Skip to main content
SpringerLink
Log in

Solutions of plane crack problems by mapping technique

  • Chapter
Methods of analysis and solutions of crack problems

Part of the book series: Mechanics of fracture ((MEFA,volume 1))

Abstract

The analysis of crack problems in plane elasticity has intrigued mathematicians for nearly sixty years. Inglis [1] found the solution for a single crack in an infinite sheet with the use of elliptic coordinates. Since then, many mathematical approaches with wide ranges of sophistication have been applied to a variety of crack configurations and loading conditions. It is easy to appreciate the mathematical interest in a problem area in which solution techniques span such diverse topics as analytic function theory, integral equations, transform methods, conformal mapping, boundary collocation, finite differences, finite elements, asymptotic methods, etc.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Inglis, C. E, Trans. Roy. Inst. Naval Architecks, 60, p. 219 (1913).

    Google Scholar 

  2. Kolosoff, G., Doctoral dissertation, Dorpat (1909).

    Google Scholar 

  3. Irwin, G. R., J. Appl. Mech., 24, p. 361 (1957).

    Google Scholar 

  4. Griffith, A. A., Phil. Trans. Roy. Soc. London, Series A221, p. 163 (1921).

    Article  ADS  Google Scholar 

  5. Bowie, O. L., J. Math. and Phys., 35, p. 60 (1956).

    MathSciNet  MATH  Google Scholar 

  6. Bowie, O. L. and D. M. Neal, Intl. J. Fracture Mech., 6, p. 199 (1970a).

    Google Scholar 

  7. Bowie, O. L. and C. E. Freese, Army Symp. on Solid Mech., AMMRC, Watertown, Mass. (To appear in Intl. J. Frac. Mech. ) (1970a).

    Google Scholar 

  8. Muskhelishvili, N. I., Some Basic Problems of Mathematical Theory of Elasticity, Noordhoff, Groningen, Holland (1953).

    Google Scholar 

  9. Leknitskii, S. G., Theory of Elasticity of an Anisotropic Elastic Body, Holden-Day, San Francisco (1963).

    Google Scholar 

  10. Timoshenko, S. and J. N. Goodier, Theory of Elasticity, McGraw-Hill, New York (1951).

    MATH  Google Scholar 

  11. Savin, G. N., Stress Concentration Around Holes, Pergamon, New York (1961).

    Google Scholar 

  12. Timoshenko, S., Theory of Elasticity, McGraw-Hill, New York (1934).

    MATH  Google Scholar 

  13. Kartzivadze, I. N., Comp. rend. de l’acad. sc. de l’U.R.S.S., 20, p. 95 (1943).

    Google Scholar 

  14. Kolosoff, G., Z. Math. Physik, 62 (1914).

    Google Scholar 

  15. Muskhelishvili, N. I., Izv. A. N. SSSR, p. 663 (1919).

    Google Scholar 

  16. Griffith, A. A., Tech. Rpt. Aeronaut. Res. Comm. (Great Britain), 2, p. 668 (1927).

    Google Scholar 

  17. Neuber, H., Ingenieur-Archiv, 5, p. 242 (1934).

    Article  Google Scholar 

  18. Sneddon, I. N. and H. A. Elliott, Quart. Appl. Math., 4, p. 262 (1946).

    MathSciNet  Google Scholar 

  19. Wilmore, T. J., Quart. J. Mech. and Appl. Math., 2, p. 53 (1949).

    Article  Google Scholar 

  20. Sneddon, I. N., Crack Problems in the Mathematical Theory of Elasticity. North Carolina State College, Raleigh, N.C. (1961).

