A Hybrid Finite Element Method for Cracks

  • J. Zhang
  • N. Katsube

Abstract

Singular elements, such as quarter-point element, were developed in order to deal with stress singularity at the crack tip [1–4]. These elements replace many traditional elements around the crack tip without sacrificing the numerical accuracy. This method, however, requires a post processing procedure to evaluate the stress intensity factors.

Keywords

Lime 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    R. S. Barsoum, On the Use of Isoparametric Finite Elements in Linear Fracture Mechanics, Int. J. Numer. Methods Eng., Vol 10 (1976), pp.25–37.MATHCrossRefGoogle Scholar
  2. [2]
    R. S. Barsoum, Triangular Quarter-Point Elements as Elastic and Perfectly-Plastic Crack Tip Elements, Int. J. Numer. Methods Eng., Vol 11 (1977), pp. 85–98.MATHCrossRefGoogle Scholar
  3. [3]
    R. D. Henshell and K. G. Shaw, Crack Tip Finite Elements are Unnecessary, Int. J. Numer. Methods Eng., Vol 9 (1975), pp. 495–507.MATHCrossRefGoogle Scholar
  4. [4]
    H. D. Hibbit, Some Properties of Singular Isoparametric Elements, Int. J. Numer. Methods Eng., Vol 11 (1977), pp. 180–184.CrossRefGoogle Scholar
  5. [5]
    P. Tong, T. H. H. Pian and S. J. Lasry, A Hybrid-Element Approach to Crack Problems in Plane Elasticity, Int. J. Numer. Methods Eng., Vol 7 (1973), pp. 297–308.MATHCrossRefGoogle Scholar
  6. [6]
    N. I. Muskhelishvili, Some Basic Problems of the Mathematical Theory of Elasticity, P. Noordhoff Ltd., Groningen, Holland (1953).Google Scholar
  7. [7]
    M. F. Kanninen and C. H. Popelar, Advanced Fracture Mechanics, Oxford University Press, New York (1985).MATHGoogle Scholar
  8. [8]
    P. Tong and T. H. H. Pian, A Variational Principle and the Convergence of a Finite Element Method Based on Assumed Stress Distribution, Int. J. Solids Structures, Vol 5 (1969), pp. 463–472.MATHCrossRefGoogle Scholar
  9. [9]
    T. H. H. Pian and D. P. Chen, On the Suppression of Zero Energy Deformation Modes, Int. J. Numer. Methods Eng., Vol 19 (1983), pp. 1741–1752.MATHCrossRefGoogle Scholar
  10. [10]
    T. H. H. Pian and C. C. Wu, A Rational Approach for Choosing Stress Terms for Hybrid Finite Formulations, Int. J. Numer. Methods Eng., Vol 26 (1988), pp. 2331–2343.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • J. Zhang
    • 1
  • N. Katsube
    • 1
  1. 1.Applied Mechanics Program, Boyd LabThe Ohio State UniversityColumbusUSA

Personalised recommendations