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 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 Dynamic analysis of a cylindrical cavity in inhomogeneous elastic half-space subjected to SH waves

2017 ◽  
Vol 24 (1) ◽  
pp. 299-311 ◽  
Author(s):  
Zailin Yang ◽  
Guanxixi Jiang ◽  
Haiyi Tang ◽  
Baitao Sun ◽  
Yong Yang
Keyword(s):  
Stress Concentration ◽  
Helmholtz Equation ◽  
Half Space ◽  
Cylindrical Cavity ◽  
Variable Coefficient ◽  
Dynamic Stress ◽  
Dynamic Stress Concentration ◽  
Mapping Technique ◽  
Concentration Factors ◽  
Stress Concentration Factors

Based on complex function methods and a multipolar coordinate system, the scattering induced by a cylindrical cavity in a radially inhomogeneous half-space is investigated. Mass density of the half-space varies depending on the distance from the centre of the cavity while the shear modulus is always constant. The wave velocity is expressed as a function of radius vector and the Helmholtz equation is a partial differential equation with a variable coefficient. By means of a conformal mapping technique, the Helmholtz equation with a variable coefficient is transferred into its normal form. Then, displacement fields and corresponding stress components are deduced. Applying the boundary conditions, dynamic stress concentration factors around the cavity are obtained and analyzed. Typical numerical results are presented to demonstrate the distribution of dynamic stress concentration factors when influencing parameters are assumed.

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.

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 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 Stresses Concentrations of SH Wave by Circular Tunnel with Lining

2011 ◽  
Vol 323 ◽  
pp. 18-22 ◽  
Author(s):  
Yi Guang Zhang ◽  
Chuan Lu Zhou ◽  
Yi Xian Liu
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Sh Wave ◽  
Circular Tunnel ◽  
Dynamic Stresses ◽  
Shear Elasticity ◽  
Concentration Factors ◽  
Stress Concentration Factors

Based on the scattering theory of elastic waves, employing the wave function expansion method, the scattering and the dynamic stresses concentration of SH wave by circular tunnel with lining are investigated. The analytical solution of the problem is derived, and the numerical solution of the dynamic stress concentration factors around the lining is presented. The effects of the shear elasticity of the surrounding rock and the lining, the wave number on the dynamic stress concentration factors are analyzed. Analysis has shown that the shear elasticity of the surrounding rock and the wave number are factors that influence dynamic stress concentration factor, and provide important theoretical foundation for the earthquake evaluation of lining.

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