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Stability and convergence analysis of singular integral equations for unequal arms branch crack problems in plane elasticity

In this paper, an unequal arms branch crack problem in a plane elasticity is treated. Using distribution dislocation function and complex variable potential method, the problem is formulated into a singular integral equation. The appropriate integration scheme, in which a point dislocation is set at...

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Main Authors: Ghorbanpoor, R., J., Saberi-Nadjafi, Nik Long, N. M .A., M., Erfanian
Format: Article
Published: Elsevier 2022
Online Access:http://psasir.upm.edu.my/id/eprint/103279/
https://www.sciencedirect.com/science/article/pii/S0307904X21005394
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spelling my.upm.eprints.1032792023-11-07T04:48:14Z http://psasir.upm.edu.my/id/eprint/103279/ Stability and convergence analysis of singular integral equations for unequal arms branch crack problems in plane elasticity Ghorbanpoor, R. J., Saberi-Nadjafi Nik Long, N. M .A. M., Erfanian In this paper, an unequal arms branch crack problem in a plane elasticity is treated. Using distribution dislocation function and complex variable potential method, the problem is formulated into a singular integral equation. The appropriate integration scheme, in which a point dislocation is set at the origin and the distribution dislocation, is applied through all arms of the branch crack to solve the obtained singular integral equations numerically. Stability, convergence, the order of convergence, and the error term of the solution are analyzed. Some numerical examples are examined to describe the behavior of stress intensity factors at the endpoints of each branch crack. Elsevier 2022 Article PeerReviewed Ghorbanpoor, R. and J., Saberi-Nadjafi and Nik Long, N. M .A. and M., Erfanian (2022) Stability and convergence analysis of singular integral equations for unequal arms branch crack problems in plane elasticity. Applied Mathematical Modelling, 103. 731 - 749. ISSN 0307-904X https://www.sciencedirect.com/science/article/pii/S0307904X21005394 10.1016/j.apm.2021.11.009
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
description In this paper, an unequal arms branch crack problem in a plane elasticity is treated. Using distribution dislocation function and complex variable potential method, the problem is formulated into a singular integral equation. The appropriate integration scheme, in which a point dislocation is set at the origin and the distribution dislocation, is applied through all arms of the branch crack to solve the obtained singular integral equations numerically. Stability, convergence, the order of convergence, and the error term of the solution are analyzed. Some numerical examples are examined to describe the behavior of stress intensity factors at the endpoints of each branch crack.
format Article
author Ghorbanpoor, R.
J., Saberi-Nadjafi
Nik Long, N. M .A.
M., Erfanian
spellingShingle Ghorbanpoor, R.
J., Saberi-Nadjafi
Nik Long, N. M .A.
M., Erfanian
Stability and convergence analysis of singular integral equations for unequal arms branch crack problems in plane elasticity
author_facet Ghorbanpoor, R.
J., Saberi-Nadjafi
Nik Long, N. M .A.
M., Erfanian
author_sort Ghorbanpoor, R.
title Stability and convergence analysis of singular integral equations for unequal arms branch crack problems in plane elasticity
title_short Stability and convergence analysis of singular integral equations for unequal arms branch crack problems in plane elasticity
title_full Stability and convergence analysis of singular integral equations for unequal arms branch crack problems in plane elasticity
title_fullStr Stability and convergence analysis of singular integral equations for unequal arms branch crack problems in plane elasticity
title_full_unstemmed Stability and convergence analysis of singular integral equations for unequal arms branch crack problems in plane elasticity
title_sort stability and convergence analysis of singular integral equations for unequal arms branch crack problems in plane elasticity
publisher Elsevier
publishDate 2022
url http://psasir.upm.edu.my/id/eprint/103279/
https://www.sciencedirect.com/science/article/pii/S0307904X21005394
_version_ 1783879947301945344
score 13.211869

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