The Ground Motion of Isosceles Triangular Hill in Right-Angle Plane Impacted by SH-Wave

2011 ◽  
Vol 121-126 ◽  
pp. 2363-2366
Author(s):  
Hui Qi ◽  
Jing Guo ◽  
Jie Yang
Keyword(s):  
Complex Function ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Free Surfaces ◽  
Scattering Wave ◽  
The Common ◽  
Solution Region ◽  
The Right ◽  
Domain I ◽  
Stress Free Boundary

The analytical solution to the problem of the scattering of SH-wave by isosceles triangular hill in right-angle plane is given by using the methods of complex function and multiple coordinate. Firstly, the solution region is divided into two domains, where domain I involves isosceles triangular hill and a semi-circular bottom, domain II involves a semi-circular hollow in right-angle plane. And a standing wave function is constructed which satisfies the zero-stress conditions at the triangular wedges. In domain II, the scattering wave functions which satisfy the stress free boundary conditions at the free surfaces for the right-angle plane are constructed. Secondly, based on the conditions of the displacement continuity and stress continuity at the “common border” in the domains, a series of infinite algebraic equations are given and solved by truncation. Finally, some examples for amplitude of displacement on the surface are given. Numerical results show that amplitude of displacement on the surface is influenced by isosceles triangular hill.

Influence on Scattering of SH-Wave by Surface Ground Isosceles Triangular Hill in Right-Angle Plane with Circular Cavity

2010 ◽  
Vol 452-453 ◽  
pp. 529-532
Author(s):  
Guo Jing ◽  
Hui Qi ◽  
Jie Yang
Keyword(s):  
Boundary Conditions ◽  
Superposition Principle ◽  
Complex Function ◽  
Mirror Image ◽  
Circular Cavity ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Polar Coordinate ◽  
The Right ◽  
Stress Free Boundary

The analytical solution to the problem of the scattering of SH-wave by isosceles triangular hill near the subsurface cavity in right-angle plane is given by using the idea of match up. Firstly, wave function was constructed by using the methods of complex function, multi-polar coordinate transformation and superposition principle, which satisfied the stress free boundary conditions at the free surfaces for the right-angle plane possessing a circular cavity. Secondly, transform the wave field from the right-angle plane to the half space by using the method of mirror image in order to obtain the total wave filed, which satisfied the boundary conditions. Finally, based on the conditions of the displacement continuity and stress continuity at the “common border” and the stress free condition at the subsurface cavity edge, a series of infinite algebraic equations were given and solved by truncation. Meanwhile, some examples and results are given and discussed.

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.

The Green’S Function Solution of Right-Angle Plane Including a Semi-Cylindrical Canyon

2013 ◽  
Vol 275-277 ◽  
pp. 830-835
Author(s):  
Chun Xiang Zhao ◽  
Hui Qi
Keyword(s):  
Free Boundary ◽  
Green’S Function ◽  
Wave Field ◽  
Green's Function ◽  
Complex Function ◽  
Algebraic Equations ◽  
Function Solution ◽  
Out Of Plane ◽  
Stress Boundary Conditions ◽  
The Right

The Green’s function of a right-angle plane including semi-cylindrical canyon while bearing out-of-plane harmonic line source load on horizontal interface have been considered using the methods of complex function and image. Firstly, the wave field of right-angle plane was imaged half space, the scattering wave field, which satisfies the free stress boundary conditions of the right-angle plane on the vertical interface could be constructed. Secondly, a series of infinite algebraic equations be obtained to settle this problem by considering the stress free boundary condition of semi-cylindrical canyon. Finally, some examples for ground motion of a right-angle plane were given and discussed. Numerical results show that displacement of the horizontal surface is influenced by right-angle free boundary.

