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.

Impact Response of a Cracked Orthotropic Medium

1983 ◽  
Vol 50 (3) ◽  
pp. 630-636 ◽  
Author(s):  
M. K. Kassir ◽  
K. K. Bandyopadhyay
Keyword(s):  
Stress Intensity ◽  
Dynamic Stress ◽  
Fourier Transforms ◽  
Dynamic Stress Intensity Factor ◽  
Orthotropic Materials ◽  
Dynamic Stress Intensity Factors ◽  
Transient Problem ◽  
Numerical Laplace Inversion ◽  
The Laplace Transform ◽  
Applied Stresses

A solution is given for the problem of an infinite orthotropic solid containing a central crack deformed by the action of suddenly applied stresses to its surfaces. Laplace and Fourier transforms are employed to reduce the transient problem to the solution of standard integral equations in the Laplace transform plane. A numerical Laplace inversion technique is used to compute the values of the dynamic stress-intensity factors, k1 (t) and k2 (t), for several orthotropic materials, and the results are compared to the corresponding elastostatic values to reveal the influence of material orthotropy on the magnitude and duration of the overshoot in the dynamic stress-intensity factor.

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.

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.

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

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.

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.

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.

scholarly journals Analytical solutions of some general classes of differential and integral equations by using the Laplace and Fourier transforms

Filomat ◽  
2020 ◽  
Vol 34 (9) ◽  
pp. 2869-2876
Author(s):  
H.M. Srivastava ◽  
Mohammad Masjed-Jamei ◽  
Rabia Aktaş
Keyword(s):  
Fourier Transform ◽  
Laplace Transform ◽  
Integral Equations ◽  
Analytical Solutions ◽  
General Class ◽  
Fourier Transforms ◽  
Laplace And Fourier Transforms ◽  
The Laplace Transform ◽  
The Fourier Transform ◽  
Differential And Integral Equations

This article deals with a general class of differential equations and two general classes of integral equations. By using the Laplace transform and the Fourier transform, analytical solutions are derived for each of these classes of differential and integral equations. Some illustrative examples and particular cases are also considered. The various analytical solutions presented in this article are potentially useful in solving the corresponding simpler differential and integral equations.

Scattering of Plane Waves by a Propagating Crack

1975 ◽  
Vol 42 (3) ◽  
pp. 705-711 ◽  
Author(s):  
E. P. Chen ◽  
G. C. Sih
Keyword(s):  
Integral Equations ◽  
Fourier Transforms ◽  
Mixed Boundary ◽  
Crack Opening ◽  
Crack Problem ◽  
Fredholm Integral Equations ◽  
Angle Of Incidence ◽  
Dual Integral Equations ◽  
Dynamic Stress Intensity Factors ◽  
Incident Wavelength

Scattering of plane harmonic waves by a running crack of finite length is investigated. Fourier transforms were used to formulate the mixed boundary-value problem which reduces to pairs of dual integral equations. These dual integral equations are further reduced to a pair of Fredholm integral equations of the second kind. The dynamic stress-intensity factors and crack opening displacements are obtained as functions of the incident wavelength, angle of incidence, Poisson’s ratio of the elastic solid and speed of crack propagation. Unlike the semi-infinite running crack problem, which does not have a static limit, the solution for the finite crack problem can be used to compare with its static counterpart, thus showing the effect of dynamic amplification.

Sign in / Sign up

Export Citation Format

Share Document