Interaction of a P-Wave With a Laterally Stiffened Slot

1983 ◽  
Vol 50 (1) ◽  
pp. 63-66 ◽  
Author(s):  
R. L. Ryan ◽  
S. Mall
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Longitudinal Wave ◽  
Singular Integral ◽  
Scattered Field ◽  
Discrete Element ◽  
P Wave

The interaction of a longitudinal wave with a narrow cavity or slot that contains an inclusion is considered. A singular integral equation is derived for the scattered field and the integral equation is solved numerically by a Gauss-Chebyshev technique. The stress intensity at the ends of the slot is obtained as a function of frequency and inclusion stiffness for both a continuous and discrete element inclusion.

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.

scholarly journals Torsional Impact Response of a Penny-Shaped Interface Crack in Bonded Materials With a Graded Material Interlayer

2002 ◽  
Vol 69 (3) ◽  
pp. 303-308 ◽  
Author(s):  
C. Li ◽  
Z. Duan ◽  
Z. Zou
Keyword(s):  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Interface Crack ◽  
Singular Integral ◽  
Dynamic Stress ◽  
Mixed Boundary ◽  
Dynamic Stress Intensity Factor ◽  
Cauchy Kernel ◽  
Dynamic Stress Intensity Factors

In this paper, the dynamic response of a penny-shaped interface crack in bonded dissimilar homogeneous half-spaces is studied. It is assumed that the two materials are bonded together with such a inhomogeneous interlayer that makes the elastic modulus in the direction perpendicular to the crack surface is continuous throughout the space. The crack surfaces are assumed to be subjected to torsional impact loading. Laplace and Hankel integral transforms are applied combining with a dislocation density function to reduce the mixed boundary value problem into a singular integral equation with a generalized Cauchy kernel in Laplace domain. By solving the singular integral equation numerically and using a numerical Laplace inversion technique, the dynamic stress intensity factors are obtained. The influences of material properties and interlayer thickness on the dynamic stress intensity factor are investigated.

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.

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.

scholarly journals The Problem of a Finite Strip Compressed Between Two Rough Rigid Stamps

1975 ◽  
Vol 42 (1) ◽  
pp. 81-87 ◽  
Author(s):  
G. D. Gupta
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Stress Intensity ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
Material Properties ◽  
Stress Singularities ◽  
Finite Strip ◽  
Strip Geometry ◽  
Elastostatic Problem

A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress-intensity factor is presented graphically.

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