Waves

The scattering of SH waves by a cylindrical elastic inclusion with a semicircular disconnected curve and linear cracks in an homogeneous medium is investigated and the solution of dynamic stress intensity factor is given by Green’s function, complex function method. Firstly, we can divide the space into up-and-down parts along the X axis. In the lower half space, a new suitable Green’s function for the present problem is constructed.In the upper half space, the Green’s function has been given by reference [5]. Thereby the semicircular disconnected curve can be constructed when the two parts are bonded along the interface and the linear cracks can be constructed using the method of crack-division and the integral equations can be obtained by the use of continuity conditions at the X axis. Finally, some examples and results of dynamic stress intensify factor are given and the influence of the parameters is discussed.

Interaction of Elliptical Inclusion and Crack in Half-Space under SH-Waves

2012 ◽  
Vol 525-526 ◽  
pp. 345-348
Author(s):  
Zai Lin Yang ◽  
Hua Nan Xu ◽  
Bao Ping Hei ◽  
Yong Yang
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Elastic Inclusion ◽  
Complex Function ◽  
Polar Coordinates ◽  
Arbitrary Length ◽  
Sh Waves ◽  
Elliptical Inclusion

The methods of Green's function, complex function and multi-polar coordinates are applied here to report interaction of an elliptical inclusion and a crack in half-space under incident SH-waves. Based on the symmetry of SH-waves scattering, the "conformal mapping" technology was developed to construct a suitable Green's function, a fundamental solution to the displacement field for the elastic half space containing elliptical inclusion while bearing out-plane line source load at arbitrary point, for creating a beeline crack with arbitrary length at any position combined with crack-division technology. The displacement field and stress field were then deduced while the inclusion coexists with the crack Lastly, numerical examples are presented to discuss the dependence of dynamic stress concentration factor (DSCF) around the elastic inclusion on different parameters.

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.

Scattering of SH-Waves and Dynamic Stress Intensity Factor by an Interacting Mode III Crack and a Lining Structure in Half Space

2008 ◽  
Vol 385-387 ◽  
pp. 273-276
Author(s):  
Zai Lin Yang ◽  
Mei Juan Xu ◽  
Bai Tao Sun
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Displacement Field ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Lining Structure

Scattering of SH wave by an elastic half space with a lining structure 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 a fundamental solution to the displacement field for the elastic space possessing circular lining structure while bearing out-of-plane harmonic line source load at arbitrary point. 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 lining structure 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 Multiple Circular Inclusions and a Linear Crack by SH-Wave

2010 ◽  
Vol 452-453 ◽  
pp. 677-680
Author(s):  
Hong Liang Li ◽  
Hong Li
Keyword(s):  
Stress Concentration ◽  
Green’S Function ◽  
Green's Function ◽  
Dynamic Stress ◽  
Analytic Solutions ◽  
Dynamic Stress Concentration ◽  
Elastic Space ◽  
Sh Wave ◽  
Sh Waves ◽  
Out Of Plane

Multiple circular inclusions exists widely in natural media, engineering materials and modern municipal construction, and defects are usually found around the inclusions. When composite material with multiple circular inclusions and a crack is impacted by dynamic load, the scattering field will be produced. The problem of scattering of SH waves by multiple circular inclusions and a linear crack is one of the important and interesting questions in mechanical engineering and civil engineering for the latest decade. It is hard to obtain analytic solutions except for several simple conditions. In this paper, the method of Green’s function is used to investigate the problem of dynamic stress concentration of multiple circular inclusions and a linear crack for incident SH wave. The train of thoughts 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 multiple circular inclusions 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 multiple circular inclusions, anti-plane stresses which are the same in quantity but opposite in direction to those mentioned before, are loaded at the region where the crack is in existent actually; Finally, the expressions of the displacement and stress are given when multiple circular inclusions and a linear crack exist at the same time. Then, by using the expression, an example is provided to show the effect of multiple circular inclusions and crack on the dynamic stress concentration.

Dynamic Stress Intensity Problem of SH-Wave by Double Linear Cracks near a Circular Hole

2008 ◽  
Vol 385-387 ◽  
pp. 105-108 ◽  
Author(s):  
Hong Liang Li ◽  
Hong Li ◽  
Yong Yang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Green’S Function ◽  
Circular Hole ◽  
Green's Function ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Elastic Space ◽  
Sh Wave

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.

Acoustical Green’s Function and Boundary Element Techniques for 3D Half-Space Problems

2017 ◽  
Vol 25 (04) ◽  
pp. 1730001 ◽  
Author(s):  
Rafael Piscoya ◽  
Martin Ochmann
Keyword(s):  
Green’S Function ◽  
Frequency Domain ◽  
Boundary Element ◽  
Half Space ◽  
Green's Function ◽  
Homogeneous Medium ◽  
Practical Implementation ◽  
Infinite Plane ◽  
Exterior Problems ◽  
Basic Concepts

This paper presents a review of basic concepts of the boundary element method (BEM) for solving 3D half-space problems in a homogeneous medium and in frequency domain. The usual BEM for exterior problems can be extended easily for half-space problems only if the infinite plane is either rigid or soft, since the necessary tailored Green’s function is available. The difficulties arise when the infinite plane has finite impedance. Numerous expressions for the Green’s function have been found which need to be computed numerically. The practical implementation of some of these formulas shows that their application depends on the type of impedance of the plane. In this work, several formulas in frequency domain are discussed. Some of them have been implemented in a BEM formulation and results of their application in specific numerical examples are summarized. As a complement, two formulas of the Green’s function in time domain are presented. These formulas have been computed numerically and after the application of the Fourier Transformation compared with the frequency domain formulas and with a FEM calculation.

Antiplane Harmonic Elastodynamic Stress Analysis of an Infinite Wedge With a Circular Cavity

2009 ◽  
Vol 76 (6) ◽  
Author(s):  
Gang Liu ◽  
Baohua Ji ◽  
Haitao Chen ◽  
Diankui Liu
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Dynamic Stress ◽  
Incident Angle ◽  
Wedge Angle ◽  
Cavity Surface ◽  
Basic Solution ◽  
Circular Cavity ◽  
Infinite Wedge

In this paper, the antiplane harmonic dynamics stress of an infinite isotropic wedge with a circular cavity is analyzed for the first time by using a novel method with Green’s function, complex functions, and multipolar coordinates. A basic solution for the displacement field of an elastic half-space containing a circular cavity subjected to antiplane harmonic point force is employed as the Green’s function. Based on the Green’s function, the infinite wedge problem is equivalently transformed into the problem of a half-space divided by a semi-infinite traction free line. The equivalent problem is solved numerically to determine the dynamic stress field in the wedge at different apex angles and cavity locations. We show that the wedge angle, cavity location, and incident angle and frequency of the external load have significant effect on the dynamic stress of the cavity surface. The dynamic stress concentration factor on the cavity surface becomes singular when the cavity is close to the boundary of the wedge.

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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