Journal of Applied Mathematics
Volume 2011 (2011), Article ID 165160, 15 pages
doi:10.1155/2011/165160
Research Article

Symplectic Analytical Solutions for the Magnetoelectroelastic Solids Plane Problem in Rectangular Domain

1School of Architecture and Civil Engineering, Shenyang University of Technology, Shenyang 110870, China
2State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116023, China

Received 20 September 2010; Accepted 12 January 2011

Academic Editor: Pablo Gonza'lez-Vera

Copyright © 2011 Xiao-Chuan Li and Wei-An Yao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.