# The numerical solution of Cauchy singular integral equations with application to fracture

Russell D. Kurtz, Thomas Farris, C. T. Sun

Research output: Contribution to journalArticle

21 Citations (Scopus)

### Abstract

The present study investigates a numerical algorithm for solving systems of Cauchy singular integral equations of the second kind such as those which often occur in the analysis of interface crack problems. The algorithm takes advantage of many standard subroutines for performing numerical integrations and can be easily applied to equations which are defined over different intervals of the dependent variable. The solution technique is illustrated by analyzing two homogeneous center cracked panels: one loaded in tension and the other loaded in shear and bending. In the second example problem, the presence of crack face friction strongly couples the underlying singular integral equations. The numerical results are compared to closed form elasticity solutions and are shown to be extremely accurate. In addition, the study also illustrates the feasibility of using various assumed forms of the undetermined functions. By assuming these slightly altered forms, many rather complex problems are either solved directly or reduced in complexity.

Original language English (US) 139-154 16 International Journal of Fracture 66 2 https://doi.org/10.1007/BF00020079 Published - Mar 1 1994 Yes

### Fingerprint

Cauchy Integral
Singular Integral Equation
Integral equations
Numerical Solution
Cracks
Subroutines
Interface Crack
Elasticity
Friction
Numerical Algorithms
Numerical integration
Crack
Closed-form
Face
Numerical Results
Interval
Dependent
Form

### All Science Journal Classification (ASJC) codes

• Computational Mechanics
• Modeling and Simulation
• Mechanics of Materials

### Cite this

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The numerical solution of Cauchy singular integral equations with application to fracture. / Kurtz, Russell D.; Farris, Thomas; Sun, C. T.

In: International Journal of Fracture, Vol. 66, No. 2, 01.03.1994, p. 139-154.

Research output: Contribution to journalArticle

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T1 - The numerical solution of Cauchy singular integral equations with application to fracture

AU - Kurtz, Russell D.

AU - Farris, Thomas

AU - Sun, C. T.

PY - 1994/3/1

Y1 - 1994/3/1

N2 - The present study investigates a numerical algorithm for solving systems of Cauchy singular integral equations of the second kind such as those which often occur in the analysis of interface crack problems. The algorithm takes advantage of many standard subroutines for performing numerical integrations and can be easily applied to equations which are defined over different intervals of the dependent variable. The solution technique is illustrated by analyzing two homogeneous center cracked panels: one loaded in tension and the other loaded in shear and bending. In the second example problem, the presence of crack face friction strongly couples the underlying singular integral equations. The numerical results are compared to closed form elasticity solutions and are shown to be extremely accurate. In addition, the study also illustrates the feasibility of using various assumed forms of the undetermined functions. By assuming these slightly altered forms, many rather complex problems are either solved directly or reduced in complexity.

AB - The present study investigates a numerical algorithm for solving systems of Cauchy singular integral equations of the second kind such as those which often occur in the analysis of interface crack problems. The algorithm takes advantage of many standard subroutines for performing numerical integrations and can be easily applied to equations which are defined over different intervals of the dependent variable. The solution technique is illustrated by analyzing two homogeneous center cracked panels: one loaded in tension and the other loaded in shear and bending. In the second example problem, the presence of crack face friction strongly couples the underlying singular integral equations. The numerical results are compared to closed form elasticity solutions and are shown to be extremely accurate. In addition, the study also illustrates the feasibility of using various assumed forms of the undetermined functions. By assuming these slightly altered forms, many rather complex problems are either solved directly or reduced in complexity.

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