Green’s Function of a Bimaterial Problem With a Cavity on the Interface—Part I: Theory

2003 ◽  
Vol 72 (3) ◽  
pp. 389-393 ◽  
Author(s):  
P. B. N. Prasad ◽  
Norio Hasebe ◽  
X. F. Wang ◽  
Y. Shirai
Keyword(s):  
Green’S Function ◽  
Half Plane ◽  
Green's Function ◽  
Elliptical Hole ◽  
Mapping Function ◽  
Complex Variables ◽  
Bimaterial Interface ◽  
Rational Mapping ◽  
Upper Half Plane ◽  
Point Dislocation

The problem of a point dislocation interacting with an elliptical hole located on a bimaterial interface is examined. Analytical solution is obtained by employing the techniques of complex variables and conformal mapping. A rational mapping function is used to map a half-plane with a semielliptical notch onto a unit circle. In the first part of this paper, complex potentials for the bimaterial system with an elliptical hole on the interface is derived when a point dislocation is present in the upper half-plane without loss of generality. The solution derived can be used as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

A Point Dislocation Interacting with an Elliptical Hole Located at a Bi-Material Interface

2012 ◽  
Vol 151 ◽  
pp. 75-79 ◽  
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe ◽  
P.B.N. Prasad
Keyword(s):  
Conformal Mapping ◽  
Unit Circle ◽  
Half Plane ◽  
Elliptical Hole ◽  
Mapping Function ◽  
Complex Stress ◽  
Complex Variables ◽  
Material Interface ◽  
Rational Mapping ◽  
Point Dislocation

The problem of a point dislocation interacting with an elliptical hole at the interface of two bonded half-planes is studied. Complex stress potentials are obtained by applying the methods of complex variables and conformal mapping. A rational mapping function that maps a half plane with a semi-elliptical notch onto a unit circle is used for mapping the bonded half-planes. The solution derived can serve as Green’s function to study internal cracks interacting with an elliptical interfacial cavity.

A Green’s Function Formulation of Anticracks and Their Interaction With Load-Induced Singularities

1989 ◽  
Vol 56 (3) ◽  
pp. 550-555 ◽  
Author(s):  
John Dundurs ◽  
Xanthippi Markenscoff
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Edge Dislocation ◽  
Weight Functions ◽  
Bimaterial Interface ◽  
Elastic Fields ◽  
Function Formulation ◽  
Concentrated Forces ◽  
Concentrated Couple ◽  
Working Out

This paper provides a Green’s function formulation of anticracks (rigid lamellar inclusions of negligible thickness that are bonded to the surrounding elastic material). Apart from systematizing several previously known solutions, the article gives the pertinent fields for concentrated forces, dislocations, and a concentrated couple applied on the line of the anticrack. There is a reason for working out these results: In contrast to concentrated forces, a concentrated couple approaching the tip of an anticrack makes the elastic fields explode. Finite limits can be achieved, however, by appropriately diminishing the magnitude of the couple, which then leads to fields that are intimately connected with the weight functions for the anticrack. An edge dislocation going to the tip of an anticrack puts a net force on the lamellar inclusion, which is shown to be related to a previously known feature of dislocations near a bimaterial interface.

Stress Concentration Factors at an Elliptical Hole on the Interface Between Bonded Dissimilar Half-Planes Under Bending Moment

1996 ◽  
Vol 63 (1) ◽  
pp. 7-14 ◽  
Author(s):  
Mohamed Salama ◽  
Norio Hasebe
Keyword(s):  
Stress Concentration ◽  
Elliptical Hole ◽  
Bending Moment ◽  
Mapping Function ◽  
Complex Stress ◽  
Function Technique ◽  
Rational Mapping ◽  
Stress Functions ◽  
Stress Concentration Factors ◽  
Thin Plate Bending

The problem of thin plate bending of two bonded half-planes with an elliptical hole on the interface and interface cracks on its both sides is presented. A uniformly distributed bending moment applied at the remote ends of the interface is considered. The complex stress functions approach together with the rational mapping function technique are used in the analysis. The solution is obtained in closed form. Distributions of bending and torsional moments, the stress concentration factor as well as the stress intensity factor, are given for all possible dimensions of the elliptical hole, various material constants, and rigidity ratios.

Application of the Wiener‐Hopf technique to the calculation of the diffraction of a cylindrical wave by a soft half‐plane embedded in a fluid half‐space

Geophysics ◽  
1999 ◽  
Vol 64 (6) ◽  
pp. 1847-1851 ◽  
Author(s):  
Tik Hing Tan
Keyword(s):  
Green’S Function ◽  
Half Space ◽  
Half Plane ◽  
Green's Function ◽  
Companion Paper ◽  
Cylindrical Wave ◽  
Auxiliary Field ◽  
Starting Point ◽  
Convolution Model ◽  
Shallow Seas

Wavelets currently are estimated directly from the data by statistical means or, for marine data, by direct measurement with deep hydrophones. The first method, based on statistical arguments, uses the convolution model of seismic traces as the starting point. In addition, it also assumes whiteness of the earth’s reflectivity series and the minimum‐phase character of the wavelet. The second method does not work very well for shallow seas because of interference with reflections by the seafloor. In a companion paper, an algorithm for the estimation of wavelets of marine sources has been presented. The algorithm starts from the reduced wave equation to describe the measured field and an auxiliary field. Physically, the auxiliary field, also known as the Green’s function, is the wavefield configuration of a line source and a soft half‐plane in a fluid half‐space. The calculation of this Green’s function is the subject of this paper.

Circular Rigid Punch With One Smooth and Another Sharp Ends on a Half-Plane With Edge Crack

1997 ◽  
Vol 64 (1) ◽  
pp. 73-79 ◽  
Author(s):  
Norio Hasebe ◽  
Jun Qian
Keyword(s):  
Half Plane ◽  
Hilbert Problem ◽  
Contact Region ◽  
Mapping Function ◽  
Contact Length ◽  
Stress Distributions ◽  
Sharp Corner ◽  
Rigid Punch ◽  
Rational Mapping ◽  
Frictional Coefficients

A circular rigid punch with friction is assumed to contact with a half-plane with one end sliding on the half-plane and another end with a sharp corner. The contact length is determined by satisfying the finite stress condition at the sliding end of the punch. The crack is initiated near the end with a sharp corner where infinite stresses exist. Coulomb’s frictional force is supposed to act on the contact region. The cracked half-plane is mapped into a unit circle by using a rational mapping function, and the problem is transformed into a standard Riemann-Hilbert problem, which is solved by introducing a Plemelj function. The contact length, the stress intensity factors of the crack, and the resultant moment about the origin of the coordinates on the contact region are calculated for different frictional coefficients, Poisson’s ratios of the half-plane, crack lengths, and distances from the crack to the punch, respectively. The stress distributions on the contact region are also shown.

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