scholarly journals Numerical solution of an integral equation arising in the problem of cruciform crack using Daubechies scale function

2019 ◽  
Vol 14 (1) ◽  
pp. 21-27
Author(s):  
Jyotirmoy Mouley ◽  
M. M. Panja ◽  
B. N. Mandal
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Numerical Solution ◽  
Present Method ◽  
Numerical Results ◽  
Scale Function ◽  
Forcing Term ◽  
Classical Integral

Abstract This paper is concerned with obtaining approximate numerical solution of a classical integral equation of some special type arising in the problem of cruciform crack. This integral equation has been solved earlier by various methods in the literature. Here, approximation in terms of Daubechies scale function is employed. The numerical results for stress intensity factor obtained by this method for a specific forcing term are compared to those obtained by various methods available in the literature, and the present method appears to be quite accurate.

Edge Crack in an Elastic Strip on a Liquid Foundation

1989 ◽  
Vol 33 (03) ◽  
pp. 214-220
Author(s):  
Paul C. Xirouchakis ◽  
George N. Makrakis
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Fourier Transform ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Edge Crack ◽  
Applied Pressure ◽  
Theory Of Elasticity ◽  
Elastic Strip ◽  
Pressure Loading

The behavior of a long elastic strip with an edge crack resting on a liquid foundation is investigated. The faces of the crack are opened by an applied pressure loading. The deformation of the strip is considered within the framework of the linear theory of elasticity assuming plane-stress conditions. Fourier transform techniques are employed to obtain integral expressions for the stresses and displacements. The boundary-value problem is reduced to the solution of a Fredholm integral equation of the second kind. For the particular case of linear pressure loading, the stress-intensity factor is calculated and its dependence is shown on the depth of the crack relative to the thickness of the strip. Application of the present results to the problem of flexure of floating ice strips is discussed.

The Homogenized Transformation Method for the Calculation of Stress Intensity Factor in Cracked FGM Structure

2020 ◽  
pp. 2050014
Author(s):  
Rong LI ◽  
Meng Yang ◽  
Bin Liang
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Functionally Graded Material ◽  
Calculation Method ◽  
Present Method ◽  
Transformation Method ◽  
Functionally Graded ◽  
Empirical Formulas ◽  
Graded Material

A convenient calculation method is proposed for the stress intensity factor (SIF) in cracked functionally graded material (FGM) structures. In this method, the complex computational problem for SIFs in cracked FGM plate and cylinder can be simplified as the calculation problem of empirical formulas of SIFs in cracked homogenous plate and cylinder with same loading conditions and the calculation problem of related transition parameters. The results show that the SIF in cracked FGM structure can be obtained accurately without using matrix and integral. The validity and usefulness of the present method are proved by comparing with the results of the conventional method.

Macrocrack-Microdefect Interaction

1986 ◽  
Vol 53 (3) ◽  
pp. 505-510 ◽  
Author(s):  
A. A. Rubinstein
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Numerical Technique ◽  
Finite Size ◽  
Numerical Procedure ◽  
Complex Stress ◽  
Elastic Interactions ◽  
Crack Tip Geometry

Elastic interactions (in terms of the stress intensity factor variation) of the macrocrack (represented as semi-infinite crack) with microdefects such as finite size, arbitrarily positioned crack, circular hole or inclusion are considered. A solution for the problem of the interaction with dilational inclusion is also given. The influence of the crack tip geometry on the surrounding stress field is studied by analyzing the case of crack-hole coalescence. Problems are considered in terms of complex stress potentials for linear elasticity and formulated as a singular integral equation on the semi-infinite interval. A stable numerical technique is developed for the solution of such equations. In a particular case, in order to evaluate the accuracy of the numerical procedure, results obtained through the numerical procedure are compared with the available analytical solution and found to be in excellent agreement.

