메뉴 건너뛰기




Volumn 197, Issue 6-8, 2008, Pages 487-504

Analysis and applications of a generalized finite element method with global-local enrichment functions

Author keywords

Extended finite element method; Fracture mechanics; Generalized finite element method; Global local; Meshfree; Multiple cracks

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; CRACKS; DEGREES OF FREEDOM (MECHANICS); FRACTURE MECHANICS;

EID: 36048939772     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.08.017     Document Type: Article
Times cited : (179)

References (58)
  • 1
    • 0035075413 scopus 로고    scopus 로고
    • Locally adapted tetrahedral meshes using bisection
    • Arnold D.N., Mukherjee A., and Pouly L. Locally adapted tetrahedral meshes using bisection. SIAM J. Sci. Comput. 22 2 (2000) 431-448
    • (2000) SIAM J. Sci. Comput. , vol.22 , Issue.2 , pp. 431-448
    • Arnold, D.N.1    Mukherjee, A.2    Pouly, L.3
  • 2
    • 34250459417 scopus 로고
    • The finite element method with lagrange multipliers
    • Babuška I. The finite element method with lagrange multipliers. Numer. Math. 20 (1973) 179-192
    • (1973) Numer. Math. , vol.20 , pp. 179-192
    • Babuška, I.1
  • 3
    • 23944523388 scopus 로고    scopus 로고
    • The splitting method as a tool for multiple damage analysis
    • Babuška I., and Andersson B. The splitting method as a tool for multiple damage analysis. SIAM J. Sci. Comput. 26 (2005) 1114-1145
    • (2005) SIAM J. Sci. Comput. , vol.26 , pp. 1114-1145
    • Babuška, I.1    Andersson, B.2
  • 4
    • 1542681822 scopus 로고    scopus 로고
    • Survey of meshless and generalized finite element methods: a unified approach
    • Babuška I., Banerjee U., and Osborn J.E. Survey of meshless and generalized finite element methods: a unified approach. Acta Numer. 12 May (2003) 1-125
    • (2003) Acta Numer. , vol.12 , Issue.May , pp. 1-125
    • Babuška, I.1    Banerjee, U.2    Osborn, J.E.3
  • 5
    • 0028483749 scopus 로고
    • Special finite element methods for a class of second order elliptic problems with rough coefficients
    • Babuška I., Caloz G., and Osborn J.E. Special finite element methods for a class of second order elliptic problems with rough coefficients. SIAM J. Numer. Anal. 31 4 (1994) 745-981
    • (1994) SIAM J. Numer. Anal. , vol.31 , Issue.4 , pp. 745-981
    • Babuška, I.1    Caloz, G.2    Osborn, J.E.3
  • 6
    • 36048947839 scopus 로고    scopus 로고
    • I. Babuška, J.M. Melenk, The partition of unity finite element method, Technical Report BN-1185, Inst. for Phys. Sci. Tech., University of Maryland, June 1995.
  • 8
    • 34250882899 scopus 로고
    • Local mesh refinement in 2 and 3 dimensions
    • Bansch E. Local mesh refinement in 2 and 3 dimensions. Impact Comput. Sci. Engrg. 3 (1991) 181-191
    • (1991) Impact Comput. Sci. Engrg. , vol.3 , pp. 181-191
    • Bansch, E.1
  • 9
    • 36048991967 scopus 로고    scopus 로고
    • R. Becker, P. Hansbo, A finite element method for domain decomposition with non-matching grids, Technical Report RR-3613, INRIA, 1999.
  • 10
    • 0032649861 scopus 로고    scopus 로고
    • Elastic crack growth in finite elements with minimal remeshing
    • Belytschko T., and Black T. Elastic crack growth in finite elements with minimal remeshing. Int. J. Numer. Methods Engrg. 45 (1999) 601-620
    • (1999) Int. J. Numer. Methods Engrg. , vol.45 , pp. 601-620
    • Belytschko, T.1    Black, T.2
  • 11
    • 0002336587 scopus 로고
    • A new non-conforming approach to domain decomposition: the mortar element method
    • Brezis H., and Lions J.L. (Eds), Pitman
    • Bernadi C., Maday Y., and Patera A. A new non-conforming approach to domain decomposition: the mortar element method. In: Brezis H., and Lions J.L. (Eds). Nonlinear Partial Differential Equations and their Applications (1994), Pitman 13-51
    • (1994) Nonlinear Partial Differential Equations and their Applications , pp. 13-51
    • Bernadi, C.1    Maday, Y.2    Patera, A.3
  • 13
    • 0343462243 scopus 로고    scopus 로고
