A Numerical Integration Formula for the Solution of the Singular Integral Equation for Classical Crack Problems in Plane and Antiplane Elasticity

A Numerical Integration Formula for the Solution of the Singular Integral Equation for Classical Crack Problems in Plane and Antiplane Elasticity

A numerical integration formula for the solution of the singular integral equation for classical crack problems in plane and antiplane elasticity is developed. The method is based on a modification of the Gauss-Chebyshev quadrature and the derivation of a finite part integral having an algebraic sin...

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Main Authors: Mostafa A. Hamed, Barry Cummins
Format: Article
Language:English
Published: Elsevier 1991-01-01
Series:Journal of King Saud University: Engineering Sciences
Online Access:http://www.sciencedirect.com/science/article/pii/S1018363918305476
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spelling doaj-9af25bbacc4f41348c7472bb10e8fbac2020-11-24T21:49:55ZengElsevierJournal of King Saud University: Engineering Sciences1018-36391991-01-0132217230A Numerical Integration Formula for the Solution of the Singular Integral Equation for Classical Crack Problems in Plane and Antiplane ElasticityMostafa A. Hamed0Barry Cummins1Associate Professor, Dept. of Prod. Eng. & Mech. System Design, King Abdulaziz University, P. 0. Box 9027, Jeddah 21413, Saudi ArabiaGraduate Student, Dept. of Mechanical Engineering, University of New Orleans, New Orleans, LA 70148, U.S.A.A numerical integration formula for the solution of the singular integral equation for classical crack problems in plane and antiplane elasticity is developed. The method is based on a modification of the Gauss-Chebyshev quadrature and the derivation of a finite part integral having an algebraic singularity of (3/2) at the limits of integration. The procedure is applied to determine the finite part integrals which have analytical solutions and the results are compared. Finally, the integration formula is applied to an actual crack problem and the stress intensity factors are computed and presented.http://www.sciencedirect.com/science/article/pii/S1018363918305476
collection DOAJ
language English
format Article
sources DOAJ
author Mostafa A. Hamed
Barry Cummins
spellingShingle Mostafa A. Hamed
Barry Cummins
A Numerical Integration Formula for the Solution of the Singular Integral Equation for Classical Crack Problems in Plane and Antiplane Elasticity
Journal of King Saud University: Engineering Sciences
author_facet Mostafa A. Hamed
Barry Cummins
author_sort Mostafa A. Hamed
title A Numerical Integration Formula for the Solution of the Singular Integral Equation for Classical Crack Problems in Plane and Antiplane Elasticity
title_short A Numerical Integration Formula for the Solution of the Singular Integral Equation for Classical Crack Problems in Plane and Antiplane Elasticity
title_full A Numerical Integration Formula for the Solution of the Singular Integral Equation for Classical Crack Problems in Plane and Antiplane Elasticity
title_fullStr A Numerical Integration Formula for the Solution of the Singular Integral Equation for Classical Crack Problems in Plane and Antiplane Elasticity
title_full_unstemmed A Numerical Integration Formula for the Solution of the Singular Integral Equation for Classical Crack Problems in Plane and Antiplane Elasticity
title_sort numerical integration formula for the solution of the singular integral equation for classical crack problems in plane and antiplane elasticity
publisher Elsevier
series Journal of King Saud University: Engineering Sciences
issn 1018-3639
publishDate 1991-01-01
description A numerical integration formula for the solution of the singular integral equation for classical crack problems in plane and antiplane elasticity is developed. The method is based on a modification of the Gauss-Chebyshev quadrature and the derivation of a finite part integral having an algebraic singularity of (3/2) at the limits of integration. The procedure is applied to determine the finite part integrals which have analytical solutions and the results are compared. Finally, the integration formula is applied to an actual crack problem and the stress intensity factors are computed and presented.
url http://www.sciencedirect.com/science/article/pii/S1018363918305476
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