Acta Mechanica Solida Sinica

, Volume 19, Issue 2, pp 128–134 | Cite as

The evaluation of stress intensity factors of plane crack for orthotropic plate with equal parameter by F2LFEM

  • Jie Fan
  • Xiaochun Zhang
  • A. Y. T. Leung
  • Weifang Zhong


In this paper, the evaluation of stress intensity factor of plane crack problems for orthotropic plate of equal-parameter is investigated using a fractal two-level finite element method (F2LFEM). The general solution of an orthotropic crack problem is obtained by assimilating the problem with isotropic crack problem, and is employed as the global interpolation function in F2LFEM. In the neighborhood of crack tip of the crack plate, the fractal geometry concept is introduced to achieve the similar meshes having similarity ratio less than one and generate an infinitesimal mesh so that the relationship between the stiffness matrices of two adjacent layers is equal. A large number of degrees of freedom around the crack tip are transformed to a small set of generalized coordinates. Numerical examples show that this method is efficient and accurate in evaluating the stress intensity factor (SIF).

Key words

plane crack orthotropic plate fractal finite element stress intensity factor 


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  1. [1]
    Yang, X.C. and Fan, T.Y., A slanting edge-crack problem in elastic half plane, Chinese Journal of Applied Mechanics, Vol.16, No.2, 1999 (in Chinese)Google Scholar
  2. [2]
    Gao, C.F. and Fan, W.X., The fundamental solutions for the plane problem in piezoelectric media with an elliptic hole or a crack, Applied Mathematics and Mechanics, Vol.19, No.11, 1998 (in Chinese)Google Scholar
  3. [3]
    Helsing, J. and Josson, A.k, Complex variable boundary integral equations for perforated infinite planes, Engineering Analysis with Boundary Elements, Vol.25, 2001, 191–202.CrossRefGoogle Scholar
  4. [4]
    Dirgantara, T. and Aliabadi, M.H., Stress intensity factors for cracks in thin plates, Engineering Fracture Mechanics, Vol.69, 2002, 1465–1486.CrossRefGoogle Scholar
  5. [5]
    Z. Cedric Xia, John W. Hutchinson, Crack tip fields in strain gradient plasticity, J. Mech. Phys. Solids, Vol.44, No.10, 1996, 1621–1648.CrossRefGoogle Scholar
  6. [6]
    Gao, C.F. and Tong, X.H., Plane problems for orthotropic plate of equal-parameter, Mechanics and Engineering, Vol.10, No.4, 1994, 28–30 (in Chinese).Google Scholar
  7. [7]
    Williams, M.L, On the Distribution at the base of stationary crack, ASME J. Appl. Mech, Vol.24, 1957, 109–114.MathSciNetzbMATHGoogle Scholar
  8. [8]
    Leung, A.Y.T. and Su, R.K.L., Mode I—Crack problems by fractal two level finite element methods, Engineering Fracture Mechanics, Vol.48, No.6, 1994, 847–856.CrossRefGoogle Scholar
  9. [9]
    Leung, A.Y.T. and Tsang, K.L., Mode III—Two-dimensional crack problem by two level finite element method, International Journal of Fracture, Vol.102, 2000, 245–258.CrossRefGoogle Scholar
  10. [10]
    Su, R.K.L. and Sun, H.Y., Numerical solutions of two-dimensional anisotropic crack problems, International Journal of Solids and Structures, Vol.40, 2003, 4615–4635.CrossRefGoogle Scholar
  11. [11]
    The Handbook of Stress Intensity Factors. China Research Institute of Aviation, Beijing: Science Press, 1981 (in Chinese).Google Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2006

Authors and Affiliations

  • Jie Fan
    • 1
  • Xiaochun Zhang
    • 1
  • A. Y. T. Leung
    • 2
  • Weifang Zhong
    • 1
  1. 1.Department of MechanicsHuazhong University of Science and TechnologyWuhanChina
  2. 2.Department of Building and ConstructionCity University of Hong KongHong KongChina

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