    • A discontinuous finite element-base domain decomposition method
    • Carmo E.G.D., and Duarte A.V.C. A discontinuous finite element-base domain decomposition method. Comput. Methods Appl. Mech. Engrg. 190 (2000) 825-843
    • (2000) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 825-843
    • Carmo, E.G.D.1    Duarte, A.V.C.2
  • 14
    • 13944273817 scopus 로고    scopus 로고
    • Stress intensity factors of semi-elliptical surface cracks in pressure vessels by global-local finite element methodology
    • Diamantoudis A.Th., and Labeas G.N. Stress intensity factors of semi-elliptical surface cracks in pressure vessels by global-local finite element methodology. Engrg. Fract. Mech. 72 (2005) 1299-1312
    • (2005) Engrg. Fract. Mech. , vol.72 , pp. 1299-1312
    • Diamantoudis, A.Th.1    Labeas, G.N.2
  • 15
    • 0342520886 scopus 로고    scopus 로고
    • Discontinuous enrichment in finite elements with a partition of unity method
    • Dolbow J., Moes N., and Belytschko T. Discontinuous enrichment in finite elements with a partition of unity method. Finite Elem. Anal. Des. 36 (2000) 235-260
    • (2000) Finite Elem. Anal. Des. , vol.36 , pp. 235-260
    • Dolbow, J.1    Moes, N.2    Belytschko, T.3
  • 16
    • 36048975246 scopus 로고    scopus 로고
    • C.A. Duarte, The hp Cloud Method. PhD dissertation, The University of Texas at Austin, December 1996. Austin, TX, USA.
  • 17
    • 0037203054 scopus 로고    scopus 로고
    • Mesh-independent directional p-enrichment using the generalized finite element method
    • Duarte C.A., and Babuška I. Mesh-independent directional p-enrichment using the generalized finite element method. Int. J. Numer. Methods Engrg. 55 12 (2002) 1477-1492
    • (2002) Int. J. Numer. Methods Engrg. , vol.55 , Issue.12 , pp. 1477-1492
    • Duarte, C.A.1    Babuška, I.2
  • 18
    • 36048934528 scopus 로고    scopus 로고
    • C.A. Duarte, I. Babuška, A global-local approach for the construction of enrichment functions for the generalized fem and its application to propagating three-dimensional cracks, in: V.M.A. Leitão, C.J.S. Alves, C.A. Duarte, (Eds.), ECCOMAS Thematic Conference on Meshless Methods, Lisbon, Portugal, 11-14 July 2005. p. 8.
  • 19
    • 36048944140 scopus 로고    scopus 로고
    • C.A. Duarte, I. Babuška, J.T. Oden, Generalized finite element methods for three dimensional structural mechanics problems, in: S.N. Atluri, P.E. O'Donoghue, (Eds.), Modeling and Simulation Based Engineering, vol. I, Proceedings of the International Conference on Computational Engineering Science, Atlanta, GA, October 5-9, 1998, Tech Science Press, 1998, pp. 53-58.
  • 20
    • 17544389134 scopus 로고    scopus 로고
    • Generalized finite element methods for three dimensional structural mechanics problems
    • Duarte C.A., Babuška I., and Oden J.T. Generalized finite element methods for three dimensional structural mechanics problems. Comput. Struct. 77 (2000) 215-232
    • (2000) Comput. Struct. , vol.77 , pp. 215-232
    • Duarte, C.A.1    Babuška, I.2    Oden, J.T.3
  • 21
    • 0035808194 scopus 로고    scopus 로고
    • A generalized finite element method for the simulation of three-dimensional dynamic crack propagation
    • Duarte C.A., Hamzeh O.N., Liszka T.J., and Tworzydlo W.W. A generalized finite element method for the simulation of three-dimensional dynamic crack propagation. Comput. Methods Appl. Mech. Engrg. 190 (2001) 2227-2262
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 2227-2262
    • Duarte, C.A.1    Hamzeh, O.N.2    Liszka, T.J.3    Tworzydlo, W.W.4
  • 22
    • 36048985886 scopus 로고    scopus 로고
    • C.A. Duarte, D.-J. Kim, I. Babuška, Chapter: A global-local approach for the construction of enrichment functions for the generalized fem and its application to three-dimensional cracks, in: V.M.A. Leitão, C.J.S. Alves, C.A. Duarte, (Eds.), Advances in Meshfree Techniques, vol. 5 Computational Methods in Applied Sciences, The Netherlands, 2007, Springer. ISBN 978-1-4020-6094-6.
