International Journal of Fracture

, Volume 134, Issue 3–4, pp 305–317 | Cite as

Analytical Solution for an Orthotropic Elastic Plate Containing Cracks



The problem of estimating the bending stress distribution in the neighborhood of a crack located on a single line in an orthotropic elastic plate of constant thickness subjected to bending moment or twisting moment is examined. Using classical plate theory and integral transform techniques, the general formulae for the bending moment and twisting moment in an elastic plate containing cracks located on a single line are derived. The solution is obtained in a closed form for the case in which there is a single crack in an infinite plate and the results are compared with those obtained from the literature.


Bending crack integral transform orthotropic plate stress intensity factor twisting 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Alwar, R.S., Ramachandran, K.N. 1983Influence of crack closure on the stress intensity factor for plates subjected to bending – A 3-D finite element analysisEngineering Fracture Mechanics17323333CrossRefGoogle Scholar
  2. Chattopadhyay, L. 2003Analytical determination of stress intensity factor for plate bending problemsInternational Journal of Computational Engineering Science4109119CrossRefGoogle Scholar
  3. Jones, D.L., Subramonian, N. 1983An analytical and experimental study of the plate tearing mode of fractureEngineering Fracture Mechanics174762Google Scholar
  4. Krenk, S. 1975The stress distribution in an infinite anisotropic plate with collinear cracksInternational Jourrnal of Solids and Structures11449460MATHGoogle Scholar
  5. Massabò, R., Brandinelli, L., Cox, B.N. 2003Mode I weight functions for an orthotropic double cantilever beamInternational Journal of Engineering Science4114971518Google Scholar
  6. Murakami, Y. 1987Stress Intensity Factors HandbookPergamon PressOxfordVol. 2Google Scholar
  7. Rybicki, E.F., Kanninen, M.F. 1977A finite element calculation of stress intensity factors by a modified crack closure integralEngineering Fracture Mechanics9931938CrossRefGoogle Scholar
  8. Sih, G.C., Paris, P.C., Erdogan, F. 1962Crack-tip, stress-intensity factors for plate extension and plate bending problemsASME Journal of Applied Mechanics9306312Google Scholar
  9. Timoshenko, S.P 1959Theory of Plates and ShellsMcGraw Hill Book CompanyAucklandGoogle Scholar
  10. Viz, M.J., Potyondy, D.O., Zehnder, A.T., Rankin, C.C., Riks, E. 1995International Journal of Fracture722138Google Scholar
  11. Williams, M.L. 1961The bending stress distribution at the base of a stationary crack, ASMEJournal of Applied Mechanics287882MATHGoogle Scholar
  12. Zehnder, A.T., Hui, C.-Y. 1994Stress intensity factors for plate bending and shearing problemsJournal of Applied Mechanics61719722Google Scholar
  13. Zucchini, A., Hui, C.-Y., Zehnder, A.T. 2000Crack tip stress fields for thin plates in bending, shear and twisting, a three dimensional finite element studyInternational Journal of Fracture104387407CrossRefGoogle Scholar

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Structures DivisionNational Aerospace LaboratoriesBangaloreIndia

Personalised recommendations