Dynamic Stress Concentration Analysis of Multiple Circular Cavities near Multiple Semi-Cylindrical Alluvial Valleys

2011 ◽  
Vol 121-126 ◽  
pp. 3253-3257
Author(s):  
Hui Wen Wang ◽  
Zai Lin Yang ◽  
Hua Nan Xu
Keyword(s):  
Dynamic Response ◽  
Complex Function ◽  
Elastic Half Space ◽  
Continuity Condition ◽  
Polar Coordinates ◽  
Algebraic Equations ◽  
Sh Waves ◽  
Common Boundary ◽  
Incident Plane ◽  
Domain I

The problem of dynamic response of multiple circular cavities near multiple semi-cylindrical alluvial valleys under incident plane SH-waves is investigated by the methods of complex function and multi-polar coordinates in this paper. Firstly, the solution domain is divided into two parts, Domain I is multiple semi-cylindrical alluvial valleys, and Domain Ⅱ is an elastic half space with several subsurface circular cavities near multiple semi-cylindrical alluvial valleys. A series of infinite algebraic equations is then obtained based on the displacement and stress continuity condition on “common boundary” of two parts after constructing the associated displacement and stresses expressions of each part. Finally some numerical expamples are prensented and dynamic response of subsurface circular cavities near semi-cylindrical alluvial valleys with respect to different parameters is discussed.

The Scattering of SH-Wave Caused by Subsurface Circular Cavities in a Layered Half-Space

2011 ◽  
Vol 488-489 ◽  
pp. 226-229
Author(s):  
Dong Ni Chen ◽  
Hui Qi ◽  
Yong Shi
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Complex Function ◽  
Expansion Method ◽  
Elastic Half Space ◽  
Wave Functions ◽  
Large Radius ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Linear Algebraic Equations

The scattering of SH-wave caused by the subsurface circular cavities in an elastic half-space covered with an elastic layer was discussed, which was based on the complex function method ,wave functions expansion method and big circular arc postulation method in which the circular boundary of large radius was used to approximate straight boundary of surface elastic layer. By the theory of Helmholtz, the general solution of the Biot’s wave function was achieved. Utilizing the complex series expansion technology and the boundary conditions, we could transform the present problem into the problem in which we needed to solve the infinite linear algebraic equations with unknown coefficients in wave functions. Finally, the dynamic stress concentration factors around the circular cavities were discussed in numerical examples.

A study on the scattering field of SH-waves in a topographical area consisting of a semi-cylindrical hill and a subsurface horizontal hole

2007 ◽  
Vol 221 (3) ◽  
pp. 451-465 ◽  
Author(s):  
G Wang ◽  
L Dai ◽  
D Liu
Keyword(s):  
Stress Condition ◽  
Numerical Solutions ◽  
Complex Function ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Sh Waves ◽  
Linear Algebraic Equations ◽  
Scattering Field ◽  
Moving Coordinate ◽  
Infinite Linear

This research intends to investigate the scattering field of SH-wave in a half-space containing a semicylindrical hill and a subsurface horizontal hole. A mathematical model is established in a two-dimensional plane on the basis of the characteristics of SH-waves, the ‘division-conjunction’ concept, the complex function, and moving-coordinate methods. The whole domain considered is divided into two subdomains, and the wave expressions are assumed in each subdomain. In the cylindrical subdomain, the wave function is constructed with the satisfaction of the zero-stress condition on the hill's surface automatically. In the other subdomain, the solution of the scattering waves is postulated under the stress-free condition on the horizontal surface. The analytical solutions of themodel established are obtained through a series of infinite linear algebraic equations, under the conditions that both the stress and displacement across the conjunction interface of the two subdomains are continuous. The numerical solutions are developed by truncating the infinite linear algebraic equations. The numerical simulations are performed for quantifying the displacements of the horizontal and semicylindrical hill surfaces subjected to incident SH waves, and the numerical results are verified with a comparison to the existing results of a case without subsurface hole.

The Effect on Scattering of SH-Wave in a Layered Half-Space with the Subsurface Circular Cavities

2011 ◽  
Vol 194-196 ◽  
pp. 1908-1911
Author(s):  
Dong Ni Chen ◽  
Hui Qi ◽  
Yong Shi
Keyword(s):  
Half Space ◽  
Elastic Layer ◽  
Complex Function ◽  
Expansion Method ◽  
Elastic Half Space ◽  
Wave Functions ◽  
Large Radius ◽  
Algebraic Equations ◽  
Sh Wave ◽  
Linear Algebraic Equations

The scattering of SH-wave caused by the subsurface circular cavities in an elastic half-space covered with an elastic layer was discussed, which was based on the complex function method and wave functions expansion method. The solution of scattering of SH-wave was given by using circular boundary of large radius to approximate straight boundary of surface elastic layer. According to boundary conditions, we needed to solve the infinite linear algebraic equations with unknown coefficients in wave functions. Finally, the dynamic stress concentration factors around circular cavities were discussed in numerical examples.

