Solution of Contact Problems for Nonlinear Gao Beam and Obstacle
Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some dist...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2015/420649 |
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| _version_ | 1850226631367458816 |
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| author | J. Machalová H. Netuka |
| author_facet | J. Machalová H. Netuka |
| author_sort | J. Machalová |
| collection | DOAJ |
| description | Contact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model. |
| format | Article |
| id | doaj-art-5d5f2cd5644d49e78845aa46d9255925 |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-5d5f2cd5644d49e78845aa46d92559252025-08-20T02:05:01ZengWileyJournal of Applied Mathematics1110-757X1687-00422015-01-01201510.1155/2015/420649420649Solution of Contact Problems for Nonlinear Gao Beam and ObstacleJ. Machalová0H. Netuka1Faculty of Science, Palacký University in Olomouc, 17. listopadu 1192/12, 771 46 Olomouc, Czech RepublicFaculty of Science, Palacký University in Olomouc, 17. listopadu 1192/12, 771 46 Olomouc, Czech RepublicContact problem for a large deformed beam with an elastic obstacle is formulated, analyzed, and numerically solved. The beam model is governed by a nonlinear fourth-order differential equation developed by Gao, while the obstacle is considered as the elastic foundation of Winkler’s type in some distance under the beam. The problem is static without a friction and modeled either using Signorini conditions or by means of normal compliance contact conditions. The problems are then reformulated as optimal control problems which is useful both for theoretical aspects and for solution methods. Discretization is based on using the mixed finite element method with independent discretization and interpolations for foundation and beam elements. Numerical examples demonstrate usefulness of the presented solution method. Results for the nonlinear Gao beam are compared with results for the classical Euler-Bernoulli beam model.http://dx.doi.org/10.1155/2015/420649 |
| spellingShingle | J. Machalová H. Netuka Solution of Contact Problems for Nonlinear Gao Beam and Obstacle Journal of Applied Mathematics |
| title | Solution of Contact Problems for Nonlinear Gao Beam and Obstacle |
| title_full | Solution of Contact Problems for Nonlinear Gao Beam and Obstacle |
| title_fullStr | Solution of Contact Problems for Nonlinear Gao Beam and Obstacle |
| title_full_unstemmed | Solution of Contact Problems for Nonlinear Gao Beam and Obstacle |
| title_short | Solution of Contact Problems for Nonlinear Gao Beam and Obstacle |
| title_sort | solution of contact problems for nonlinear gao beam and obstacle |
| url | http://dx.doi.org/10.1155/2015/420649 |
| work_keys_str_mv | AT jmachalova solutionofcontactproblemsfornonlineargaobeamandobstacle AT hnetuka solutionofcontactproblemsfornonlineargaobeamandobstacle |