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Sub-Region Mixed Element I — Fundamental Theory and Crack Problem

  • Yu-Qiu Long
  • Song Cen
Chapter

Abstract

This chapter firstly gives a brief review of the variational fundamentals and computational method of the sub-region mixed element method in the first two sections. Then, in the next three sections, the applications of this method in the 2D crack problem, cracked thick plate problem and surface crack problem in 3D body are introduced, respectively. Numerical examples show that the proposed sub-region mixed element method is an efficient tool for solving the various crack problems.

Keywords

finite element sub-region mixed element crack problem 

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References

  1. [1]
    Long YQ, Zhi BC, Kuang WQ, Shan J (1982) Sub-region mixed finite element method for the calculation of stress intensity factor. In: He GQ et al (eds) Proceedings of International Conference on FEM. Science Press, Shanghai, pp 738–740Google Scholar
  2. [2]
    Benzley SE (1974) Representation of singularities with isoparametric finite elements. International Journal for Numerical Methods in Engineering 8:537–545CrossRefzbMATHGoogle Scholar
  3. [3]
    Chien WZ, Xie ZC, Gu QL, Yang ZF, Zhou CT (1980) The superposition of the finite element method on the singularity terms in determining the stress intensity factors. Journal of Tsinghua University 2: 15–24 (in Chinese)Google Scholar
  4. [4]
    Long YQ, Zhao YQ (1985) Calculation of stress intensity factors in plane problems by the sub-region mixed finite element method. Engineering Software 7(1): 32–35Google Scholar
  5. [5]
    Huang MF, Long YQ (1988) Calculation of stress intensity factors of cracked Reissner plates by the sub-region mixed finite element method. Computers & Structures 30(4): 837–840CrossRefzbMATHGoogle Scholar
  6. [6]
    Long YQ, Qian J (1992) Calculation of stress intensity factors for surface cracks in a 3D body by the subregion mixed FEM. Computers & Structures 44(1/2): 75–78zbMATHGoogle Scholar
  7. [7]
    Fan Z, Long YQ (1992) Sub-region mixed finite element analysis of V-notched plates. International Journal of Fracture 56: 333–344CrossRefGoogle Scholar
  8. [8]
    Long YQ, Qian J (1990) Fracture analysis of V-notch in composite material. In: Proceeding of WCCM-II. Stuttgart, pp 332–335Google Scholar
  9. [9]
    Long YQ, Qian J (1992) Sub-region mixed finite element analysis of V-notches in a bimaterial. In: Zhu DC (ed) Advances in Engineering Mechanics. Peking University Press, Beijing, pp 54–59Google Scholar
  10. [10]
    Qian J, Long YQ (1992) The expression of stress and strain at the tip of notch in Reissner plate. Applied mathematics and Mechanics (English Edition) 13(4): 315–324CrossRefzbMATHGoogle Scholar
  11. [11]
    Qian J, Long YQ (1994) The expression of stress and strain at the tip of 3-D notch. Applied mathematics and Mechanics (English Edition) 15(3): 211–221CrossRefMathSciNetzbMATHGoogle Scholar
  12. [12]
    Bao SH, Yang C, Fan Z (1984) Analysis of shear wall supported by beam column system and shear wall with opening by subregion mixed FEM. In: Proc: 3rd Int. Conf. on Tall Buildings. Hong Kong, pp 586–591Google Scholar
  13. [13]
    Atluri SN, Kobayashi AS, Nakagaki M (1975) An assumed displacement hybrid finite element model for linear fracture mechanics. International Journal of Fracture 11: 257–271CrossRefGoogle Scholar
  14. [14]
    Kelly JW, Sun CT (1977) A singular finite element for computing stress intensity factors. In: Sih GC (ed) Proceedings of an International Conference on Fracture Mechanics and Technology (Vol 2), Sijthoff and Noordhoff International Publishers, Hong Kong, pp 1483–1498Google Scholar
  15. [15]
    Gross B, Strawley JE, Brown WE (1964) Stress intensity factors for a single edge notch tension specimen by boundary collocation of a stress function. NASA, TN-D-2395Google Scholar
  16. [16]
    Isida M (1971) Effect of width and length on stress intensity factors of internally cracked plates under various boundary conditions. International Journal of Fracture 7: 301–316Google Scholar
  17. [17]
    Rooke DP, Cartwright DJ (1976) Compendium of Stress Intensity Factors. Her Majesty’s Stationery Office, LondonGoogle Scholar
  18. [18]
    Wilson WK (1971) Numerical methods for determining stress intensity factors of an interior crack in a finite plate. ASME Journal of Basic Engineering 93:685–690CrossRefGoogle Scholar
  19. [19]
    Barsoum RS (1976) A degenerate solid element for linear fracture analysis of plate bending and general shells. International Journal for Numerical Methods in Engineering 10:551–564CrossRefzbMATHGoogle Scholar
  20. [20]
    Yagawa G (1979) Finite element analysis of stress intensity factors for plate extension and plate bending problems. International Journal for Numerical Methods in Engineering 14(5): 727–740CrossRefMathSciNetzbMATHGoogle Scholar
  21. [21]
    Li YZ, Liu CT (1983) Analysis of Reissner’s plate bending fracture problem. Acta Mechanica Sinica 15(4): 366–375 (in Chinese)Google Scholar
  22. [22]
    Hartranft RJ, Sih GC (1968) Effect of plate thickness on the bending stress distribution around through cracks. Journal of Mathematics and Physics 47: 276–291CrossRefzbMATHGoogle Scholar
  23. [23]
    Wang NM (1970) Twisting of an elastic plate containing a crack. International Journal of Fracture 6: 367–378Google Scholar
  24. [24]
    Nishioka T, Atluri SN (1983) An alternating method for analysis of surface flawed aircraft structural components. AIAA Journal 21(5): 749–757CrossRefzbMATHGoogle Scholar
  25. [25]
    Niu X, Glinka G (1989) Stress intensity factors for semi-elliptical surface cracks in welded joints. International Journal of Fracture 40: 255–270CrossRefGoogle Scholar
  26. [26]
    Heliot J, Labbens R, Pellissier-Tannon A (1979) Semi-elliptical cracks in a cylinder subjected to stress gradients. In: Smith GW (eds) Fracture Mechanics. ASTM STP 677. American Society for Testing and Materials, Philadelphia, pp 341–364CrossRefGoogle Scholar
  27. [27]
    Li YZ (1988) Crack tip stress and strain fields for surface cracks in 3D body and the calculation of stress intensity factors. Chinese Science (A) 8: 828–842Google Scholar
  28. [28]
    Newman JC, Raju IS (1979) NASA, TP-1578Google Scholar

Copyright information

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

Authors and Affiliations

  • Yu-Qiu Long
    • 1
  • Song Cen
    • 2
  1. 1.Department of Civil Engineering, School of Civil EngineeringTsinghua UniversityBeijingChina
  2. 2.Department of Engineering Mechanics, School of AerospaceTsinghua UniversityBeijingChina

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