Dynamic Singular Stresses for a Griffith Crack in a Soft Ferromagnetic Elastic Solid Subjected to a Uniform Magnetic Field

1983 ◽  
Vol 50 (1) ◽  
pp. 50-56 ◽  
Author(s):  
Y. Shindo
Keyword(s):  
Magnetic Field ◽  
Integral Equations ◽  
Fourier Transforms ◽  
Dynamic Stress Intensity Factor ◽  
Elastic Solid ◽  
Griffith Crack ◽  
Dual Integral Equations ◽  
Singular Stress ◽  
Magnetostatic Field ◽  
Soft Ferromagnetic

The problem of the diffraction of normally incident longitudinal waves on a Griffith crack located in an infinite soft ferromagnetic elastic solid is considered. It is assumed that the solid is a homogeneous and isotropic one and is permeated by a uniform magnetostatic field normal to the crack surfaces. Fourier transforms are used to reduce the problem to two simultaneous dual integral equations. The solution to the integral equations is expressed in terms of a Fredholm integral equation of the second kind having the kernel that is a finite integral. The dynamic singular stress field near the crack tip is obtained and the influence of the magnetic field on the dynamic stress intensity factor is shown graphically in detail. Approximate analytical expressions valid at low frequencies are also obtained and the range of validity of these expressions is examined.

Flexural Wave Scattering at a Through Crack in a Conducting Plate Under a Uniform Magnetic Field

1997 ◽  
Vol 64 (4) ◽  
pp. 828-834 ◽  
Author(s):  
Y. Shindo ◽  
I. Ohnishi ◽  
S. Tohyama
Keyword(s):  
Magnetic Field ◽  
Integral Equations ◽  
Uniform Magnetic Field ◽  
Fourier Transforms ◽  
Flexural Wave ◽  
Crack Plane ◽  
Dual Integral Equations ◽  
Conducting Plate ◽  
Time Harmonic ◽  
The Magnetic Field

Following a classical plate bending theory of magneto-elasticity, we consider the scattering of time-harmonic flexural waves by a through crack in a conducting plate under a uniform magnetic field normal to the crack surface. An incident wave giving rise to moments symmetric about the crack plane is applied. It is assumed that the plate has the electric and magnetic permeabilities of the free space. By the use of Fourier transforms we reduce the problem to solving a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic moment intensity factor versus frequency is computed and the influence of the magnetic field on the normalized values is displayed graphically. It is found that the existence of the magnetic field produces higher singular moments near the crack tip.

Torsional Impact Response of a Thick-Walled Cylinder With a Circumferential Edge Crack

1990 ◽  
Vol 112 (4) ◽  
pp. 367-373 ◽  
Author(s):  
Y. Shindo ◽  
W. Li
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Edge Crack ◽  
Dynamic Stress Intensity Factor ◽  
Impact Response ◽  
Cauchy Kernel ◽  
Dual Integral Equations ◽  
Singular Stress ◽  
Singular Stress Field ◽  
Walled Cylinder

This paper considers the torsional impact response of a long thick-walled cylinder containing an internal or external circumferential edge crack. Laplace and Hankel transforms are used to reduce the elastodynamic problem to a pair of dual integral equations. The dual integral equations are solved by using the standard transform technique, and the result is expressed in terms of an integral equation which has a generalized Cauchy kernel as the dominant part. The kernel of the integral equation is improved in order that the calculation may be made easy. A numerical Laplace inversion technique is used to recover the time dependence of the solution. The dynamic singular stress field is determined, and the numerical results on the dynamic stress intensity factor are obtained to show the influence of inertia, geometry, and their interactions.

