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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| Format: | Article |
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Elsevier
2022
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| author | Ghorbanpoor, R. J., Saberi-Nadjafi Nik Long, N. M .A. M., Erfanian |
| author_facet | Ghorbanpoor, R. J., Saberi-Nadjafi Nik Long, N. M .A. M., Erfanian |
| author_sort | Ghorbanpoor, R. |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T11:18:04Z |
| format | Article |
| id | upm.eprints-103279 |
| institution | Universiti Putra Malaysia |
| last_indexed | 2024-03-06T11:18:04Z |
| publishDate | 2022 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | 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 |
| 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 |
| title | 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_short | 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 |
| work_keys_str_mv | AT ghorbanpoorr stabilityandconvergenceanalysisofsingularintegralequationsforunequalarmsbranchcrackproblemsinplaneelasticity AT jsaberinadjafi stabilityandconvergenceanalysisofsingularintegralequationsforunequalarmsbranchcrackproblemsinplaneelasticity AT niklongnma stabilityandconvergenceanalysisofsingularintegralequationsforunequalarmsbranchcrackproblemsinplaneelasticity AT merfanian stabilityandconvergenceanalysisofsingularintegralequationsforunequalarmsbranchcrackproblemsinplaneelasticity |