On the numerical solution of Cauchy type singular integral equations and the determination of stress intensity factors in case of complex singularities

1977 ◽  
Vol 28 (6) ◽  
pp. 1085-1098 ◽  
Author(s):  
P. S. Theocaris ◽  
N. I. Ioakimidis
Keyword(s):  
Stress Intensity ◽  
Numerical Solution ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Singular Integral Equations ◽  
Cauchy Type ◽  
Intensity Factors ◽  
Complex Singularities

Transient Stress Intensity Factors of an Interfacial Crack Between Two Dissimilar Anisotropic Half-Spaces, Part 2: Fully Anisotropic Materials

1984 ◽  
Vol 51 (4) ◽  
pp. 780-786 ◽  
Author(s):  
A.-Y. Kuo
Keyword(s):  
Stress Intensity ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Jacobi Polynomials ◽  
Mathematical Problem ◽  
Stress Singularity ◽  
Interfacial Crack ◽  
Singular Integral Equations ◽  
Intensity Factors

Dynamic stress intensity factors for an interfacial crack between two dissimilar elastic, fully anisotropic media are studied. The mathematical problem is reduced to three coupled singular integral equations. Using Jacobi polynomials, solutions to the singular integral equations are obtained numerically. The orders of stress singularity and stress intensity factors of an interfacial crack in a (θ(1)/θ(2)) composite solid agree well with the finite element solutions.

Stress Analysis for a Double Lap Joint

1975 ◽  
Vol 42 (2) ◽  
pp. 353-357 ◽  
Author(s):  
L. M. Keer ◽  
K. Chantaramungkorn
Keyword(s):  
Stress Intensity ◽  
Stress Analysis ◽  
Integral Equations ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Integral Transform ◽  
Singular Integral Equations ◽  
Geometrical Parameters ◽  
Lap Joint ◽  
Intensity Factors

The problem of a double lap joint is analyzed and solved by using integral transform techniques. Singular integral equations are deduced from integral transform solutions using boundary and continuity conditions appropriate to the problem. Numerical results are obtained for the case of identical materials for the cover and central layers. Stress-intensity factors are calculated and presented in the form of a table and contact stresses are shown in the form of curves for various values of geometrical parameters.

Boundary-Singular Integral Equation Method to Calculate the Bending Center and Stress Intensity Factors of Cracked Cylinder under Saint-Venant Bending

2007 ◽  
Vol 348-349 ◽  
pp. 197-200
Author(s):  
Xin Yan Tang
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Integral Equations ◽  
Cross Section ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Singular Integral Equations ◽  
Intensity Factors ◽  
Cracked Cylinder

Using single crack solution and regular plane harmonic function, the Saint-Venant bending problem of a cracked cylinder with general cross section is formulated in terms of two sets of boundary-singular integral equations, which can be solved by using the methods for combination of boundary element and singular integral equation methods. The concept of bending center used in strength of materials is extended to this bending problem. Theoretical formulae to calculate the bending center and stress intensity factors in cracked cylinder are derived and expressed by the solutions of the integral equations. Based on these results, some numerical examples are given for different configurations of the cylinder cross section as well as the crack parameters.

scholarly journals Biaxial Loading of a Plate Containing a Hole and Two Co-Axial Through Cracks

2018 ◽  
Vol 12 (3) ◽  
pp. 237-242
Author(s):  
Heorgij Sulym ◽  
Viktor Opanasovych ◽  
Mykola Slobodian ◽  
Yevhen Yarema
Keyword(s):  
Stress Intensity ◽  
Closed Form ◽  
Integral Equations ◽  
Singular Integral ◽  
Linear Elasticity ◽  
Stress Intensity Factors ◽  
Biaxial Loading ◽  
Isotropic Plate ◽  
Singular Integral Equations ◽  
Intensity Factors

Abstract The paper presents the solution linear elasticity problem for an isotropic plate weakened by a hole and two co-axial cracks. The plate is exerted by uniform traction at infinity. The corresponding 2D problem is solved by the method of Kolosova-Muskhelishvili complex potentials. The method implies reduction of the problem to simultaneous singular integral equations (SIE) for the functions defined the region of the cracks and hole. For particular case the solution the SIE is obtained analytically in a closed form. A thorough analysis of the stress intensity factors (SIF) is carried out for various cases of the hole shape: penny-shaped, elliptical and rectangular.

Analysis of Branched Interface Cracks Between Dissimilar Anisotropic Media

1989 ◽  
Vol 56 (4) ◽  
pp. 844-849 ◽  
Author(s):  
G. R. Miller ◽  
W. L. Stock
Keyword(s):  
Stress Intensity ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Crack Problem ◽  
Singular Integral Equations ◽  
Crack Branching ◽  
Intensity Factors ◽  
Function Solution ◽  
Special Cases ◽  
Branch Crack

A solution is presented for the problem of a crack branching off the interface between two dissimilar anisotropic materials. A Green’s function solution is developed using the complex potentials of Lekhnitskii (1981) allowing the branched crack problem to be expressed in terms of coupled singular integral equations. Numerical results for the stress intensity factors at the branch crack tip are presented for some special cases, including the no-interface case which is compared to the isotropic no-interface results of Lo (1978).

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