Transient stress concentration at an elliptical discontinuity

1969 ◽  
Vol 4 (4) ◽  
pp. 261-266 ◽  
Author(s):  
W G James ◽  
W P T North
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Stress Wave Propagation ◽  
Transient Stress ◽  
Simplifying Assumptions ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
The One ◽  
Two Parameters ◽  
Laser Light Source

In this investigation, the photoelastic technique with a modulated-ruby-laser light source was used to determine the maximum dynamic-stress concentration factors in a strut containing a symmetrically located elliptical discontinuity. The two parameters, time after impact and size of discontinuity, were considered. Some simplifying assumptions and the one- and two-dimensional theory of stress-wave propagation were used to develop a theoretical solution which agrees well with experimental results.

Dynamic Antiplane Interaction of Subsurface Circular Cavities in a Semi-Infinite Piezoelectric Medium

2009 ◽  
Author(s):  
Tianshu Song ◽  
Tamman Merhej ◽  
Qingna Shang ◽  
Dong Li
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Numerical Solutions ◽  
Piezoelectric Medium ◽  
Dynamic Stress Concentration ◽  
Characteristic Parameters ◽  
Time Harmonic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Piezoelectric Characteristic

In the present work, dynamic interaction is investigated theoretically between several circular cavities near the surface in a semi-infinite piezoelectric medium subjected to time-harmonic incident anti-plane shearing. The analyses are based upon the use of complex variable and multi coordinates. Dynamic stress concentration factors at the edges of the subsurface circular cavities are obtained by solving boundary value problems with the method of orthogonal function expansion. Some numerical solutions about two interacting subsurface circular cavities in a semi-infinite piezoelectric medium are plotted so as to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the structural geometries influence on the dynamic stress concentration factors.

Dynamic Anti-Plane Behaviors of Interacting Circular Cavities in an Infinite Piezoelectric Medium

2008 ◽  
Author(s):  
Tianshu Song ◽  
Dong Li ◽  
Lili Sun
Keyword(s):  
Stress Concentration ◽  
Dynamic Stress ◽  
Piezoelectric Medium ◽  
Dynamic Stress Concentration ◽  
Wave Load ◽  
Plane Shear ◽  
Time Harmonic ◽  
Concentration Factors ◽  
Stress Concentration Factors ◽  
Piezoelectric Characteristic

In this article, dynamic interaction is investigated theoretically between several circular cavities in an infinite piezoelectric medium under time-harmonic incident anti-plane shear wave load. The theoretical formulations are based upon the use of complex variable and multi-coordinates. Dynamic stress concentration factors at the edges of the circular cavities are obtained by solving boundary value problems with the method of orthogonal function expansion. As examples, some calculating results of two interacting circular cavities in an infinite piezoelectric medium are plotted to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the structural geometries influence on the dynamic stress concentration factors.

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.

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.

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.

Dynamic Anti-Plane Behavior of the Interaction Between a Crack and a Circular Cavity in a Piezoelectric Medium

2006 ◽  
Vol 324-325 ◽  
pp. 29-32 ◽  
Author(s):  
Tian Shu Song ◽  
Hong Liang Li ◽  
Jung Qiang Dong
Keyword(s):  
Stress Intensity ◽  
Stress Concentration ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Piezoelectric Medium ◽  
Circular Cavity ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Concentration Factors ◽  
Stress Concentration Factors

In this paper, the dynamic interaction is investigated theoretically between a crack and a circular cavity in an infinite piezoelectric medium under time-harmonic incident anti-plane shearing. The formulations are based on the method of complex variable and Green’s function. The resulting dynamic stress intensity factors at the crack’s tip and dynamic stress concentration factors at the cavity’s edge are obtained with crack-division technique. Numerical results are plotted to show how the frequencies of incident wave, the piezoelectric characteristic parameters of the material and the geometry of the crack and the circular cavity influence upon the dynamic stress intensity factors and dynamic stress concentration factors.

Dynamic Stress of a Circular Cavity Buried in a Semi-Infinite Functionally Graded Material Subjected to Shear Waves

2006 ◽  
Vol 74 (5) ◽  
pp. 916-922 ◽  
Author(s):  
Xue-qian Fang ◽  
Chao Hu ◽  
Shan-yi Du
Keyword(s):  
Boundary Condition ◽  
Stress Concentration ◽  
Functionally Graded Material ◽  
Dynamic Stress ◽  
Shear Waves ◽  
Functionally Graded ◽  
Circular Cavity ◽  
Graded Material ◽  
Concentration Factors ◽  
Stress Concentration Factors

The multiple scattering of shear waves and dynamic stress in a semi-infinite functionally graded material with a circular cavity is investigated, and the analytical solution of this problem is derived. The analytical solutions of wave fields are expressed by employing the wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary condition of the cavity. The image method is used to satisfy the traction-free boundary condition of the material structure. As an example, the numerical solution of the dynamic stress concentration factors around the cavity is also presented. The effects of the buried depth of the cavity, the incident wave number, and the nonhomogeneity parameter of materials on the dynamic stress concentration factors are analyzed. Analyses show that when the nonhomogeneity parameter of materials is <0, it has less influence on the maximum dynamic stress around the cavity; however, it has greater influence on the distribution of dynamic stress around the cavity. When the nonhomogeneity parameter of materials is >0, it has greater influence on both the maximum dynamic stress and the distribution of dynamic stress around the cavity, especially in the case that the buried depth is comparatively small.

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