Dynamic Stress Concentration of a Cylindrical Cavity in Half-Plane Excited by Standing Goodier-Bishop Stress Wave

2012 ◽  
Vol 28 (2) ◽  
pp. 269-277 ◽  
Author(s):  
W.-I Liao ◽  
T.-J. Teng
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Stress Wave ◽  
Half Plane ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Scattering Problem ◽  
Ground Surface ◽  
Wave Number ◽  
Dynamic Stress Concentration

AbstractBased on expansion technique, the dynamic stress concentration of a cylindrical cavity buried in an elastic half-plane is studied in the paper. The cavity and the half-plane are excited by a harmonic standing Goodier-Bishop stress wave which, as a result of taking the normalized frequency tends to zero, is equivalent to a simple uniform static tension parallel to the ground surface. In the formulation, the scattered waves are represented by a series expansion, and their associated modal fields of the expansion satisfy the boundary conditions on the ground surface as well as the radiation condition at infinity. As a consequence, the scattering problem is reduced to the determination of the expansion coefficients by matching the boundary conditions on the cavity. The numerical technique based on the steepest descent method is used to calculate the integral representation of potential functions in wave-number domain. Numerical results for the dynamic hoop stresses around the wall of the cavity and the dynamic stress concentration factors with various buried depth and excitation frequencies are presented.

Dynamic Stress Concentration of a Cylindrical Cavity Buried in an Elastic Half-Plane Subjected to a Standing Goodier-Bishop Stress Wave

2002 ◽  
Author(s):  
C. S. Yeh ◽  
T. J. Teng ◽  
W. I. Liao ◽  
W. S. Shyu
Keyword(s):  
Stress Concentration ◽  
Boundary Conditions ◽  
Stress Wave ◽  
Half Plane ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Scattering Problem ◽  
Ground Surface ◽  
Radiation Condition ◽  
Dynamic Stress Concentration

In this paper, based on a expansion technique proposed by Yeh et al. (1995), the dynamic stress concentration of a cylindrical cavity buried in an elastic half-plane is studied. The cavity and the half-plane are excited by a harmonic standing Goodier-Bishop stress wave which, as a result of taking the normalized frequency tends to zero, is equivalent to a simple uniform static tension parallel to the ground surface. In the formulation, the scattered waves are represented by series expansion and their associated modal fields of the expansion satisfy the boundary conditions on the ground surface as well as the radiation condition at infinity, thus the scattering problem is reduced to the determination of the expansion coefficients by matching the boundary conditions on the cavity. Some numerical results for the dynamic hoop stresses around the wall of the cavity as well as the dynamic stress concentration factors with various buried depth and excitation frequencies are presented.

On the Effects of Source Proximity on the Dynamic Stresses Around a Cylindrical Cavity

1967 ◽  
Vol 34 (2) ◽  
pp. 359-364 ◽  
Author(s):  
M. T. Jakub ◽  
C. C. Mow
Keyword(s):  
Stress Concentration ◽  
Plane Wave ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Poisson Ratio ◽  
Cylindrical Wave ◽  
Wave Number ◽  
Dynamic Stress Concentration ◽  
Concentration Factors ◽  
Stress Concentration Factors

Analysis of the interaction of a cylindrical wave impinging on a cylindrical cavity is presented. It is assumed that a line source is located an arbitrary distance from the cavity and that its strength varies harmonically in time. The resulting dynamic stress concentration factors at the cavity wall are determined by considering the wave-diffraction effects. Numerical results indicate that the dynamic stress concentration factors around the cavity are dependent upon (a) distance from the source to the cavity, (b) wave number, and (c) the Poisson ratio of the medium. At high wave number (high frequency), the response to an incident cylindrical wave becomes almost identical with the response to an incident plane wave. At low wave number, however, the response departs drastically from all previous investigations where the incident wave was assumed to be a plane wave. Stress concentration factors substantially higher than those determined in earlier studies were noted in the present analysis.

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 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.

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.

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

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.

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