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Analytical Trial Function Method II — Singular Elements with Crack and Notch

  • Song Cen
  • Zhi-Fei Long

Abstract

This chapter continues to discuss the analytical trial function method. Here, the analytical trial function method is applied to develop the singular hybrid elements with crack and notch for the analysis of the crack and notch problems. During the analysis, the singular hybrid element is collocated in the region around the tips of the crack and notch, while the conventional displacement-based elements are used in the periphery region. Furthermore, this chapter also gives detailed discussions on the convergence of the singular element, zero energy mode, and improvement for the iteration solution method of eigenvalues. From the contents of this chapter and the previous chapter, it can be seen that, in the analytical trial function method, analytical and discrete methods can complement each other; and as a result, some challenging problems existing in FEM can be successfully solved.

Keywords

finite element analytical trial function method singular element crack notch 

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References

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    Williams ML (1957) On the stress distribution at the base of a statinary crack. Journal of Applied Mechanics 24: 109–114zbMATHGoogle Scholar
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    Fu XR, Long YQ (2001) Fracture analysis with the sub-region mixed element method. Gong Cheng Li Xue/Engineering Mechanics 18(6): 39–46 (in Chinese)Google Scholar
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    Williams ML (1952) Stress singularities resulting from various boundary conditions in angular corners of plates in extention. Journal of Applied Mechanics 14: 526–528Google Scholar
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    Fan Z, Long YQ (1992) Sub-region mixed finite element analysis of V-notched plates. International Journal of Fracture 56: 333–344CrossRefGoogle Scholar
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    Fu XR, Long YQ (2002) Calculation of the eigenvalues—the sub-region accelerated Müller method. In: Proceedings of the Eleventh National Conference on Structural Engineering (Vol. I), China, Changsha, pp226–232 (in Chinese)Google Scholar
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    Gross B, Mendelson A (1972) Plane elastostatic analysis of V-notched plates. International Journal of Fracture 8: 267–276CrossRefGoogle Scholar

Copyright information

© Tsinghua University Press, Beijing and Springer-Verlag GmbH Berlin Heidelberg 2009

Authors and Affiliations

  • Song Cen
    • 1
  • Zhi-Fei Long
    • 2
  1. 1.Department of Engineering Mechanics, School of AerospaceTsinghua UniversityBeijingChina
  2. 2.School of Mechanics & Civil EngineeringChina University of Mining & TechnologyBeijingChina

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