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Symmetric Galerkin BEM in 3D Elasticity: Computational Aspects and Applications to Fracture Mechanics

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Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 433))

Abstract

The formulation of the symmetric Galerkin BEM for 3D elastic fracture mechanics problems and some relevant computational aspects are presented in this paper; the method is employed for the evaluation of stress intensity factors and for the modeling of fatigue crack growth. In the latter context a propagation algorithm has been developed and implemented into a fully automated numerical code which is used to analyze two example problems concerning the fatigue growth of surface breaking cracks.

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References

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

    Article  MATH  MathSciNet  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.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  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.

    Article  Google Scholar 

  • Crouch, S.L. and Starfield, A.M. (1983) Boundary Element Methods in Solid Mechanics,George Allen and Unwin,.

    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.

    Article  MATH  MathSciNet  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.

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  • Frangi, A., Novati, G., Springhetti, R. and Rovizzi, M. (2001) 3D fracture analysis by the symmetric Galerkin BEM, Computat. Mech.,accepted for publication.

    Google Scholar 

  • Ganguly, S., Layton, J.B. and Balakrishna, C. (2000) Symmetric coupling of multi-zone curved Galerkin boundary elements with finite elements in elasticity, Int. J. Num. Meth. Engng., 48, 633–654.

    Article  MATH  Google Scholar 

  • Hartranft, R.J. and Sih, G.C. (1970) An approximate three-dimensional theory of plates with application to crack problems, Int. J. Engng. Sci., 8, 711–729.

    Article  MATH  Google Scholar 

  • Hills, D.A., Kelly, P.A. (1996) Solution of Crack Problems, Kluwer Academic Press, Dortrecht.

    Book  MATH  Google Scholar 

  • Kassir, M.K. and Sih, G.C. (1966) Three dimensional stress distribution around an elliptical crack under arbirary loadings, J. Applied Mech., 33, 602–615.

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Maier, G., Miccoli, S., Novati, G. and Sirtori, S. (1992) A Galerkin symmetric boundary element method in plasticity: formulation and implementation, in Kane, J.H., Maier, G., Tosaka, N. and Atluri, S.N. (eds.), Advances in Boundary Elements Techniques, Springer Verlag, 288–328.

    Google Scholar 

  • Nishimura, N. and Kobayashi, S. (1989) A regularized boundary integral equation method for elastodynamic crack problems, Computat. Mech., 4, 319–328.

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Paulino, G.H. and Gray, L.J. (1999) Galerkin residuals for adaptive symmetric-Galerkin boundary element methods, Journal of Engineering Mechanics (ASCE), 125, 575–585.

    Article  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

  • 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. Fracture Mech., 11, 817–829.

    Article  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  • Sirtori, S. (1979) General stress analysis method by means of integral equations and boundary elements, Meccanica, 14, 210–218.

    Article  MATH  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.

    Article  MATH  MathSciNet  Google Scholar 

  • Tada, S., Paris, P. and Irwin, G. (1985) The Stress Analysis of Cracks Handbook, Dell Research Corporation, St. Louis.

    Google Scholar 

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

    Article  Google Scholar 

  • Wawrzynek, P.A., Martha, L.F. and Ingraffea, A.R. (2000) A computational environment for the simulation of fracture processes in three dimensions, in Rosakis, A.J. (eds.), Annal. Numer. Exper. Aspects of Three Dimensional Fracture Processes, ASME, AND-91, 321–327.

    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.

    Article  MATH  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.

    Article  MATH  Google Scholar 

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© 2002 Springer-Verlag Wien

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Giorgio, N., Attilio, F. (2002). Symmetric Galerkin BEM in 3D Elasticity: Computational Aspects and Applications to Fracture Mechanics. In: Kompiš, V. (eds) Selected Topics in Boundary Integral Formulations for Solids and Fluids. International Centre for Mechanical Sciences, vol 433. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2548-9_13

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  • DOI: https://doi.org/10.1007/978-3-7091-2548-9_13

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-83693-4

  • Online ISBN: 978-3-7091-2548-9

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