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A 3-D six-noded finite element containing a λ singularity

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Abstract

A three-dimensional six-noded prism (wedge) finite element containing a singularity of order λ is developed. The interpolation functions of the displacement allow for variations proportional to the power λ of the distance from the crack front along the crack surface and to the distance in the perpendicular direction. The element is compatible with standard wedge (6-noded) and brick (8-noded) isoparametric elements. Three problems are studied to examine the proposed element, namely, a penny-shaped crack in a cylinder, an edge crack in an homogeneous material, and a crack perpendicular to a bimaterial interface.

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References

  1. D.B. Bogy, Journal of Applied Mechanics, 12 (1971) 911–918.

    Google Scholar 

  2. M.L. Williams, Transactions, ASME, Journal of Applied Mechanics 19 (1952) 526–528.

    Google Scholar 

  3. J.P. Benthem, International Journal of Solids and Structures 13 (1977) 479–492.

    Google Scholar 

  4. Z.P. Bazant and L.F. Estenssoro, International Journal of Solids and Structures 15 (1979) 405–426.

    Google Scholar 

  5. P.D. Hilton and G.C. Sih, in Mechanics of Fracture, G.C. Sih (ed.), Vol. 1, Noordhoff, Amsterdam (1973) 426–483.

    Google Scholar 

  6. A.J. Akin, International Journal of Numerical Methods in Engineering 10 (1976) 1249–1259.

    Google Scholar 

  7. Dennis M. Tracy and Thomas S. Cook, International Journal of Numerical Methods in Engineering 11 (1977) 1225–1233.

    Google Scholar 

  8. Roshdi El Abdi, Engineering Fracture Mechanics 39 (1991) 1061–1065.

    Google Scholar 

  9. Roshdy S. Barsoum, International Journal of Numerical Methods in Engineering 10 (1976) 25–37.

    Google Scholar 

  10. W.S. Blackburn and T.K. Hellen, International Journal of Numerical Methods in Engineering 11 (1977) 211–229.

    Google Scholar 

  11. Robert. D. Cook, Davis S. Malkus and Michael E. Phesha, Concept and Application of Finite Element Analysis, John Wiley & Sons, 3rd edn. (1982).

  12. Ph. Geyskens, W. Marien and G. De Roeck, Computer Analysis Language (modified version), Katholieke Universiteit, Leuven (1991).

    Google Scholar 

  13. Leslie Banks-Sills and Dov Sherman, International Journal of Fracture 53 (1992) 1–20.

    Google Scholar 

  14. T.S. Cook and F. Erdogan, International Journal of Engineering 10 (1972) 667–697.

    Google Scholar 

  15. R.S. Barsoum and Tzi-Kang Chen, International Journal of Fracture 50 (1991) 221–237.

    Google Scholar 

  16. R.S. Barsoum, International Journal of Numerical Methods in Engineering 26 (1988) 531–539.

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Katholieke Universiteit, Leuven, Belgium

    M. M. Abdel Wahab & G. De Roeck

Authors
  1. M. M. Abdel Wahab
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  2. G. De Roeck
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Abdel Wahab, M.M., De Roeck, G. A 3-D six-noded finite element containing a λ singularity. Int J Fract 70, 347–356 (1994). https://doi.org/10.1007/BF00032452

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  • DOI: https://doi.org/10.1007/BF00032452

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