Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials
We consider a class of evolutionary variational inequalities arising in quasistatic frictional contact problems for linear elastic materials. We indicate sufficient conditions in order to have the existence, the uniqueness and the Lipschitz continuous dependence of the solution with respect to the d...
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| Format: | Article |
| Language: | English |
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Wiley
1999-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337599000172 |
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| _version_ | 1832549493655994368 |
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| author | Dumitru Motreanu Mircea Sofonea |
| author_facet | Dumitru Motreanu Mircea Sofonea |
| author_sort | Dumitru Motreanu |
| collection | DOAJ |
| description | We consider a class of evolutionary variational inequalities arising in quasistatic frictional contact problems for linear elastic materials. We indicate sufficient conditions in order to have the existence, the uniqueness and the Lipschitz continuous dependence of the solution with respect to the data, respectively. The existence of the solution is obtained using a time-discretization method, compactness and lower semicontinuity arguments. In the study of the discrete problems we use a recent result obtained by the authors (2000). Further, we apply the abstract results in the study of a number of mechanical problems modeling the frictional contact between a deformable body and a foundation. The material is assumed to have linear elastic behavior and the processes are quasistatic. The first problem concerns a model with
normal compliance and a version of Coulomb's law of dry friction, for which we prove the existence of a weak solution. We then consider a problem of bilateral contact with Tresca's friction law and a problem involving a simplified version of Coulomb's friction law. For these two problems we prove the existence, the uniqueness and the Lipschitz continuous dependence of the weak solution with respect to the data. |
| format | Article |
| id | doaj-art-276b1a18bc6643b5abb02e2a1f9c4221 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 1999-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-276b1a18bc6643b5abb02e2a1f9c42212025-02-03T06:11:12ZengWileyAbstract and Applied Analysis1085-33751687-04091999-01-014425527910.1155/S1085337599000172Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materialsDumitru Motreanu0Mircea Sofonea1Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, Perpignan 66860, FranceLaboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, Perpignan 66860, FranceWe consider a class of evolutionary variational inequalities arising in quasistatic frictional contact problems for linear elastic materials. We indicate sufficient conditions in order to have the existence, the uniqueness and the Lipschitz continuous dependence of the solution with respect to the data, respectively. The existence of the solution is obtained using a time-discretization method, compactness and lower semicontinuity arguments. In the study of the discrete problems we use a recent result obtained by the authors (2000). Further, we apply the abstract results in the study of a number of mechanical problems modeling the frictional contact between a deformable body and a foundation. The material is assumed to have linear elastic behavior and the processes are quasistatic. The first problem concerns a model with normal compliance and a version of Coulomb's law of dry friction, for which we prove the existence of a weak solution. We then consider a problem of bilateral contact with Tresca's friction law and a problem involving a simplified version of Coulomb's friction law. For these two problems we prove the existence, the uniqueness and the Lipschitz continuous dependence of the weak solution with respect to the data.http://dx.doi.org/10.1155/S1085337599000172 |
| spellingShingle | Dumitru Motreanu Mircea Sofonea Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials Abstract and Applied Analysis |
| title | Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials |
| title_full | Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials |
| title_fullStr | Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials |
| title_full_unstemmed | Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials |
| title_short | Evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials |
| title_sort | evolutionary variational inequalities arising in quasistatic frictional contact problems for elastic materials |
| url | http://dx.doi.org/10.1155/S1085337599000172 |
| work_keys_str_mv | AT dumitrumotreanu evolutionaryvariationalinequalitiesarisinginquasistaticfrictionalcontactproblemsforelasticmaterials AT mirceasofonea evolutionaryvariationalinequalitiesarisinginquasistaticfrictionalcontactproblemsforelasticmaterials |