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Finite element analysis for stress intensity factors

  • Finite Elements
  • Conference paper
  • First Online:
Computing Methods in Applied Sciences and Engineering, 1977, I

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 704))

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Abstract

The finite element method is developed on the basis of the concept of superposition of solutions for stress intensity factor analyses. The method is discussed in a general form for boundary value problems with geometric singularities, and numerical results are shown for two-and three-dimensional problems.

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References

  1. Irwin, G.R., Fracture. Handbuch der Physik, Bd. 4, Springer, 1958, 551–590.

    Google Scholar 

  2. Paris, P.C., & Sih, G.C., Stress Analysis of Cracks. Proc. of the Symposium on Fracture Toughness and its Applications, STP 381, ASTM, 1965, 38–80.

    Google Scholar 

  3. Sih, G.C. (ed.), Mechanics of Fracture, Vol. 1, Noordhoff, 1973.

    Google Scholar 

  4. Motz, H., The Treatment of Singularities of Partial Differential Equations by Relaxation Methods. Quart. Appl. Mech., Vol. 6, 1953, 371–377.

    MathSciNet  MATH  Google Scholar 

  5. Woods, L.C., The Relaxation Treatment of Singular Points in Poisson's Equation, Q. J. Mech. & Appl. Math., Vol. 6, 1953, 163–185.

    Article  MATH  Google Scholar 

  6. Wilson, W.K., Finite Element Methods for Elastic Bodies Containing Cracks, in Ref. 3, 484–515.

    Google Scholar 

  7. Dixon, J. R., & Pook, L.P., Stress Intensity Factors Calculated Generally by the Finite Element Technique. Nature, Vol.224, 1969, 166–167.

    Article  Google Scholar 

  8. Rice, J.R., A Path Independent Integral and the Approximate Analysis of Stress Concentration by Notches and Cracks, J. Appl. Mech., Vol. 35, 1968, 379–386.

    Article  Google Scholar 

  9. Miyata, H., Shida, S., & Kusumoto, S., The Simple Method of Evaluation of Stress Intensity Factor Using the Finite Element Method. Proc. 1974 Symp. on Mech. Behavior of Materials, Vol. 1, Soc. of Material Sci., Japan, 1974, 63–80.

    Google Scholar 

  10. Yamamoto, Y., Finite Element Approaches with the Aid of Analytical Solutions, Recent Advances on Matrix Meth. of Struct. Analysis and Design, Univ. of Alabama Press, 1971, 85–103.

    Google Scholar 

  11. Yamamoto, Y., & Tokuda, N., Determination of Stress Intensity Factors in Cracked Plates by the Finite Element Method. Int. J. Numer. Meth. in Engng., Vol. 6, 1973, 427–439.

    Article  MATH  Google Scholar 

  12. Yamamoto, Y., Tokuda, N., & Sumi, Y., Finite Element Treatment of Singularities of Boundary Value Problems and its Application to Analysis of Stress Intensity Factors. Theory and Practice in Finite Element Structural Analysis, Univ. of Tokyo Press, 1973, 75–90.

    Google Scholar 

  13. Yamamoto, Y., & Sumi, Y., Stress Intensity Factors of a Twisted-Round-Bar with a Circumferential Crack. Int. J. of Fracture, Vol. 10, 1974, 269–271.

    Article  Google Scholar 

  14. Yamamoto, Y., Sumi, Y, & Ao, K., Stress Intensity Factors of Cracks Emanating from Semi-Elliptical Side Notches in Plates. Int. J. of Fracture, Vol. 10, 1974, 593–595.

    Article  Google Scholar 

  15. Yamamoto, Y., & Ao, K., Stress Intensity Factors of Cracks in Notched Bend Specimens. Int. J. of Fracture, Vol. 12, 1976, 495–498.

    Google Scholar 

  16. Yamamoto, Y., & Sumi, Y., Stress Intensity Factors for Three-Dimensional Cracks. to be published in Int. J. of Fracture.

    Google Scholar 

  17. Pian, T.H.H., Tong, P., & Luk, C.H., Elastic Crack Analysis by a Finite Element Hybrid Method. Proc. Third Conf. on Matrix Method of Struct. Mech., AFFDL-TR-71-160, 1971, 690–711.

    Google Scholar 

  18. Yagawa, G., Nishioka, T., Ando, Y., & Ogura, N., The Finite-Element Calculation of Stress Intensity Factors Using Superposition, Computational Fracture Mechanics, ASME Special Publicstion, 1974, 21–34.

    Google Scholar 

  19. Williams, M.L., On the Stress Distribution at the Base of a Stationary Crack. J. Appl. Mech., Vol. 24, 1957, 109–114.

    MathSciNet  MATH  Google Scholar 

  20. Westergaard, H.M., Bearing Pressures and Cracks, J. Appl. Mech., Vol. 6, 1939, A49–A53.

    Google Scholar 

  21. Sih, G.C., & Liebowitz, H., Mathematical Theory of Brittle Fracture. Fracture: An Advanced Treatise, Vo. 2, Academic Press, 1968, 67–190.

    Google Scholar 

  22. Benthem, J. P., & Koiter, W.T., Asymptotic Approximations to Crack Problems. in Ref. 3, 131–178.

    Google Scholar 

  23. Benthem, J.P., Three-Dimensional State of Stress at the Vertex of a Quarter-Infinite Crack in a Half Space. Rep. No. 563, Laboratory of Engng. Mechanics, Delft Univ. of Technology, 1975.

    Google Scholar 

  24. Benthem, J.P., State of Stress at the Vertex of a Quarter-Infinite Crack in a Half-Space. Int. J. of Solids & Struct., Vol. 13, 1977, 479–497.

    Article  MATH  Google Scholar 

  25. Bazant, Z.P., & Estenssoro, L.F., General Numerical Method for Three-Dimensional Singularities in Cracked or Notched Elastic Solid, Fracture 1977, Vol. 3, ICF4, Waterloo, Canada, 1977, 371–385.

    Google Scholar 

  26. Sih, G.C., A Review of the Three-Dimensional Stress Problem for a Cracked Plate. Int. J. of Fracture Mech., Vol. 7, 1971, 39–385.

    Article  Google Scholar 

  27. Wilson, E.L., SOLID SAP, UCSESM 71-19, Struct. Engng. Laboratory, Univ. of California, Berkeley, California, 1971.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Dept. of Naval Architecture, Univ. of Tokyo, Bunkyo-ku, 113, Tokyo, Japan

    Yoshiyuki Yamamoto

  2. Dept. of Naval Architecture, Yokohama National University, Hodogaya-ku, 240, Yokohama, Japan

    Yoichi Sumi

Authors
  1. Yoshiyuki Yamamoto
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  2. Yoichi Sumi
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Editor information

R. Glowinski J. L. Lions Iria Laboria

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© 1979 Springer-Verlag

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Yamamoto, Y., Sumi, Y. (1979). Finite element analysis for stress intensity factors. In: Glowinski, R., Lions, J.L., Laboria, I. (eds) Computing Methods in Applied Sciences and Engineering, 1977, I. Lecture Notes in Mathematics, vol 704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0063619

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  • DOI: https://doi.org/10.1007/BFb0063619

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09123-3

  • Online ISBN: 978-3-540-35411-6

  • eBook Packages: Springer Book Archive

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