Skip to main content
SpringerLink
Log in

Mixed mode cracks in Reissner plates

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Based on the sixth order Reissner plate theory, the generalized displacement functions for a cracked plate are derived by eigenfunction expansion method. The fractal two-level finite element method is employed to obtain the stress (moment and shear) intensity factors for the center cracked plate subjected to out-of-plane bending and twisting loads. The numerical results from the present method are checked with those available in literature. Highly accurate stress intensity factors are predicted for a wide range of thickness to crack length ratio and a full range of PoissonÆs ratio provided that the radius of fractal mesh to thickness ratio is not less than \(\frac{1}{{10}}\).

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Alwar, R.S. and Ramachandran Nambissan, K.N. (1983). Three-dimensional finite element analysis of cracked thick plates in bending. International Journal for Numerical Methods in Engineering 19, 293-303.

    Google Scholar 

  • Barsoum, R.S. (1976). A degenrate solid element for linear fracture analysis of plate bending and general shells. International Journal for Numerical Methods in Engineering 10, 551-564.

    Google Scholar 

  • Boduroglu, H. and Erdogan, F. (1983). Internal and edge cracks in a plate of finite width under bending. Journal of Applied Mechanics 50 621-629.

    Google Scholar 

  • Hartranft, R.J. and Sih, G.C. (1968). Effect of plate thickness on the bending stress distribution around through cracks. Journal of Mathematics and Physics 47, 276-291.

    Google Scholar 

  • Hartranft, R.J. and Sih, G.C. (1969). The use of eigenfunction expansions in general solution of three-dimensional crack problem. Journal of Mathematics and Mechanics 19, 123-138.

    Google Scholar 

  • Huang, M. and Long, Y. (1988). Calculation of stress intensity factors of cracked Reissner plates by the sub-region mixed finite element method. Computers and Structures 30, 837-840.

    Google Scholar 

  • Hui, C.Y. and Zehnder, A.T. (1993). A theory for the fracture of thin plates subjected to bending and twisting moments. International Journal of Fracture 61, 211-229.

    Google Scholar 

  • Irwin, G.R. (1957). Analysis of stresses and strains near the end of a crack transversing a plate. Journal of Applied Mechanics 24, 361-364.

    Google Scholar 

  • Joseph, P.F. and Erdogan, F. (1991). Bending of a thin Reissner plate with a through crack. Journal of Applied Mechanics 58, 842-846.

    Google Scholar 

  • Joseph, P.F. and Erdogan, F. (1989). Surface crack problems in plates. International Journal of Fracture 41, 105-131.

    Google Scholar 

  • Knowles, J.K. and Wang, N.M. (1960). On the bending of n elastic plate containing a crack. Journal of Mathematics and Physics 39, 223-236.

    Google Scholar 

  • Leung, A.Y.T. and Su, R.K.L. (1996a). Fractal two-level finite element analysis of cracked Reissner's plate. Thin Walled Structures 24, 315-334.

    Google Scholar 

  • Leung, A.Y.T and Su, R.K.L. (1996b). Fractal two-level finite element method for cracked classical plates using DKT elements. Engineering Fracture Mechanics 54, 703-711.

    Google Scholar 

  • Leung, A.Y.T. and Su, R.K.L. (1994). Mode I crack problems by fractal two-level finite element methods. Engineering Fracture Mechanics 48, 847-856.

    Google Scholar 

  • Leung, A.Y.T. and Su, R.K.L. (1995a). Mixed mode two-dimensional crack problems by fractal two-level finite element method. Engineering Fracture Mechanics 51, 889-895.

    Google Scholar 

  • Leung, A.Y.T. and Su, R.K.L. (1995b). Body-force linear elastic stress intensity factor calculation using fractal two-level finite element method. Engineering Fracture Mechanics 51, 879-888.

    Google Scholar 

  • Murthy, M.V.V. Raju, K.N. and Viswanath, S. (1981). On the bending stress distribution at the tip of a stationary crack from Reissner's theory. International Journal of Fracture 17, 537-552.

    Google Scholar 

  • Murthy, M.V.V. Viswanath, S. Krishna Murty, A.V. and Rao, K.P. (1988). A two-dimensional model for crack closure effect in plates under bending. Engineering Fracture Mechanics 29, 435-452.

    Google Scholar 

  • Rhee, H.C. and Atluri, S.N. (1982). Hybrid stress finite element analysis of bending of a plate with a through flaw. International Journal for Numerical Methods in Engineering 18, 259-271.

    Google Scholar 

  • Sih, G.C. Paris, P.C. and Erdogan, F. (1962). Crack-tip, stress intensity factors for the plane extension and plate bending problem. Journal of Applied Mechanics 29, 306-312.

    Google Scholar 

  • Sosa, H.A. and Eischen, J.W. (1986). Computation of stress intensity factors for plate bending via a pathindependent integral. Engineering Fracture Mechanics 25, 451-462.

    Google Scholar 

  • Sosa, H.A. (1986). On The Analysis of Bars, Beams and Plates with Defects, Ph.D. Thesis, Stanford University.

  • Viswanath, S. and Murthy, M.V.V. (1989). A special crack tip element for bending of plates with through cracks from a sixt-order plate theory. Engineering Fracture Mechanics 32, 91-109.

    Google Scholar 

  • Viswanath, S. Lakshminarayana, H.V. and Ravindranath, D.D. (1989). A modified crack closure integral method for calculating stress intensity factors for cracked plates subject to bending loads. International Journal of Fracture 41, R45-50.

    Google Scholar 

  • Wahba, N.N. (1985). On the use of singular displacement finite elements for cracked plate in bending. International Journal of Fracture 27, 3-30.

    Google Scholar 

  • Wang, N.M. (1968). Effects of plate thickness on the bending of an elastic plate containing a crack. Journal of Mathematics and Physics 47, 371-390.

    Google Scholar 

  • Wang, N.M. (1970). Twisting of an elastic plate containing a crack. International Journal of Fracture Mechanics 6, 367-378.

    Google Scholar 

  • Yagawa, G. and Nishioka, T. (1979). Finite element analysis of stress intensity factors for plane extnsion and plate bending problems. International Journal for Numerical Methods in Engineering 14, 727-740.

    Google Scholar 

  • Young, M.J. and Sun, C.T. (1993a). Cracked plates subjected to out-of-plane tearing loads. International Journal of Fracture 60, 1-18.

    Google Scholar 

  • Young, M.J. and Sun, C.T. (1993b). On the strain energy release rate for a cracked plate subjected to out-to-plane bending moment. International Journal of Fracture 60, 227-247.

    Google Scholar 

  • Zienkiewicz, O.C. and Taylor, R.L. (1991). The Finite Element Method, fourth edition, 2, McGraw-Hill, New York.

Download references

Author information

Authors and Affiliations

  1. Department of Civil Engineering, University of Hong Kong, Pokfulam Road, Hong Kong

    R.K.L. Su

  2. Department of Building and Construction Engineering, City University of Hong Kong, Tat Chee Avenue, Hong Kong

    A.Y.T. Leung

Authors
  1. R.K.L. Su
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A.Y.T. Leung
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Su, R., Leung, A. Mixed mode cracks in Reissner plates. International Journal of Fracture 107, 235–257 (2001). https://doi.org/10.1023/A:1007652028645

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1007652028645

Search

Navigation