    Google Scholar 

  21. Sneddon, I. N., Proc. Roy. Soc. (London) Series A187, p. 229 (1946).

    Article  MathSciNet  ADS  Google Scholar 

  22. Williams, M. L., J. Appl. Mech., 24, p. 109 (1957).

    MathSciNet  MATH  Google Scholar 

  23. Irwin, G. R., in: Structure Mechanics; Proc. 1st. Symposium on Naval Structure Mechanics, Pergamon, New York (1960).

    Google Scholar 

  24. Sih, G. C., P. C. Paris and G. R. Irwin, Int. J. Fracture Mech., 1, p. 189 (1965).

    Google Scholar 

  25. Sih, G. C., P. C. Paris and F. Erdogan, J. Appl. Mech., 29, p. 306 (1962).

    Article  ADS  Google Scholar 

  26. Bowie, O. L., J. Appl. Mech., 31, p. 208 (1964a).

    Article  ADS  Google Scholar 

  27. Andersson, H., J. Mech. Phys. Solids, 17, p. 405 (1969).

    Article  ADS  MATH  Google Scholar 

  28. Morkovin, V., Quart. Appl. Math., 2, p. 350 (1945).

    MathSciNet  MATH  Google Scholar 

  29. Bowie, O. L. and C. E. Freese, Unpublished data at AMMRC, (1970b).

    Google Scholar 

  30. Koiter, W. T., J. Appl. Mech., 32, p. 237 (1965).

    Article  ADS  Google Scholar 

  31. Bowie, O. L., J. Appl. Mech., 31, p. 726 (1964b).

    Article  ADS  Google Scholar 

  32. Bloom, J. M., Int. J. Fract. Mech., Vol. 2, p. 597.

    Google Scholar 

  33. Bowie, O. L. and D. M. Neal, J. Appl. Mech., 32, p. 708, (1965).

    Article  ADS  Google Scholar 

  34. Gross, B., J. E. Srawley and W. F. Brown, NASA TND-2395, Lewis Research Center, Cleveland, Ohio (1964).

    Google Scholar 

  35. Akao, H. T., A. S. Kobayashi, J. of Basic Engineering, 89 (1967).

    Google Scholar 

  36. Brown, R. C. and A. S. Kobayashi, The Trend. University of Washington, 19, p. 8 (1967).

    Google Scholar 

  37. Rich, T. P. and R. Roberts, J. of Appl. Mech., 34, p. 777 (1967).

    Article  ADS  Google Scholar 

  38. Wieselmann, P. A., Doctoral Dissertation, Mass. Inst. of Tech., Cambridge, Mass. (1969).

    Google Scholar 

  39. Bowie, O. L., J. Math. and Phys., 45, p. 356 (1966).

    MATH  Google Scholar 

  40. Bowie, O. L. and J. J. McLaughlin, AMRA TR66–16, Army Materials Research Agency, Watertown, Mass. (1966).

    Google Scholar 

  41. Nehari, F., Conformal Mapping, McGraw-Hill, New York (1952).

    MATH  Google Scholar 

  42. Kobayashi, A. S., Document No. D2–23551 Boeing Co., Seattle, Washington (1964).

    Google Scholar 

  43. Bowie, O. L. and D. M. Neal, Eng. Fracture Mech., 2, p. 181 (1970b).

    Article  Google Scholar 

  44. Bowie, O. L. and C. E. Freese, Fourth National Symposium on Fracture Mechanics, Carnegie-Mellon, Pittsburgh, Pa., (To appear in J. Eng. Fract. Mech.) 1970c.

    Google Scholar 

  45. Newman, J. C., Jr., Master’s Thesis, Virginia Poly. Inst., Blacksburg, Va. (1969).

    Google Scholar 

  46. Newman, J. C., Jr., NASA TN. D-6376, Langley Research Center, Hampton, Va. (1971).

    Google Scholar 

  47. Sih, G. C. and H. Liebowitz, In Fracture (ed. H. Liebowitz) Academic Press, New York (1968).

    Google Scholar 

  48. Gandhi, K., J. of Strain Analysis, (To be published (1970)).

    Google Scholar 

  49. Freese, C. E., Private communication (1971).

    Google Scholar 

  50. Srawley, J. E. and B. Gross, NASA TN-D3820 Lewis Research Center, Cleveland, Ohio (1967).

    Google Scholar 

Download references

Authors
  1. O. L. Bowie
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, Pennsylvania, USA

    George C. Sih (Professor Mechanics and Director of the Institute of Fracture and Solid Mechanics) (Professor Mechanics and Director of the Institute of Fracture and Solid Mechanics)

Rights and permissions

Reprints and permissions

Copyright information

© 1973 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Bowie, O.L. (1973). Solutions of plane crack problems by mapping technique. In: Sih, G.C. (eds) Methods of analysis and solutions of crack problems. Mechanics of fracture, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2260-5_1

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-2260-5_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8246-6

  • Online ISBN: 978-94-017-2260-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation