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.

Interface Stress Analysis of the Bending Cylinder Containing Inclusion

2011 ◽  
Vol 201-203 ◽  
pp. 951-955
Author(s):  
Xin Yan Tang
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Stress Analysis ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Integral Equation Method ◽  
Equation Method ◽  
Intensity Factors ◽  
Engineering Structures

Using the elasticity and the singular integral equation method, an analysis of a bending cylinder containing inclusions is carried out. The disturbing interface stresses on the inclusion sides and the stress intensity factors at the inclusion tips are obtained. The results given in this paper are useful for the strength design of the engineering structures or mechanical components containing inclusions.

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.

Transient Stress Intensity Factors of an Interfacial Crack Between Two Dissimilar Anisotropic Half-Spaces, Part 1: Orthotropic Materials

1984 ◽  
Vol 51 (1) ◽  
pp. 71-76 ◽  
Author(s):  
A.-Y. Kuo
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Jacobi Polynomials ◽  
Interfacial Crack ◽  
Orthotropic Materials ◽  
Intensity Factors ◽  
Orthotropic Solids

Transient response of an interfacial crack between two dissimilar elastic, orthotropic solids is investigated. The interfacial crack is excited by tractions suddenly applied on the crack surfaces. Governing equations, boundary conditions, and continuity conditions along the interface are reduced to a singular integral equation. Solution of the singular integral equation is obtained by the use of Jacobi polynomials. Expressions for stress intensity factors at the crack tip are given. As a sample problem, an interfacial crack in a 0 deg/90 deg fiber-reinforced composite solid excited by a suddenly applied uniform pressure on the crack surfaces is studied.

Transient Response of a Finite Bimaterial Plate Containing a Crack Perpendicular to and Terminating at the Interface

2005 ◽  
Vol 73 (4) ◽  
pp. 544-554 ◽  
Author(s):  
Xian-Fang Li ◽  
L. Roy Xu
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Transient Response ◽  
Singular Integral ◽  
Stress Intensity Factors ◽  
Dynamic Stress ◽  
Cauchy Kernel ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors

The transient response of a finite bimaterial plate with a crack perpendicular to and terminating at the interface is analyzed for two types of boundaries (free-free and clamped-clamped). The crack surface is loaded by arbitrary time-dependent antiplane shear impact. The mixed initial-boundary value problem is reduced to a singular integral equation of a generalized Cauchy kernel for the crack tearing displacement density or screw dislocation density. The Gauss-Jacobi quadrature technique is employed to numerically solve the singular integral equation, and then the dynamic stress intensity factors are determined by implementing a numerical inversion of the Laplace transform. As an example, numerical calculations are carried out for a cracked bimaterial plate composed of aluminum (material I) and epoxy or steel (material II). The effects of material properties, geometry, and boundary types on the variations of dynamic stress intensity factors are discussed in detail. Results indicate that an overshoot of the normalized stress intensity factor of the crack tip at the interface decreases for a cracked bimaterial plate, and the occurrence of which is delayed for a cracked aluminum/epoxy plate compared to a pure aluminum plate with the same crack.

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