An Application of the BEM Numerical Green’s Function Procedure to Study Cracks in Reissner’s Plates


The Numerical Green’s Function (NGF) technique, previously proposed by the present authors, is here extended to fracture mechanics problems involving Reissner’s plate theory. The technique numerically produces a plate bending fundamental Green’s function that automatically includes embedded cracks to be used in the classical boundary element method (BEM) to solve this class of problems. The applications discussed include torsion, bending moment and shear force loadings. In addition, also presented is a series of numerical results computed in terms of normalized stress intensity factors to illustrate the good accuracy of the procedure.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Boduroglu, H., Erdogan, F.: Internal and edge cracks in a plate of finite width under bending, Journal of Applied Mechanics, ASME, 50, 621–629, (1983).MATHGoogle Scholar
  2. Guimarães, S., Figueiredo, V.S., Telles, J.C.F.: Reissner’s Plate Green’s function for fracture mechanics (in Portuguese), XXI CILAMCE – Ibero-Latin-American Congress on Computational Methods in Engineering, (L. Vaz, ed.), Rio de Janeiro, November, (2000).Google Scholar
  3. Karam, V.J., Telles, J.C.F.: On boundary elements for Reissner’s plate bending, Engineering Analysis with Boundary Elements, 5, 1 21–27, (1988).CrossRefGoogle Scholar
  4. Murthy, M.V.V., Raju, K.N., Viswanath, S.: On the bending stress distribution at the tip of a stationary crack form Reissner’s theory, International Journal of Fracture, 17, 537–552, (1981).CrossRefGoogle Scholar
  5. Reissner, E: On the bending of elastic plates, Quarterly of Applied Mechanics, 5, 55–68, (1947).MATHMathSciNetGoogle Scholar
  6. Silveira, N.P.P., Guimarães, S., Telles, J.C.F.: A numerical Green’s function BEM formulation for crack growth simulation, Engineering Analysis with Boundary Elements, 29(11) 978–985, (2005).CrossRefGoogle Scholar
  7. Telles, J.C.F.. A Self-adaptive co-ordinate transformation for efficient numerical evaluation of general boundary element integrals, International Journal for Numerical Methods in Engineering, 24 959–973, (1987).MATHCrossRefGoogle Scholar
  8. Telles, J.C.F., Castor, G.S., Guimarães, S.: A numerical Green’s function approach for boundary elements applied to fracture mechanics, International Journal for Numerical Methods in Engineering, 38, 3259–3274, (1995).MATHCrossRefGoogle Scholar
  9. Telles, J.C.F., Guimarães, S.: Green’s function: a numerical generation for fracture mechanics problems via boundary elements, Computer Methods in Applied Mechanics and Engineering, 188 847–858, (2000).MATHCrossRefGoogle Scholar
  10. Vander Weeën, F.: Application of the boundary integral equation method to Reissner’s plate model, International Journal for Numerical Methods in Engineering, 18, 1–10, (1982).MATHCrossRefGoogle Scholar
  11. Wang, N.M. Effects of plate thickness on the bending of an elastic plate containing a crack, Journal of Mathematics and Physics, 47, 371–390, (1968).MATHGoogle Scholar
  12. Wang, N.M. Twisting of an elastic plate containing a crack, International Journal of Fracture Mechanics, 6(4) 367–378, (1970).CrossRefGoogle Scholar
  13. Wearing, J.L., Ahmadi-Brooghami, S.Y.: Fracture analysis of plate bending problems using the boundary element method, In: Plate Bending Analysis With Boundary Elements, (M.H. Aliabadi, ed.), Computational Mechanics Publications, Southampton, (1998).Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Programa de Engenharia CivilCOPPE/UFRJRio de JaneiroBrazil

Personalised recommendations