  • 23
    • 35248895308 scopus 로고    scopus 로고
    • C.A. Duarte, L.G. Reno, A. Simone, A high-order generalized FEM for through-the-thickness branched cracks, Int. J. Numer. Methods Engrg., in Press .
  • 24
    • 36048930021 scopus 로고    scopus 로고
    • C.A.M. Duarte, J.T. Oden, Hp clouds-a meshless method to solve boundary-value problems. Technical Report 95-05, TICAM, The University of Texas at Austin, May 1995.
  • 27
    • 0027110443 scopus 로고
    • The s-version of the finite element method
    • Fish J. The s-version of the finite element method. Comput. Struct. 43 (1992) 539-547
    • (1992) Comput. Struct. , vol.43 , pp. 539-547
    • Fish, J.1
  • 30
    • 0031161210 scopus 로고    scopus 로고
    • A multiscale finite element method for elliptic problems in composite materials and porous media
    • Hou T.Y., and Wu X.-H. A multiscale finite element method for elliptic problems in composite materials and porous media. J. Comput. Phys. 134 (1997) 169-189
    • (1997) J. Comput. Phys. , vol.134 , pp. 169-189
    • Hou, T.Y.1    Wu, X.-H.2
  • 32
    • 0030380578 scopus 로고    scopus 로고
    • The partition of unity finite element method: Basic theory and applications
    • Melenk J.M., and Babuška I. The partition of unity finite element method: Basic theory and applications. Comput. Methods Appl. Mech. Engrg. 139 (1996) 289-314
    • (1996) Comput. Methods Appl. Mech. Engrg. , vol.139 , pp. 289-314
    • Melenk, J.M.1    Babuška, I.2
  • 34
    • 0033349534 scopus 로고    scopus 로고
    • A finite element method for crack growth without remeshing
    • Moes N., Dolbow J., and Belytschko T. A finite element method for crack growth without remeshing. Int. J. Numer. Methods Engrg. 46 (1999) 131-150
    • (1999) Int. J. Numer. Methods Engrg. , vol.46 , pp. 131-150
    • Moes, N.1    Dolbow, J.2    Belytschko, T.3
  • 35
    • 0037140062 scopus 로고    scopus 로고
    • Non-planar 3D crack growth by the extended finite element and level sets - Part I: Mechanical model
    • Moës N., Gravouil A., and Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets - Part I: Mechanical model. Int. J. Numer. Methods Engrg. 53 (2002) 2549-2568
    • (2002) Int. J. Numer. Methods Engrg. , vol.53 , pp. 2549-2568
    • Moës, N.1    Gravouil, A.2    Belytschko, T.3
  • 36
    • 0003331317 scopus 로고
    • Elliptic problems in domains with piecewise smooth boundaries
    • Walter de Gruyter, Berlin
    • Nazarov S.A., and Plamenevsky B.A. Elliptic problems in domains with piecewise smooth boundaries. De Gruyter Expositions in Mathematics vol. 13 (1994), Walter de Gruyter, Berlin
    • (1994) De Gruyter Expositions in Mathematics , vol.13
    • Nazarov, S.A.1    Plamenevsky, B.A.2
  • 37
    • 0022900583 scopus 로고
    • Global-local methodologies and their applications to nonlinear analysis
    • Noor A.K. Global-local methodologies and their applications to nonlinear analysis. Finite Elem. Anal. Des. 2 (1986) 333-346
    • (1986) Finite Elem. Anal. Des. , vol.2 , pp. 333-346
    • Noor, A.K.1
  • 39
    • 36048953582 scopus 로고    scopus 로고
    • J.T. Oden, C.A. Duarte, Chapter: Clouds, Cracks and FEM's, in: B.D. Reddy, (Ed.), Recent Developments in Computational and Applied Mechanics, Barcelona, Spain, 1997. International Center for Numerical Methods in Engineering, CIMNE, pp. 302-321.
  • 42
    • 0037196858 scopus 로고    scopus 로고
    • A simple algorithm for localized construction of non-matching structural interfaces
    • Park C., Felippa C.A., and Rebel G. A simple algorithm for localized construction of non-matching structural interfaces. Int. J. Numer. Methods Engrg. 53 (2002) 2117-2142
    • (2002) Int. J. Numer. Methods Engrg. , vol.53 , pp. 2117-2142
    • Park, C.1    Felippa, C.A.2    Rebel, G.3
  • 43
    • 0037399641 scopus 로고    scopus 로고
    • Efficient finite element analysis using mesh superposition technique
    • Park J.W., Hwang J.W., and Kim Y.H. Efficient finite element analysis using mesh superposition technique. Finite Elem. Anal. Des. 39 (2003) 619-638
