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.

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 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.

scholarly journals Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Hongmei Wu ◽  
Zhiying Ou
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Numerical Solutions ◽  
Surface Effects ◽  
Numerical Results ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Sh Wave ◽  
Special Cases ◽  
Variable Function

By using the complex variable function theory and the conformal mapping method, the scattering of plane shear wave (SH-wave) around an arbitrary shaped nano-cavity is studied. Surface effects at the nanoscale are explained based on the surface elasticity theory. According to the generalized Yong–Laplace equations, the boundary conditions are given, and the infinite algebraic equations for solving the unknown coefficients of the scattered wave solutions are established. The numerical solutions of the stress field can be obtained by using the orthogonality of trigonometric functions. Lastly, the numerical results of dynamic stress concentration factor around a circular hole, an elliptic hole and a square hole as the special cases are discussed. The numerical results show that the surface effect and wave number have a significant effect on the dynamic stress concentration, and prove that our results from theoretical derivation are correct.

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.

scholarly journals Dynamic Analysis of a Shallow Buried Tunnel Influenced by a Neighboring Semi-cylindrical Hill and Semi-cylindrical Canyon

2019 ◽  
Author(s):  
Xiaotang Lv ◽  
Cuiling Ma ◽  
Meixiang Fang
Keyword(s):  
Stress Concentration ◽  
Dynamic Analysis ◽  
Half Space ◽  
Dynamic Stress ◽  
Mixed Boundary ◽  
Scattered Wave ◽  
Dynamic Stress Concentration ◽  
Algebraic Equations ◽  
Sh Waves ◽  
Linear Algebraic Equations

This paper provides a dynamic analysis of the response of a subsurface cylindrical tunnel to SH waves influenced by a neighboring semi-cylindrical hill and semi-cylindrical canyon in half-space using complex functions. For convenience in finding a solution, the half-space is divided into two parts and the scattered wave functions are constructed in both parts. Then the mixed boundary conditions are satisfied by moving coordinates. Finally, the problem is reduced to solving a set of infinite linear algebraic equations, for which the unknown coefficients are obtained by truncation of the infinite set of equations. The effects of the incident angles and frequencies of SH waves, as well as of the radius of the tunnel, hill, and canyon on the dynamic stress concentration of the tunnel are studied. The results show that the hill and canyon have a significant effect on the dynamic stress concentration of the tunnel.

Surface Displacement of a Semi-Cylindrical Hill above a Subsurface Elastic Cylindrical Inclusion under SH-Wave

2011 ◽  
Vol 243-249 ◽  
pp. 4037-4040
Author(s):  
Xiao Tang Lv
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Complex Variable ◽  
Surface Displacement ◽  
Cylindrical Inclusion ◽  
Computational Results ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Complex Variable Function ◽  
Variable Function

Scattering of SH-wave by a semi-cylindrical hill above a subsurface elastic cylindrical inclusion in half-space is studied by complex variable function. Firstly, the whole solution domain is divided into two parts, and the solutions that satisfied the boundary conditions are constructed in two parts respectively. Then according to the “conjunction” condition of junction interface and the boundary condition around the subsurface elastic cylindrical inclusion, a set of infinite algebraic equations about the problem can be obtained. Finally the computational results of surface displacement were provided and discussed.

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.

Interaction of Circular Lining and Interior Linear Crack by Incident SH-Wave

2007 ◽  
Vol 348-349 ◽  
pp. 521-524 ◽  
Author(s):  
Hong Liang Li ◽  
Guang Cai Han ◽  
Hong Li
Keyword(s):  
Stress Concentration ◽  
Fundamental Solution ◽  
Green’S Function ◽  
Green's Function ◽  
Dynamic Stress ◽  
Dynamic Stress Concentration ◽  
Elastic Space ◽  
Sh Wave ◽  
Out Of Plane ◽  
Train Of Thought

In this paper, the method of Green’s function is used to investigate the problem of dynamic stress concentration of circular lining and interior linear crack 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 lining while bearing out-of-plane harmonic line source force at any point in the lining. In terms of the solution of SH-wave’s scattering by an elastic space with a circular lining, 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 existent actually, we called this process “crack-division”. Finally, the expressions of the displacement and stress are given when the lining and the crack exist at the same time. Then, by using the expressions, some example is provided to show the effect of crack on the dynamic stress concentration around circular lining.

scholarly journals Scattering of Magnetoacoustic Waves and Dynamic Stress Concentration around Double Openings in Piezomagnetic Composites

Materials ◽  
2021 ◽  
Vol 14 (22) ◽  
pp. 6878
Author(s):  
Huanhuan Xue ◽  
Chuanping Zhou ◽  
Gaofei Cheng ◽  
Junqi Bao ◽  
Maofa Wang ◽  
...  
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Expansion Method ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Acoustic Wave Scattering ◽  
Dynamic Stress Concentration Factor ◽  
Magnetoacoustic Waves ◽  
Wave Function Expansion Method ◽  
Dynamic Stress Distribution

Based on the magnetoacoustic coupled dynamics theory, the wave function expansion method is used to solve the problem of acoustic wave scattering and dynamic stress concentration around the two openings in e-type piezomagnetic composites. To deal with the multiple scattering between openings, the local coordinate method is introduced. The general analytical solution to the problem and the expression of the dynamic stress concentration are derived. As an example, the numerical results of the dynamic stress distribution around two openings with equal diameters are given. The effects of the parameters, such as the incident wave number and the spacing between the openings, on the dynamic stress concentration factor are analyzed.

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