Impact Response of a Single Edge Crack in an Orthotropic Strip

1992 ◽  
Vol 59 (2S) ◽  
pp. S152-S157 ◽  
Author(s):  
Yasuhide Shindo ◽  
Hiroaki Higaki ◽  
Hideaki Nozaki
Keyword(s):  
Integral Equations ◽  
Edge Crack ◽  
Fourier Transforms ◽  
Dynamic Stress Intensity Factor ◽  
Single Edge ◽  
Dual Integral Equations ◽  
Orthotropic Strip ◽  
Transient Problem ◽  
Reinforced Composite ◽  
The Laplace Transform

The elastodynamic response of a single edge crack in an orthotropic strip under normal impact is considered in this study. The edge crack is oriented in a direction normal to the edge of the strip. Laplace and Fourier transforms are used to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution to the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion routine is used to recover the time dependence of the solution. Numerical values on the dynamic stress intensity factor for several fiber-reinforced composite materials are obtained, and the results are graphed to display the influence of the material orthotropy.

Dynamic Singular Moments in a Perfectly Conducting Mindlin Plate With a Through Crack Under a Magnetic Field

1998 ◽  
Vol 67 (3) ◽  
pp. 503-510 ◽  
Author(s):  
Y. Shindo ◽  
I. Ohnishi ◽  
S. Toyama
Keyword(s):  
Magnetic Field ◽  
Integral Equations ◽  
Fourier Transforms ◽  
Mindlin Plate ◽  
Crack Plane ◽  
Flexural Waves ◽  
Dual Integral Equations ◽  
Conducting Plate ◽  
Time Harmonic ◽  
The Magnetic Field

Following Mindlin’s theory of plate bending of magnetoelasticity, we consider the scattering of time-harmonic flexural waves by a through crack in a perfectly conducting plate under a uniform magnetic field normal to the crack surface. An incident wave giving rise to moments symmetric about the crack plane is applied. It is assumed that the plate has the electric and magnetic permeabilities of the free space. By the use of Fourier transforms we reduce the problem to solving a pair of dual integral equations. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic moment intensity factor versus frequency is computed and the influence of the magnetic field on the normalized values is displayed graphically. It is found that the existence of the magnetic field produces lower singular moments near the crack tip. [S0021-8936(00)02603-9]

Dual integral equations associated with Fourier transforms

1986 ◽  
Vol 38 (2) ◽  
pp. 165-171
Author(s):  
Nguyen Van Ngok ◽  
G. Ya. Popov
Keyword(s):  
Integral Equations ◽  
Fourier Transforms ◽  
Dual Integral Equations

The Linear Magnetoelastic Problem for a Soft Ferromagnetic Elastic Solid With a Finite Crack

1977 ◽  
Vol 44 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Y. Shindo
Keyword(s):  
Integral Transform ◽  
Elastic Solid ◽  
Elastic Solids ◽  
Infinite Body ◽  
Magnetostatic Field ◽  
Multidomain Structure ◽  
Soft Ferromagnetic ◽  
Finite Crack ◽  
Integral Transform Technique ◽  
Maxwell Stresses

Following a linear theory for the soft ferromagnetic elastic materials of multidomain structure, the distribution of magnetoelastic stresses and Maxwell stresses in an infinite body with a finite crack permeated by an uniform magnetostatic field normal to the crack surfaces is investigated. The soft ferromagnetic elastic solids with a finite crack are considered to be composed of materials with isotropic, cubic, or uniaxial symmetry. A solution for the infinite solid is obtained by the use of integral transform technique. The magnetoelastic stresses and the Maxwell stresses are expressed in closed forms.

DIFFRACTION BY A CONDUCTING HALF-PLANE IN AN ANISOTROPIC PLASMA

1964 ◽  
Vol 42 (8) ◽  
pp. 1455-1468 ◽  
Author(s):  
E. V. Jull
Keyword(s):  
Magnetic Field ◽  
Half Plane ◽  
Scattered Field ◽  
Plane Electromagnetic Wave ◽  
Plane Waves ◽  
Angular Spectrum ◽  
Anisotropic Plasma ◽  
Angle Of Incidence ◽  
Dual Integral Equations ◽  
Magnetostatic Field

