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Singularities of cracks with generalized finite elements

Part of the Lecture Notes in Mathematics book series (LNM,volume 1121)

Abstract

Pian's hybrid method is frequently used for computing stress intensity factors in fracture mechanics. It has been shown, however, that this method has its limitations. In using this method, it is found that the resulting stiffness matrix is often poorly conditioned and it is not possible to determine surface displacements of notch or crack zones accurately. Most of these aforementioned difficulties can be eliminated by using a modified hybrid stress model in combination with the displacement method. The proposed modified hybrid method will be shown to offer some significant advantages for plane, axi-symmetric and three dimensionel problems of fracture mechanics.

Keywords

  • Stress Intensity Factor
  • Crack Front
  • Crack Opening Displacement
  • Linear Elastic Fracture Mechanic
  • Trial Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. M. Wolf: Lösung von ebenen Kerb-und Rißproblemen mit der Methode der finiten Elemente. Diss. Techn. Univ. München, 1977.

    Google Scholar 

  2. P. Tong, T.H.H. Pian, S.J. Lasry: A hybrid element approach to crack problems in plane elasticity. Int. J. Num. Meth. Engng., Bd. 7, 1973, pp. 297–308.

    CrossRef  MATH  Google Scholar 

  3. M. Stern, E.B. Becker: A confirming crack-tip element with quadratic variation in the singular fields. Int. J. Num. Meth. Engng., Vol. 12, 1978, pp. 279–288.

    CrossRef  MATH  Google Scholar 

  4. T.H.H. Pian, P. Tong: Basis of finite element methods for solid continua. Int. J. Num. Meth. Engng., Bd. 1, 1969, pp. 3–28.

    CrossRef  MATH  Google Scholar 

  5. P. Tong, T.H.H. Pian: Variational principle and the convergence of a finite element method based on assumed stress distribution. Int. J. Solids Structures, Bd. 5, 1969, pp. 463–472.

    CrossRef  MATH  Google Scholar 

  6. E. Schnack: Beitrag zur Berechnung rotationssymmetrischer Spannungskonzentrationsprobleme mit der Methode der finiten Elemente. Diss. Techn. Univ. München, 1973.

    Google Scholar 

  7. E. Schnack, M. Wolf: Application of displacement and hybrid stress methods to plane notch and crack problems. Int. J. Num. Meth. Engng., Vol. 12, No. 6, 1978, pp. 963–975.

    CrossRef  MATH  Google Scholar 

  8. J.P. Wolf: Generalized stress models for finite element analysis. Ph.D. Thesis, ETH Zürich, 1974.

    Google Scholar 

  9. S.N. Atluri, H.C. Rhee: Traction boundary conditions in hybrid stress finite element model. AIAA Bd. 16, Nr. 5, 1978, pp. 529–531.

    CrossRef  MATH  Google Scholar 

  10. R. Drumm: Zur effektiven FEM-Analyse ebener Spannungskonzentrationsprobleme. Fortschritt-Bericht der VDI-Z, Reihe 18, Nr. 13, Düsseldorf 1983.

    Google Scholar 

  11. T.H.H. Pian, K. Moriya: Three dimensional fracture analysis by assumed stress hybrid elements. in Luxmoore, A.R., Owen, D.R.J.: Proc. 1st and 2nd International Conference on “Numerical Methods in Fracture Mechanics”. Pineridge Press, Swansea 1978 und 1980, S. 363–373.

    Google Scholar 

  12. M. Kuna: Konstruktion und Anwendung hybrider Rißspitzenelemente für dreidimensionale bruchmechanische Aufgaben. Techn. Mechanik Bd. 2 (1982), S. 37–43.

    Google Scholar 

  13. E. Schnack, R. Drumm: Zur exakten Erfassung des Randspannungsvektors bei der Hybridmethode. ZAMM Bd. 62, 1982, pp. 167–170.

    MATH  Google Scholar 

  14. H. Neuber: Elastostatik und Festigkeitslehre. Springer-Verlag, Berlin, Heidelberg, New York, 1971.

    MATH  Google Scholar 

  15. R. Drumm: Zur effektiven FEM-Analyse ebener Spannungskonzentrationsprobleme, Diss. Univ. Karlsruhe, 1982.

    Google Scholar 

  16. E. Schnack: An optimization procedure for stress concentrations by the finiteelement-technique. Int. J. Num. Meth. Engng., Vol. 14, No. 1, 1979, pp. 115–124.

    CrossRef  MATH  Google Scholar 

  17. E. Schnack, M. Wolf: Die Konstruktion von Spannungsansätzen der Hybridspannungsmethode. Forsch. Ing.-Wes., Bd. 44, Nr. 3, 1978, pp. 74–79.

    CrossRef  Google Scholar 

  18. E. Schnack: Zur Berechnung rotationsyymmetrischer Kerbprobleme mit der Methode der finiten Elemente. Forsch. Ing.-Wes. Bd. 42, Nr. 3, 1976, pp. 73–81.

    CrossRef  Google Scholar 

  19. V.Ph. Nguyen: Automatic mesh generation with tetrahedron elements. Int. J. Num. Meth. Engng., Vol. 18, 1982, pp. 273–289.

    CrossRef  MATH  Google Scholar 

  20. E. Schnack: Effektivitätsuntersuchung für numerische Verfahren bei Festigkeitsberechnungen. VDI-Z 119, 1977, Nr. 1/2, pp. 43–50.

    Google Scholar 

  21. J.R. Rice: A path independent integral and the approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. Trans. ASME Series, E 35, 2, 1968, pp. 379–386.

    CrossRef  Google Scholar 

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Dedicated to Prof. Dr. Dr. Heinz Neuber for his 78th birthday

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© 1985 Springer-Verlag

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Schnack, E. (1985). Singularities of cracks with generalized finite elements. In: Grisvard, P., Wendland, W.L., Whiteman, J.R. (eds) Singularities and Constructive Methods for Their Treatment. Lecture Notes in Mathematics, vol 1121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076275

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  • DOI: https://doi.org/10.1007/BFb0076275

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-15219-4

  • Online ISBN: 978-3-540-39377-1

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