Collinear Crack Problem in Antiplane Elasticity for a Strip of Functionally Graded Materials

2004 ◽  
Vol 20 (3) ◽  
pp. 167-175 ◽  
Author(s):  
Y. Z. Chen
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Crack Problem ◽  
Functionally Graded ◽  
Elementary Solution ◽  
Collinear Crack ◽  
Graded Materials ◽  
Antiplane Elasticity

AbstractIn this paper, elastic analysis for a collinear crack problem in antiplane elasticity of functionally graded materials (FGMs) is present. An elementary solution is obtained, which represents the traction applied at a point “x” on the real axis caused by a point dislocation placed at a point “t” on the same real axis. The Fourier transform method is used to derive the elementary solution. After using the obtained elementary solution, the singular integral equation is formulated for the collinear crack problem. Furthermore, from the solution of the singular integral equation the stress intensity factor at the crack tip can be evaluated immediately. In the solution of stress intensity factor, influence caused by the materials property “α” is addressed. Finally, numerical solutions are presented.

A Crack Terminating at a Slipping Interface Between Two Materials

1991 ◽  
Vol 58 (4) ◽  
pp. 960-963 ◽  
Author(s):  
V. M. Gharpuray ◽  
J. Dundurs ◽  
L. M. Keer
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Singular Integral Equation ◽  
Numerical Method ◽  
Singular Integral ◽  
Edge Crack ◽  
Asymptotic Nature

The paper investigates an edge crack that terminates at a slipping interface with a different material. The formulation is reduced to a singular integral equation. The integral equation is solved and the stress intensity factor extracted using a numerical method. Moreover, the asymptotic nature of the stresses at the open tip of the crack is studied.

scholarly journals A closed form for the Stress Intensity Factor of a small embedded square-like flaw

2020 ◽  
Vol 14 (54) ◽  
pp. 182-191
Author(s):  
Paolo Livieri ◽  
Fausto Segala
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Closed Form ◽  
Numerical Results ◽  
Explicit Equation ◽  
Minimum Value ◽  
Axes Of Symmetry

In the present work, the stress intensity factor (SIF) of a small embedded square-like flaw is calculated by means of a procedure based on the Oore-Burns integral. An explicit equation is given to evaluate the SIF along the two axes of symmetry that correspond to the points where the SIF takes its maximum and minimum value on the contour crack. The SIF is calculated in accordance with FE numerical results.

Interaction Between Interfacial Cavity/Crack and Internal Crack—Part II: Simulation

2003 ◽  
Vol 72 (3) ◽  
pp. 394-399 ◽  
Author(s):  
P. B. N. Prasad ◽  
Norio Hasebe ◽  
X. F. Wang
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Singular Integral Equation ◽  
Internal Crack ◽  
Uniform Loading ◽  
Distributed Dislocation ◽  
Point Dislocation ◽  
Dislocation Technique

This paper discusses the interaction of an interfacial cavity/crack with an internal crack in a bimaterial plane under uniform loading at infinity. The point dislocation solution is used to simulate internal crack by using the distributed dislocation technique. The resulting singular integral equation is solved numerically and the stress intensity factor variations are plotted for some cases of internal crack interacting with interfacial cavity/crack.

Accurate Determination of Stress Intensity Factor for Interface Crack by Finite Element Method

2007 ◽  
Vol 353-358 ◽  
pp. 3124-3127 ◽  
Author(s):  
Kazuhiro Oda ◽  
Naoaki Noda ◽  
Satya N. Atluri
Keyword(s):  
Finite Element Method ◽  
Stress Intensity Factor ◽  
Finite Element ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Interface Crack ◽  
Present Method ◽  
Crack Problem ◽  
Simple Method ◽  
Element Method

This paper presents the simple method to determine the complex stress intensity factor of interface crack problem by the finite element method. The proportional method is extended to the interface crack problem. In the present method, the stress values at the crack tip calculated by FEM are used and the stress intensity factors of interface crack are evaluated from the ratio of stress values between a given and a reference problems. A single interface crack in an infinite bi-material plate subjected to tension and shear is selected as the reference problem in this study. The accuracy of the present analysis is discussed through the results obtained by other methods. As the result, it is confirmed that the present method is useful for analyzing the interface crack problem.

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