Skip to main content
SpringerLink
Log in

Fracture propagation in 3D by the symmetric Galerkin boundary element method

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

Abstract

The numerical simulation of fatigue crack propagation in 3D linear elastic bodies is addressed. The symmetric Galerkin BEM is employed, thus drastically reducing the remeshing work compared to what is needed by domain formulations. The propagation algorithm adopted has been implemented into a fully automated numerical code and utilized to analyze two examples concerning surface breaking cracks.

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

  • Andrä, H. and Schnack, E. (1997) Integration of singular Galerkin-type boundary element integrals for 3D elasticity, Numerische Mathematik 76, 143–165.

    Google Scholar 

  • Balakrishna, C., Gray, L.J. and Kane, J.H. (1994) Efficient analytical integration of symmetric Galerkin boundary integrals over curved elements: elasticity, Comp. Meth. Appl. Mech. Engng. 117, 157–179.

    Google Scholar 

  • Bonnet, M., Maier, G. and Polizzotto, C. (1998) Symmetric Galerkin boundary element method, Appl. Mech. Rev. 51, 669-704.

    Google Scholar 

  • Bonnet, M. (1993) A regularized Galerkin symmetric BIE formulation for mixed 3D elastic boundary values problems, Boundary Elements Abstracts & Newsletters 4, 109–113.

    Google Scholar 

  • Brown, M.W., Hay, E. and Miller, K.J. (1985) Fatigue at notches subjected to reversed torsion and static axial loads, Fatigue Fract. Engng. Mater. Struct. 8, 243–258.

    Google Scholar 

  • Cisilino, A.P. and Aliabadi, M.H. (1997) Three-dimensional BEM analysis for fatigue crack growth in welded components, Int. J. for Pressure Vessels and Piping 70, 135–144.

    Google Scholar 

  • Frangi, A. and Novati, G. (1996) Symmetric BE method in two dimensional elasticity: evaluation of double integrals for curved elements, Computat. Mech. 19, 58–68.

    Google Scholar 

  • Frangi, A. (1998) Regularization of boundary element formulations by the derivative transfer method, in Sládek, V., Sládek, J. (eds.), Singular Integrals in Boundary Element Methods, Advances in Boundary Elements, chap. 4, Computational Mechanics Publications, 125–164.

  • Frangi, A., Novati, G., Springhetti, R. and Rovizzi, M. (2002) 3D fracture analysis by the symmetric Galerkin BEM, Computat. Mech., 28, 221–231.

    Google Scholar 

  • Erichsen, S. and Sauter, S.A. (1998) Efficient automatic quadrature in 3-D Galerkin BEM, Comp. Meth. Appl. Mech. Engng. 157, 215–224.

    Google Scholar 

  • Lage, C. and Schwab, C. (2000) Advanced boundary element algorithms, in Whiteman, J.R. (eds.), Majelap 1999, Elsevier, 283–306.

  • Li, X. and Keer, L.M. (1992) A direct method for solving crack growth problems I, Int. J. Solids Struct. 29, 2735–2747.

    Google Scholar 

  • Li, X. and Keer, L.M. (1992) A direct method for solving crack growth problems Shear mode problems II, Int. J. Solids Struct. 29, 2749–2760.

    Google Scholar 

  • Li, S., Mear, M.E. and Xiao, L. (1998) Symmetric weak-form integral equation method for three-dimensional fracture analysis, Camp. Meth. Appl. Mech. Engng. 151, 435–459.

    Google Scholar 

  • Mi, Y. and Aliabadi, M.H. (1994) Three-dimensional crack growth simulation using BEM, Comp. Struct. 52, 871–878.

    Google Scholar 

  • Mi, Y. (1996) Three-dimensional Analysis of Crack Growth, Computational Mechanics Publications, Southampton.

    Google Scholar 

  • Pook, L.P. (1994) Some implications of corner point singularities, Engng. Fract. Mech. 48, 367–378.

    Google Scholar 

  • Raju, I.S. and Newman, J.C. (1977) Three dimensional finite-element analysis of finite-thickness fracture specimens, NASA-TN, D-8414.

  • Raju, I.S. and Newman, J.C. (1979) Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates, Engng. Fract. Mech. 11, 817–829.

    Google Scholar 

  • Sauter, S.A. and Schwab, C. (1997) Quadrature for hp-Galerkin BEM in 3-d, Numerische Mathematik 78, 211–258.

    Google Scholar 

  • Sirtori, S., Maier, G., Novati, G. and Miccoli, S. (1992) A Galerkin symmetric boundary element method in elasticity: formulation and implementation, Int. J. Num. Meth. Engng. 35, 255-)282.

    Google Scholar 

  • Thomson, K.D. and Sheppard, S.D. (1992) Stress intensity factors in shafts subjected to torsion and axial loading, Engng. Fract. Mech. 42, 1019–1034.

    Google Scholar 

  • Carter, B.J., Wawrzynek, P.A. and Ingraffea, A.R. (2000) Automated 3D Crack Growth Simulation, Int. J. Num. Meth. Engng. 47, 229–253.

    Google Scholar 

  • Wilde, A. and Aliabadi, M.H. (1999) A 3-D Dual BEM formulation for the analysis of crack growth, Computat. Mech. 23, 250–257.

    Google Scholar 

  • Xu, G. and Ortiz, M. (1993) A variational boundary integral method for the analysis of 3-D cracks of arbitrary geometry modelled as continuous distributions of dislocation loops, Int. J. Num. Meth. Engng. 36, 3675–3701.

    Google Scholar 

  • Yoshida, K., Nishimura, N. and Kobayashi, S. (2001) Application of fast multipole Galerkin boundary integral equation method to elastostatic crack problems, Int. J. Num. Meth. Engng. 50, 525–547.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Structural Engineering, Politecnico of Milano, P.za L. da Vinci 92, 20133, Milan, Italy

    A. Frangi

Authors
  1. A. Frangi
    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

Frangi, A. Fracture propagation in 3D by the symmetric Galerkin boundary element method. International Journal of Fracture 116, 313–330 (2002). https://doi.org/10.1023/A:1020770506931

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1020770506931

Search

Navigation