    • (2003) Finite Elem. Anal. Des. , vol.39 , pp. 619-638
    • Park, J.W.1    Hwang, J.W.2    Kim, Y.H.3
  • 44
    • 36048933229 scopus 로고    scopus 로고
    • M.L. Parks, E. de Sturler, G. Mackey, D.D. Johnson, S. Maiti, Recycling Krylov subspaces for sequences of linear systems, Technical Report UIUCDCS-R-2004-2421, UILU-ENG-2004-1722, University of Illinois at Urbana-Champaign, Urbana, IL, March 2004.
  • 45
    • 36048931923 scopus 로고    scopus 로고
    • J.P. Pereira, X. Jiao, C.A. Duarte, A robust geometry engine for modeling 3D crack problems with the generalized finite element method, in: Seventh World Congress on Computational Mechanics, Los Angeles, CA, USA, 16-22 July 2006. Invited abstract.
  • 47
    • 33747440027 scopus 로고    scopus 로고
    • A generalized finite element method for polycrystals with discontinuous grain boundaries
    • Simone A., Duarte C.A., and van der Giessen E. A generalized finite element method for polycrystals with discontinuous grain boundaries. Int. J. Numer. Methods Engrg. 67 8 (2006) 1122-1145
    • (2006) Int. J. Numer. Methods Engrg. , vol.67 , Issue.8 , pp. 1122-1145
    • Simone, A.1    Duarte, C.A.2    van der Giessen, E.3
  • 49
  • 50
    • 0033904722 scopus 로고    scopus 로고
    • The generalized finite element method: An example of its implementation and illustration of its performance
    • Strouboulis T., Copps K., and Babuška I. The generalized finite element method: An example of its implementation and illustration of its performance. Int. J. Numer. Methods Engrg. 47 8 (2000) 1401-1417
    • (2000) Int. J. Numer. Methods Engrg. , vol.47 , Issue.8 , pp. 1401-1417
    • Strouboulis, T.1    Copps, K.2    Babuška, I.3
  • 52
    • 0043157619 scopus 로고    scopus 로고
    • Generalized finite element method using mesh-based handbooks: Application to problems in domains with many voids
    • Strouboulis T., Zhang L., and Babuška I. Generalized finite element method using mesh-based handbooks: Application to problems in domains with many voids. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3109-3161
    • (2003) Comput. Methods Appl. Mech. Engrg. , vol.192 , pp. 3109-3161
    • Strouboulis, T.1    Zhang, L.2    Babuška, I.3
  • 53
    • 3242689474 scopus 로고    scopus 로고
    • p-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems
    • Strouboulis T., Zhang L., and Babuška I. p-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems. Int. J. Numer. Methods Engrg. 60 (2004) 1639-1672
    • (2004) Int. J. Numer. Methods Engrg. , vol.60 , pp. 1639-1672
    • Strouboulis, T.1    Zhang, L.2    Babuška, I.3
  • 54
    • 0035860267 scopus 로고    scopus 로고
    • Modeling holes and inclusions by level sets in the extended finite element method
    • Sukumar N., Chopp D., Moes N., and Belytschko T. Modeling holes and inclusions by level sets in the extended finite element method. Comput. Methods Appl. Mech. Engrg. 190 (2001) 6183-6200
    • (2001) Comput. Methods Appl. Mech. Engrg. , vol.190 , pp. 6183-6200
    • Sukumar, N.1    Chopp, D.2    Moes, N.3    Belytschko, T.4
  • 55
    • 0034255073 scopus 로고    scopus 로고
    • Extended finite element method for three-dimensional crack modelling
    • Sukumar N., Moes N., Moran B., and Belytschko T. Extended finite element method for three-dimensional crack modelling. Int. J. Numer. Methods Engrg. 48 11 (2000) 1549-1570
    • (2000) Int. J. Numer. Methods Engrg. , vol.48 , Issue.11 , pp. 1549-1570
    • Sukumar, N.1    Moes, N.2    Moran, B.3    Belytschko, T.4
  • 57
    • 0036880243 scopus 로고    scopus 로고
    • A comparison of dual lagrange multiplier spaces for mortar finite element discretizations
    • Wohlmuth B.I. A comparison of dual lagrange multiplier spaces for mortar finite element discretizations. Math. Model. Numer. Anal. 36 6 (2002) 995-1012
    • (2002) Math. Model. Numer. Anal. , vol.36 , Issue.6 , pp. 995-1012
    • Wohlmuth, B.I.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.