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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 367018, 7 pages
http://dx.doi.org/10.1155/2014/367018
Research Article

On Symplectic Analysis for the Plane Elasticity Problem of Quasicrystals with Point Group 12 mm

College of Sciences, Inner Mongolia University of Technology, Hohhot 010051, China

Received 13 March 2014; Accepted 29 May 2014; Published 23 June 2014

Academic Editor: Patricia J. Y. Wong

Copyright © 2014 Hua Wang et al. 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 symplectic approach, the separation of variables based on Hamiltonian systems, for the plane elasticity problem of quasicrystals with point group 12 mm is developed. By introducing appropriate transformations, the basic equations of the problem are converted to two independent Hamiltonian dual equations, and the associated Hamiltonian operator matrices are obtained. The study of the operator matrices shows the feasibility of the method. Without any assumptions, the general solution is presented for the problem with mixed boundary conditions.