The diffraction of a plane electromagnetic wave by a perfectly conducting half-plane in an anisotropic plasma is considered. The plasma is characterized by a permittivity tensor and the wave is assumed to propagate in a direction normal to the magnetostatic field and the diffracting edge, but its angle of incidence is otherwise arbitrary. Only the H-polarized wave of the incident field, which has a single magnetic field component parallel to the edge, is affected by the anisotropy and the analysis is restricted accordingly. Representing the scattered field as an angular spectrum of plane waves leads to dual integral equations from which an expression for the scattered field is obtained. The total field is then reduced to Fresnel integrals and its far-field behavior is investigated. Agreement with Seshadri and Rajagopal's result for a wave normally incident on the conductor, which was obtained by using the Wiener–Hopf technique, is found. The differences between isotropic and anisotropic solutions to this problem, which arise from the differing boundary conditions on the tangential magnetic field, are examined.

Anti-Plane Moving Crack in Functionally-Graded Material

2010 ◽  
Vol 29-32 ◽  
pp. 549-553
Author(s):  
Qi Liu
Keyword(s):  
Integral Equations ◽  
Functionally Graded Material ◽  
Integral Transform ◽  
Mixed Boundary ◽  
Dynamic Stress Intensity Factor ◽  
Functionally Graded ◽  
Dual Integral Equations ◽  
Moving Crack ◽  
Fourier Cosine ◽  
Graded Material

In this paper the anti-plane moving crack in a functionally-graded material is studied by the analytical method. First the governing equations for a functionally-graded material are obtained using a Fourier cosine integral transform. Then the dual integral equations for moving crack are established according to the mixed boundary value conditions. It is shown that the dual integral equations can be reduced to the Fredholm integral equation of the second kind. Numerical results shown in the present paper indicate that the non-homogeneity of material has an important influence on the dynamic stress intensity factor.

The Magnetoelastic Problem for a Soft Ferromatnetic Elastic Half-Plane with a Crack and a Constant Magneic Induction

2009 ◽  
Vol 25 (1) ◽  
pp. 95-102 ◽  
Author(s):  
C.-S. Yeh ◽  
C.-W. Ren
Keyword(s):  
Magnetic Field ◽  
Stress Intensity Factor ◽  
Free Surface ◽  
Stress Intensity ◽  
Stress State ◽  
Intensity Factor ◽  
Half Plane ◽  
Elastic Solid ◽  
Soft Ferromagnetic ◽  
The Magnetic Field

AbstractThe stress state of a magnetized elastic half-plane with a uniformly pressurized crack parallel to the free surface subjected to a uniform magnetic induction Bo is considered. The linear theory for a soft ferromagnetic elastic solid with muti-domain structure, which has been developed by Pao and Yeh [1] is adopted to investigate this problem. A numerical method is developed to determine the magnetoelastic stress intensity factor. The effect of the magnetic field and the boundary conditions on the magnetoelasitc stress intensity factor are shown graphically and numerically.

Intervallic Coiflets for Numerical Calculation of Dynamic Stress Intensity Factor

2012 ◽  
Vol 562-564 ◽  
pp. 668-671
Author(s):  
Jian Ping Xuan ◽  
Yuan Feng Liu ◽  
Tie Lin Shi
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Equations ◽  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
High Accuracy ◽  
Fredholm Integral Equations ◽  
Wavelet Expansion ◽  
Dual Integral Equations

There are lots of practical problems which are related to the solution of Fredholm integral equations of the second kind. The present work proposes intervallic Coiflets for solving the equations. Illustrative problem involving dynamic stress and electric fields of a cracked piezoelectric excited by anti-plane shear wave is addressed. Permeable boundary condition has been used to obtain a pair of dual integral equations of the symmetric and antisymmetric parts which can be reduced to the solutions of two Fredholm integral equations of the second kind. The dynamic stress intensity factor is expressed in terms of the right-end values of two unknown functions in Fredholm integral equations. The two unknown functions are solved by intervallic Coiflets which have less the endpoints error. And intervallic Coiflets have low calculation cost and high accuracy due to the wavelet expansion coefficients are exactly obtained without calculating the wavelet integrations. The calculation results agree well with the existing method, which show the high accuracy of the estimation and demonstrate validity and applicability of the method.

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