Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2002 | 12 | 1 | 59-70

Tytuł artykułu

Error estimation and adaptivity for nonlinear FE analysis

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear problem: the failure analysis of a single-edge notched beam. The quasi-brittle response of concrete is modelled by means of a nonlocal damage model.

Rocznik

Tom

12

Numer

1

Strony

59-70

Opis fizyczny

Daty

wydano
2002
otrzymano
2001-09-01
poprawiono
2002-01-01

Twórcy

  • Departament de Matemàtica Aplicada III, E.T.S. de Ingenieros de Caminos, Edifici C2, Campus Nord, Universitat Politècnica de Catalunya, E08034 Barcelona, Spain
  • Departament de Matemàtica Aplicada III, E.T.S. de Ingenieros de Caminos, Edifici C2, Campus Nord, Universitat Politècnica de Catalunya, E08034 Barcelona, Spain
autor
  • Departament de Matemàtica Aplicada III, E.T.S. de Ingenieros de Caminos, Edifici C2, Campus Nord, Universitat Politècnica de Catalunya, E08034 Barcelona, Spain

Bibliografia

  • Ainsworth M. and Oden J.T. (1993): A unified approach to a posteriori error estimation using element residual methods. - Num. Math., Vol. 65, No. 1, pp. 23-50.
  • Bank R.E. and Weiser A. (1985): Some a posteriori error estimators for elliptic partial differential equations. - Math. Comp., Vol. 44, No. 1, pp. 283-301.
  • Bauzant Z.P. and Pijaudier-Cabot G. (1988): Nonlocal continuum damage localization instability and convergence. - J. Appl. Mech., Vol. 55, No. 2, pp. 287-293.
  • Carpinteri A., Valente S., Ferrara G. and Melchiorri G. (1993): Is mode ii fracture energy a real material property? - Comp. Struct., Vol. 48, No. 3, pp. 397-413.
  • Chow S.S. and Carey G.F. (1993): Superconvergence phenomena in nonlinear two-point boundary-value problems. - Num. Meth. Part. Diff. Eqns., Vol. 9, No. 5, pp. 561-577.
  • Ciarlet P.G. (1983): Introduction à L'analyse Matricielle et à L'optimisation. - Paris: Masson.
  • Díez P., Arroyo M. and Huerta A. (2000): Adaptivity based on error estimation for viscoplastic softening materials. - Mech. Cohes.-Frict. Mat., Vol. 5, No. 2, pp. 87-112.
  • Díez P. and Egozcue J.J. (2001): Probabilistic analysis of an a posteriori error estimator for finite elements. - Math. Models Meth. Appl. Sci., Vol. 5, No. 5, pp. 841-854.
  • Díez P. and Huerta A. (1999): A unified approach to remeshing strategies for finite element h-adaptivity. - Comp. Meth. Appl. Mech. Eng., Vol. 176, No. 1-4, pp. 215-229.
  • Díez P. and Huerta A. (2000): Error estimation for adaptive computations of shell structures. - Revue Europeenne des Elements Finis, Vol. 9, No. 1-2, pp. 49-66.
  • Díez P., Egozcue J.J. and Huerta A. (1998): A posteriori error estimation for standard finite element analysis. - Comp. Meth. Appl. Mech. Eng., Vol. 163, No. 1-4, pp. 141-157.
  • Fourment L. and Chenot J.L. (1995): Error estimators for viscoplastic materials: application to forming processes. - Eng. Comp., Vol. 12, No. 5, pp. 469-490.
  • Gallimard L., Ladevèze P. and Pelle J.P. (1996): Error estimation and adaptivity in elastoplasticity. - Int. J. Num. Meth. Eng., Vol. 39, No. 2, pp. 189-217.
  • Huerta A. and Díez P. (2000): Error estimation including pollution assessment for nonlinear finite element analysis. - Comp. Meth. Appl. Mech. Eng., Vol. 181, No. 12, pp. 21-41.
  • Huerta A., Rodríguez-Ferran A., Díez P. and J. Sarrate (1999): Adaptive finite element strategies based on error assessment. - Int. J. Num. Meth. Eng., Vol. 46, No. 10, pp. 1803-1818.
