Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics
In this paper we consider a mixed boundary value problem for biharmonic equation of the Airy stress function which models a crack problem of a solid elastic plate. An iterative method for reducing the problem to a sequence of mixed problems for Poisson equations is proposed and investigated. The con...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2013-02-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Subjects: | |
| Online Access: | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/11728 |
| _version_ | 1818536153164283904 |
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| author | Dang Quang A Mai Xuan Thao |
| author_facet | Dang Quang A Mai Xuan Thao |
| author_sort | Dang Quang A |
| collection | DOAJ |
| description | In this paper we consider a mixed boundary value problem for biharmonic equation of the Airy stress function which models a crack problem of a solid elastic plate. An iterative method for reducing the problem to a sequence of mixed problems for Poisson equations is proposed and investigated. The convergence of the method is established theoretically and illustrated on many numerical experiments. |
| first_indexed | 2024-12-11T18:34:16Z |
| format | Article |
| id | doaj.art-3ade0a68b9cb432eb9925d2db6908e07 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-12-11T18:34:16Z |
| publishDate | 2013-02-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-3ade0a68b9cb432eb9925d2db6908e072022-12-22T00:54:49ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882013-02-013116578Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanicsDang Quang AMai Xuan ThaoIn this paper we consider a mixed boundary value problem for biharmonic equation of the Airy stress function which models a crack problem of a solid elastic plate. An iterative method for reducing the problem to a sequence of mixed problems for Poisson equations is proposed and investigated. The convergence of the method is established theoretically and illustrated on many numerical experiments.http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/11728Iterative methodBiharmonic equationMixed boundary conditionsCrack problem. |
| spellingShingle | Dang Quang A Mai Xuan Thao Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics Boletim da Sociedade Paranaense de Matemática Iterative method Biharmonic equation Mixed boundary conditions Crack problem. |
| title | Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics |
| title_full | Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics |
| title_fullStr | Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics |
| title_full_unstemmed | Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics |
| title_short | Iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics |
| title_sort | iterative method for solving a problem with mixed boundary conditions for biharmonic equation arising in fracture mechanics |
| topic | Iterative method Biharmonic equation Mixed boundary conditions Crack problem. |
| url | http://www.periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/11728 |
| work_keys_str_mv | AT dangquanga iterativemethodforsolvingaproblemwithmixedboundaryconditionsforbiharmonicequationarisinginfracturemechanics AT maixuanthao iterativemethodforsolvingaproblemwithmixedboundaryconditionsforbiharmonicequationarisinginfracturemechanics |