Dynamics of a Mode III Crack Impacted by Elastic Wave in Half Space with a Removable Rigid Cylindrical Inclusion

2006 ◽  
Vol 324-325 ◽  
pp. 679-682 ◽  
Author(s):  
Zai Lin Yang ◽  
Dian Kui Liu ◽  
Xiao Lang Lv
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Complex Function ◽  
Elastic Half Space ◽  
Cylindrical Inclusion ◽  
Sh Wave ◽  
Mode Iii ◽  
Scattering Wave ◽  
Moving Coordinate

Scattering of SH wave by a crack is studied in elastic half space with a removable rigid cylindrical inclusion by Green’s function, complex function and moving coordinate method. In half space, firstly the scattering wave function of removable rigid cylindrical inclusion is constructed; next a suitable Green’s function is solved for present problem, then using crack-division to make a crack. Thus the solution of problem can be obtained. Numerical examples are provided and discussed.

Our Bodies, Whose Property?

2013 ◽  
Author(s):  
Anne Phillips
Keyword(s):  
Labor Markets ◽  
Personal Autonomy ◽  
The Body ◽  
Body Parts ◽  
Complex Issue ◽  
Human Organs ◽  
Property Owners ◽  
The Common ◽  
The Difference ◽  
The Right

No one wants to be treated like an object, regarded as an item of property, or put up for sale. Yet many people frame personal autonomy in terms of self-ownership, representing themselves as property owners with the right to do as they wish with their bodies. Others do not use the language of property, but are similarly insistent on the rights of free individuals to decide for themselves whether to engage in commercial transactions for sex, reproduction, or organ sales. Drawing on analyses of rape, surrogacy, and markets in human organs, this book challenges notions of freedom based on ownership of our bodies and argues against the normalization of markets in bodily services and parts. The book explores the risks associated with metaphors of property and the reasons why the commodification of the body remains problematic. The book asks what is wrong with thinking of oneself as the owner of one's body? What is wrong with making our bodies available for rent or sale? What, if anything, is the difference between markets in sex, reproduction, or human body parts, and the other markets we commonly applaud? The book contends that body markets occupy the outer edges of a continuum that is, in some way, a feature of all labor markets. But it also emphasizes that we all have bodies, and considers the implications of this otherwise banal fact for equality. Bodies remind us of shared vulnerability, alerting us to the common experience of living as embodied beings in the same world. Examining the complex issue of body exceptionalism, the book demonstrates that treating the body as property makes human equality harder to comprehend.

Ameloblastic Fibroma Associated With Impacted 3rd Molar: A Case Report

2017 ◽  
Vol 1 (7) ◽  
pp. 18-21
Author(s):  
K Indira Priyadarshini ◽  
Karthik Raghupathy ◽  
K V Lokesh ◽  
B Venu Naidu
Keyword(s):  
Relative Frequency ◽  
Posterior Region ◽  
Radiographic Examination ◽  
Dental Eruption ◽  
Ameloblastic Fibroma ◽  
Odontogenic Origin ◽  
The Common ◽  
The Times ◽  
The Right ◽  
Slow Growing

Ameloblastic fibroma is an uncommon mixed neoplasm of odontogenic origin with a relative frequency between 1.5 – 4.5%. It can occur either in the mandible or maxilla, but predominantly seen in the posterior region of the mandible. It occurs in the first two decades of life. Most of the times it is associated with tooth enclosure, causing a delay in eruption or altering the dental eruption sequence. The common clinical manifestation is a slow growing painless swelling and is detected during routine radiographic examination. There is controversy in the mode of treatment, whether conservative or aggressive. Here we reported a 38 year old male patient referred for evaluation of painless swelling on the right posterior region of the mandible associated with clinically missing 3rd molar. The lesion was completely enucleated under general anesthesia along with the extraction of impacted molar.

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