A New Mapped Weighted Essentially Non-oscillatory Method Using Rational Mapping Function

2015 ◽  
Vol 67 (2) ◽  
pp. 540-580 ◽  
Author(s):  
Rong Wang ◽  
Hui Feng ◽  
Cong Huang
Keyword(s):  
Mapping Function ◽  
Rational Mapping

Analysis of the Second Mixed Boundary Value Problem for a Thin Plate

1994 ◽  
Vol 61 (3) ◽  
pp. 555-559 ◽  
Author(s):  
Norio Hasebe ◽  
Takuji Nakamura ◽  
Yoshihiro Ito
Keyword(s):  
Boundary Value Problem ◽  
Thin Plate ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mapping Function ◽  
Complex Stress ◽  
Mixed Boundary Value Problem ◽  
Rational Mapping ◽  
Before And After ◽  
External Forces

The second mixed boundary value problem is solved by the classical theory of thin plate bending. The mixed boundary consists of a boundary (M) on which one respective component of external force and deflective angle are given, and on the remaining boundary the external forces are given. The boundary (M) is straight and the remaining boundary is arbitrary configuration. A closed solution is obtained. Complex stress functions and a rational mapping function are used. A half-plane with a crack is analyzed under a concentrated torsional moment. Stress distributions before and after the crack initiation, and stress intensity factors are obtained for from short to long cracks and for some Poisson’s ratio.

Analysis of a Heat Flux over a Region with a Crack near a Rigid Inclusion

2010 ◽  
Vol 163-167 ◽  
pp. 4482-4485
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Heat Flux ◽  
Rigid Inclusion ◽  
Mapping Function ◽  
Function Technique ◽  
Uniform Heat Flux ◽  
Principle Of Superposition ◽  
Rational Mapping ◽  
Displacement Boundary ◽  
Crack Tips ◽  
Crack Faces

The thermoelastic problem of a heat flux over a region with a crack near a rigid inclusion is studied. The inclusion is assumed fixed, which implies the translation and the rotation are restrained. The crack faces are assumed free of stress. Both of the inclusion and the crack are under thermal adiabatic condition. In the analysis, the original problem was reduced to a series of displacement boundary value problems by using the principle of superposition. The Green’s function method is used to obtain the solution of the prescribed problem in the forms of integral equations. The basic problems therefore become those for an edge dislocation, and for a heat source couple, as well as the problem of a plane containing the inclusion under a uniform heat flux. These problems are solved using the complex variable method along with the rational mapping function technique. The variations of the stress intensity factors at the crack tips with various crack lengths and heat flux angles are shown. The effects of the inclusion shape and size are also investigated.

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.

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.

scholarly journals Fundamental problems for infinite plate with a curvilinear hole having finite poles

2001 ◽  
Vol 7 (6) ◽  
pp. 485-501 ◽  
Author(s):  
M. A. Abdou ◽  
A. A. El-Bary
Keyword(s):  
Complex Variable ◽  
Arbitrary Shape ◽  
Infinite Plate ◽  
Mapping Function ◽  
Curvilinear Hole ◽  
Two Dimensional ◽  
Rational Mapping ◽  
Special Cases ◽  
Elasticity Problems ◽  
Different Shapes

In the present paper Muskhelishvili's complex variable method of solving two-dimensional elasticity problems has been applied to derive exact expressions for Gaursat's functions for the first and second fundamental problems of the infinite plate weakened by a hole having many poles and arbitrary shape which is conformally mapped on the domain outside a unit circle by means of general rational mapping function. Some applications are investigated. The interesting cases when the shape of the hole takes different shapes are included as special cases.

scholarly journals Stress Intensity of Debonding for A Rigid Inclusion Near An Angle Dislocation

2011 ◽  
Vol 5 (1) ◽  
pp. 190-194
Author(s):  
Xianfeng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Stress Intensity ◽  
Rigid Inclusion ◽  
Stress Function ◽  
Hilbert Problem ◽  
Infinite Plate ◽  
Mapping Function ◽  
Function Technique ◽  
Rational Mapping ◽  
Stress Functions ◽  
Point Dislocation

The study of debonding is of importance in providing a good understanding of the bonded interfaces of dissimilar materials. The problem of debonding of an arbitrarily shaped rigid inclusion in an infinite plate with a point dislocation of thin plate bending is investigated in this paper. Herein, the point dislocation is defined with respect to the difference of the plate deflection angle. An analytical solution is obtained by using the complex stress function approach and the rational mapping function technique. In the derivation, the fundamental solutions of the stress boundary value problem are taken as the principal parts of the corresponding stress functions, and through analytical continuation, the problem of obtaining the complementary stress function is reduced to a Riemann-Hilbert problem. Without loss of generality, numerical results are calculated for a square rigid inclusion with a debonding. It is noted that the stress components are singular at the dislocation point, and a stress concentration can be found in the vicinity of the inclusion corner. We also obtain the stress intensity of a debonding in terms of the stress functions. It can be found that when a debonding starts from a corner of the inclusion and extends to another corner progressively, the stress intensity of the debonding increases monotonously; once the debonding extends over the corner points, the value of the stress intensity of the debonding gradually decreases. The relationships between the stress intensity of the debonding and the direction and position of the dislocation are also presented in this paper.

Green Function of a Point Dislocation in Thin Plate with a Partially Debonded Inclusion

2010 ◽  
Vol 156-157 ◽  
pp. 1684-1687
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Thin Plate ◽  
Rigid Inclusion ◽  
Stress Function ◽  
Hilbert Problem ◽  
Infinite Plate ◽  
Dissimilar Materials ◽  
Mapping Function ◽  
Function Technique ◽  
Rational Mapping ◽  
Point Dislocation

The study of debonding is of importance in providing a good understanding of the bonded interfaces of dissimilar materials. The problem of debonding of an arbitrarily shaped rigid inclusion in an infinite plate with a point dislocation of thin plate bending is investigated in this paper. Herein, the point dislocation is defined with respect to the difference of the plate deflection angle. An analytical solution is obtained by using the complex stress function approach and the rational mapping function technique. In the derivation, the fundamental solutions of the stress boundary value problem are taken as the principal parts of the corresponding stress functions, and through analytical continuation, the problem of obtaining the complementary stress function is reduced to a Riemann-Hilbert problem. Without loss of generality, numerical results are calculated for a square rigid inclusion with a debonding. It is noted that the stress components are singular at the dislocation point, and a stress concentration can be found in the vicinity of the inclusion corner.

Bonded Bi-material Half-Planes With Semi-elliptical Notch Under Tension Along the Interface

1992 ◽  
Vol 59 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Norio Hasebe ◽  
Mikiya Okumura ◽  
Takuji Nakamura
Keyword(s):  
Stress Concentration ◽  
Elliptical Hole ◽  
Mapping Function ◽  
Approximate Expression ◽  
Complex Stress ◽  
Stress Distributions ◽  
Rational Mapping ◽  
Stress Functions ◽  
Elliptical Holes ◽  
Stress Concentration Factors

A problem of two bonded, dissimilar half-planes containing an elliptical hole on the interface is solved. The external load is uniform tension parallel to the interface. A rational mapping function and complex stress functions are used and an analytical solution is obtained. Stress distributions are shown. Stress concentration factors are also obtained for arbitrary lengths of debonding and for several material constants. In addition, an approximate expression of the stress concentration factor is given for elliptical holes and the accuracy is investigated.

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.

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