Numerical solution for an epicycloid crack
A flat crack, , is lying in a three-dimensional homogenous isotropic elastic solid subjected to shear loading. A mathematical formulation is developed based on the mixed boundary values for such that the problem of finding the resulting force can be written in the form of hypersingular integral equa...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/34684/ http://psasir.upm.edu.my/id/eprint/34684/1/Numerical%20Solution%20for%20an%20Epicycloid%20Crack.pdf |
| _version_ | 1848847842533179392 |
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| author | Nik Long, Nik Mohd Asri Koo, Lee Feng Wong, Tze Jin Eshkuvatov, Zainidin K. |
| author_facet | Nik Long, Nik Mohd Asri Koo, Lee Feng Wong, Tze Jin Eshkuvatov, Zainidin K. |
| author_sort | Nik Long, Nik Mohd Asri |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A flat crack, , is lying in a three-dimensional homogenous isotropic elastic solid subjected to shear loading. A mathematical formulation is developed based on the mixed boundary values for such that the problem of finding the resulting force can be written in the form of hypersingular integral equation. Employing conformal mapping, the integral equation is transformed to a similar equation over a circular region, . By making a suitable representation of hypersingular integral equation, the problem is reduced to solve a system of linear equations. Numerical solution for the shear stress intensity factors, maximum stress intensity, and strain energy release rate is obtained. Our results give an excellent agreement to the existing asymptotic solutions. |
| first_indexed | 2025-11-15T09:25:02Z |
| format | Article |
| id | upm-34684 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:25:02Z |
| publishDate | 2014 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-346842015-12-18T01:35:45Z http://psasir.upm.edu.my/id/eprint/34684/ Numerical solution for an epicycloid crack Nik Long, Nik Mohd Asri Koo, Lee Feng Wong, Tze Jin Eshkuvatov, Zainidin K. A flat crack, , is lying in a three-dimensional homogenous isotropic elastic solid subjected to shear loading. A mathematical formulation is developed based on the mixed boundary values for such that the problem of finding the resulting force can be written in the form of hypersingular integral equation. Employing conformal mapping, the integral equation is transformed to a similar equation over a circular region, . By making a suitable representation of hypersingular integral equation, the problem is reduced to solve a system of linear equations. Numerical solution for the shear stress intensity factors, maximum stress intensity, and strain energy release rate is obtained. Our results give an excellent agreement to the existing asymptotic solutions. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/34684/1/Numerical%20Solution%20for%20an%20Epicycloid%20Crack.pdf Nik Long, Nik Mohd Asri and Koo, Lee Feng and Wong, Tze Jin and Eshkuvatov, Zainidin K. (2014) Numerical solution for an epicycloid crack. Journal of Applied Mathematics, 2014. art. no. 213478. pp. 1-12. ISSN 1110-757X; ESSN: 1687-0042 http://www.hindawi.com/journals/jam/2014/213478/abs/ 10.1155/2014/213478 |
| spellingShingle | Nik Long, Nik Mohd Asri Koo, Lee Feng Wong, Tze Jin Eshkuvatov, Zainidin K. Numerical solution for an epicycloid crack |
| title | Numerical solution for an epicycloid crack |
| title_full | Numerical solution for an epicycloid crack |
| title_fullStr | Numerical solution for an epicycloid crack |
| title_full_unstemmed | Numerical solution for an epicycloid crack |
| title_short | Numerical solution for an epicycloid crack |
| title_sort | numerical solution for an epicycloid crack |
| url | http://psasir.upm.edu.my/id/eprint/34684/ http://psasir.upm.edu.my/id/eprint/34684/ http://psasir.upm.edu.my/id/eprint/34684/ http://psasir.upm.edu.my/id/eprint/34684/1/Numerical%20Solution%20for%20an%20Epicycloid%20Crack.pdf |