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Mathematical Problems in Engineering
Volume 2013, Article ID 593640, 11 pages
Research Article

The Characteristic Solutions to the V-Notch Plane Problem of Anisotropy and the Associated Finite Element Method

1Department of Civil Engineering, China Agricultural University, Beijing 100083, China
2Department of Mechanics and Engineering Science, Peking University, Beijing 100871, China

Received 17 July 2013; Accepted 13 August 2013

Academic Editor: Song Cen

Copyright © 2013 Ge Tian 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.


This paper presents a novel way to calculate the characteristic solutions of the anisotropy V-notch plane problem. The material eigen equation of the anisotropy based on the Stroh theory and the boundary eigen equation of the V-notch plane problem are studied separately. A modified Müller method is utilized to calculate characteristic solutions of anisotropy V-notch plane problem, which are employed to formulate the analytical trial functions (ATF) in the associated finite element method. The numerical examples show that the proposed subregion accelerated Müller method is an efficient method to calculate the solutions of the equation involving the complex variables. The proposed element ATF-VN based on the analytical trial functions, which contain the characteristic solutions of the anisotropy V-notch problem, presents good performance in the benchmarks.