  • Hughes T.J.R. (1987): The finite element method. - Stanford: Prentice Hall.
  • Ladevèze P. and Rougeot Ph. (1997): New advances on a posteriori error on constitutive relation in fe analysis. - Comp. Meth. Appl. Mech. Eng., Vol. 150, No. 1-4, pp. 239-249.
  • Ladevèze P., Pelle J.P. and Rougeot Ph. (1991): Error estimation and mesh optimization for classical finite elements. -Eng. Comp., Vol. 8, No. 1, pp. 69-80.
  • Lamain LG. and Donea J. (1987): A modified representation of transverse shear in C^0 quadrilateral plate elements. - Comp. Meth. Appl. Mech. Eng., Vol. 63, No. 2, pp. 183-207.
  • Lee C.K., Sze K.Y. and Lo S.H. (1999): On using degenerated solid shell elements in adaptive refinement analysis. - Int. J. Numer. Meth. Eng., Vol. 45, No. 6, pp. 627-659.
  • Lemaitre J. and Chaboche J.-L. (1990): Mechanics of Solid Materials. - Cambridge: Cambridge University Press.
  • Mazars J. and Pijaudier-Cabot G. (1989): Continuum damage theory: application to concrete. - J. Eng. Mech., Vol. 115, No. 2, pp. 345-365.
  • Oden J.T., Demkowicz L., Rachowicz W. and Westermann T.A. (1989): Toward a universal h-p adaptive finite element strategy, Part 2. A posteriori error estimation. - Comp. Meth. Appl. Mech. Eng., Vol. 77, No. 1-2, pp. 113-180.
  • Ortiz M. and Quigley IV J.J. (1991): Adaptive mesh refinement in strain localization problems. - Comp. Meth. Appl. Mech. Eng., Vol. 90, No. 1-3, pp. 781-804.
  • Peerlings R.H.J., de Borst R., Brekelmans W.A.M. and Geers M.G.D. (1998): Gradient-enhanced damage modelling of concrete fracture. - Mech. Cohes.-Frict. Mat., Vol. 3, No. 4, pp. 323-342.
  • Pijaudier-Cabot G. and Bau zant Z.P. (1987): Nonlocal damage theory. - J. Eng. Mech., Vol. 113, No. 10, pp. 1512-1533.
  • Rodríguez-Ferran A. and Huerta A. (2000): Error estimation and adaptivity for nonlocal damage models. - Int. J. Solids Struct., Vol. 37, No. 48-50, pp. 7501-7528.
  • Rodríguez-Ferran A., Arbós I. and Huerta A. (2001): Adaptive analysis based on error estimation for nonlocal damage models. - Revue europeenne des elements finis (Special issue: Numerical Modelling in Damage Mechanics), Vol. 10, No. 2-4, pp. 193-207.
  • Sarrate J. and Huerta A. (2000): Efficient unstructured quadrilateral mesh generation. - Int. J. Num. Meth. Eng., Vol. 49, No. 10, pp. 1327-1350.
  • Strouboulis T. and Haque K.A. (1992a): Recent experiences with error estimation and adaptivity, Part i: Review of error estimators for scalar elliptic problems. - Comp. Meth. Appl. Mech. Eng., Vol. 97, No. 3, pp. 399-436.
  • Strouboulis T. and Haque K.A. (1992b): Recent experiences with error estimation and adaptivity, Part ii: Error estimation for h-adaptive approximations on grids of triangles and quadrilaterals. - Comp. Meth. Appl. Mech. Eng., Vol. 100, No. 3, pp. 359-430.
  • Zhu J.Z. (1997): A posteriori error estimation-the relationship between different procedures. - Comp. Meth. Appl. Mech. Eng., Vol. 150, No. 1-4, pp. 411-422.
  • Zienkiewicz O.C. and Huang G.C. (1990): A note on localization phenomena and adaptive finite-element analysis in forming processes. - Comm. Appl. Num. Meth., Vol. 26, No. 8, pp. 71-76.
  • Zienkiewicz O.C. and Zhu J.Z. (1987): A simple error estimator and adaptive procedure for practical engineering analysis. - Int. J. Num. Meth. Eng., Vol. 24, No. 1, pp. 337-357.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.bwnjournal-article-amcv12i1p59bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.