Numerical solution for an almost square crack
This paper studied the behaviour of the solution for an almost square crack, Ω, in the plane elasticity. The problem of sliding the resulting shear forces can be formulated as a hypersingular integral equation over a considered domain, Ω. The sharp corner of the square is rounded up such that the st...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/34683/ http://psasir.upm.edu.my/id/eprint/34683/1/Numerical%20solution%20for%20an%20almost%20square%20crack.pdf |
| _version_ | 1848847842223849472 |
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| author | Koo, Lee Feng Nik Long, Nik Mohd Asri Eshkuvatov, Zainidin K. Wong, Tze Jin |
| author_facet | Koo, Lee Feng Nik Long, Nik Mohd Asri Eshkuvatov, Zainidin K. Wong, Tze Jin |
| author_sort | Koo, Lee Feng |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper studied the behaviour of the solution for an almost square crack, Ω, in the plane elasticity. The problem of sliding the resulting shear forces can be formulated as a hypersingular integral equation over a considered domain, Ω. The sharp corner of the square is rounded up such that the stress singularity is kept uniform form along the entire crack contour. The equation is then transformed into a similar hypersingular integral equation over a circular disc, D, using conformal mapping. The transformed hypersingular integral equation is afterward reduced to a system of linear algebraic equations using Galerkin method. The system of linear equations is solved numerically for the unknown coefficients, which later will be used in determining the stress intensity factors, maximum stress intensity and energy release rate. Comparison with the existing asymptotic solutions show a good agreement. |
| first_indexed | 2025-11-15T09:25:02Z |
| format | Conference or Workshop Item |
| id | upm-34683 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:25:02Z |
| publishDate | 2014 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-346832016-09-19T07:13:51Z http://psasir.upm.edu.my/id/eprint/34683/ Numerical solution for an almost square crack Koo, Lee Feng Nik Long, Nik Mohd Asri Eshkuvatov, Zainidin K. Wong, Tze Jin This paper studied the behaviour of the solution for an almost square crack, Ω, in the plane elasticity. The problem of sliding the resulting shear forces can be formulated as a hypersingular integral equation over a considered domain, Ω. The sharp corner of the square is rounded up such that the stress singularity is kept uniform form along the entire crack contour. The equation is then transformed into a similar hypersingular integral equation over a circular disc, D, using conformal mapping. The transformed hypersingular integral equation is afterward reduced to a system of linear algebraic equations using Galerkin method. The system of linear equations is solved numerically for the unknown coefficients, which later will be used in determining the stress intensity factors, maximum stress intensity and energy release rate. Comparison with the existing asymptotic solutions show a good agreement. AIP Publishing LLC 2014 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/34683/1/Numerical%20solution%20for%20an%20almost%20square%20crack.pdf Koo, Lee Feng and Nik Long, Nik Mohd Asri and Eshkuvatov, Zainidin K. and Wong, Tze Jin (2014) Numerical solution for an almost square crack. In: 3rd International Conference on Quantitative Sciences and Its Applications (ICOQSIA 2014), 12–14 Aug. 2014, Langkawi, Kedah. (pp. 125-130). 10.1063/1.4903573 |
| spellingShingle | Koo, Lee Feng Nik Long, Nik Mohd Asri Eshkuvatov, Zainidin K. Wong, Tze Jin Numerical solution for an almost square crack |
| title | Numerical solution for an almost square crack |
| title_full | Numerical solution for an almost square crack |
| title_fullStr | Numerical solution for an almost square crack |
| title_full_unstemmed | Numerical solution for an almost square crack |
| title_short | Numerical solution for an almost square crack |
| title_sort | numerical solution for an almost square crack |
| url | http://psasir.upm.edu.my/id/eprint/34683/ http://psasir.upm.edu.my/id/eprint/34683/ http://psasir.upm.edu.my/id/eprint/34683/1/Numerical%20solution%20for%20an%20almost%20square%20crack.pdf |