Numerical Solution for an Epicycloid Crack
A flat crack, Ω, 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 Ω such that the problem of finding the resulting force can be written in the form of hypersingular integral e...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/213478 |
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| _version_ | 1849306396978315264 |
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| author | Nik Mohd Asri Nik Long Koo Lee Feng Wong Tze Jin Z. K. Eshkuvatov |
| author_facet | Nik Mohd Asri Nik Long Koo Lee Feng Wong Tze Jin Z. K. Eshkuvatov |
| author_sort | Nik Mohd Asri Nik Long |
| collection | DOAJ |
| description | A flat crack, Ω, 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 Ω 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, D. 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. |
| format | Article |
| id | doaj-art-34899f7cf6ef4c81bdfd1ed3f67cd1f4 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-34899f7cf6ef4c81bdfd1ed3f67cd1f42025-08-20T03:55:06ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/213478213478Numerical Solution for an Epicycloid CrackNik Mohd Asri Nik Long0Koo Lee Feng1Wong Tze Jin2Z. K. Eshkuvatov3Department of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaInstitute for Mathematical Research, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics, Universiti Putra Malaysia, 43400 Serdang, Selangor, MalaysiaA flat crack, Ω, 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 Ω 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, D. 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.http://dx.doi.org/10.1155/2014/213478 |
| spellingShingle | Nik Mohd Asri Nik Long Koo Lee Feng Wong Tze Jin Z. K. Eshkuvatov Numerical Solution for an Epicycloid Crack Journal of Applied Mathematics |
| 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://dx.doi.org/10.1155/2014/213478 |
| work_keys_str_mv | AT nikmohdasriniklong numericalsolutionforanepicycloidcrack AT kooleefeng numericalsolutionforanepicycloidcrack AT wongtzejin numericalsolutionforanepicycloidcrack AT zkeshkuvatov numericalsolutionforanepicycloidcrack |