Symplectic Analytical Solutions for the Magnetoelectroelastic Solids Plane Problem in Rectangular Domain
The transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain is derived to Hamiltonian system. In symplectic geometry space with the origin variables—displacements, electric potential, and magnetic potential, as well as their duality variables—lengthways stress, electr...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/165160 |
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| author | Xiao-Chuan Li Wei-An Yao |
| author_facet | Xiao-Chuan Li Wei-An Yao |
| author_sort | Xiao-Chuan Li |
| collection | DOAJ |
| description | The transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain is derived to Hamiltonian system. In symplectic geometry space with the origin variables—displacements, electric potential, and magnetic potential, as well as their duality variables—lengthways stress, electric displacement, and magnetic induction, on the basis of the obtained eigensolutions of zero-eigenvalue, the eigensolutions of nonzero-eigenvalues are also obtained. The former are the basic solutions of Saint-Venant problem, and the latter are the solutions which have the local effect, decay drastically with respect to distance, and are covered in the Saint-Venant principle. So the complete solution of the problem is given out by the symplectic eigensolutions expansion. Finally, a few examples are selected and their analytical solutions are presented. |
| format | Article |
| id | doaj-art-2bb1774dcc2541e79d4cfdbf332ee25b |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2bb1774dcc2541e79d4cfdbf332ee25b2025-02-03T01:25:29ZengWileyJournal of Applied Mathematics1110-757X1687-00422011-01-01201110.1155/2011/165160165160Symplectic Analytical Solutions for the Magnetoelectroelastic Solids Plane Problem in Rectangular DomainXiao-Chuan Li0Wei-An Yao1School of Architecture and Civil Engineering, Shenyang University of Technology, Shenyang 110870, ChinaState Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, ChinaThe transversely isotropic magnetoelectroelastic solids plane problem in rectangular domain is derived to Hamiltonian system. In symplectic geometry space with the origin variables—displacements, electric potential, and magnetic potential, as well as their duality variables—lengthways stress, electric displacement, and magnetic induction, on the basis of the obtained eigensolutions of zero-eigenvalue, the eigensolutions of nonzero-eigenvalues are also obtained. The former are the basic solutions of Saint-Venant problem, and the latter are the solutions which have the local effect, decay drastically with respect to distance, and are covered in the Saint-Venant principle. So the complete solution of the problem is given out by the symplectic eigensolutions expansion. Finally, a few examples are selected and their analytical solutions are presented.http://dx.doi.org/10.1155/2011/165160 |
| spellingShingle | Xiao-Chuan Li Wei-An Yao Symplectic Analytical Solutions for the Magnetoelectroelastic Solids Plane Problem in Rectangular Domain Journal of Applied Mathematics |
| title | Symplectic Analytical Solutions for the Magnetoelectroelastic Solids Plane Problem in Rectangular Domain |
| title_full | Symplectic Analytical Solutions for the Magnetoelectroelastic Solids Plane Problem in Rectangular Domain |
| title_fullStr | Symplectic Analytical Solutions for the Magnetoelectroelastic Solids Plane Problem in Rectangular Domain |
| title_full_unstemmed | Symplectic Analytical Solutions for the Magnetoelectroelastic Solids Plane Problem in Rectangular Domain |
| title_short | Symplectic Analytical Solutions for the Magnetoelectroelastic Solids Plane Problem in Rectangular Domain |
| title_sort | symplectic analytical solutions for the magnetoelectroelastic solids plane problem in rectangular domain |
| url | http://dx.doi.org/10.1155/2011/165160 |
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