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

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  • Ge Tian
  • Xiang-Rong Fu
  • Ming-Wu Yuan
  • Meng-Yan Song

Abstract

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.

Suggested Citation

  • Ge Tian & Xiang-Rong Fu & Ming-Wu Yuan & Meng-Yan Song, 2013. "The Characteristic Solutions to the V-Notch Plane Problem of Anisotropy and the Associated Finite Element Method," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-11, September.
    • Handle: RePEc:hin:jnlmpe:593640
    DOI: 10.1155/2013/593640
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