Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Remeshing techniques for r-adaptive and combined h/r-adaptive analysis with application to 2D/3D crack propagation

  • Askes, H. (Faculty of Civil Engineering and Geosciences, Koiter Institute Delft, Delft University of Technology) ;
  • Sluys, L.J. (Faculty of Civil Engineering and Geosciences, Koiter Institute Delft, Delft University of Technology) ;
  • de Jong, B.B.C. (TNO Building and Construction Research)
  • Published : 2001.11.25
⟨ Previous Next ⟩

Abstract

Remeshing strategies are formulated for r-adaptive and h/r-adaptive analysis of crack propagation. The relocation of the nodes, which typifies r-adaptivity, is a very cheap method to optimise a given discretisation since the element connectivity remains unaltered. However, the applicability is limited. To further improve the finite element mesh, a combined h/r-adaptive method is proposed in which h-adaptivity is applied whenever r-adaptivity is not capable of further improving the discretisation. Two and three-dimensional examples are presented. It is shown that the r-adaptive approach can optimise a discretisation at minimal computational costs. Further, the combined h/r-adaptive approach improves the performance of a fully r-adaptive technique while the number of h-remeshings is reduced compared to a fully h-adaptive technique.

Keywords

References

  1. Askes, H. (2000), "Advanced spatial discretisation strategies for localised failure-mesh adaptivity and meshless methods", Dissertation, Delft University of Technology.
  2. Askes, H., Bode, L., and Sluys, L.J. (1998), "ALE analyses of localization in wave propagation problems", Mechanics of Cohesive-Frictional Materials, 3, 105-125. https://doi.org/10.1002/(SICI)1099-1484(199804)3:2<105::AID-CFM43>3.0.CO;2-C
  3. Askes, H., and Rodríguez-Ferran, A. (2001), "A combined rh-adaptive scheme based on domain subdivision- formulation and linear examples", Int. J. Numer. Meth. in Eng., 51, 253-273. https://doi.org/10.1002/nme.142
  4. Askes, H., Rodríguez-Ferran, A., and Huerta, A. (1999), "Adaptive analysis of yield line patterns in plates with the arbitrary Lagrangian-Eulerian method", Comput. and Struct., 70, 257-271. https://doi.org/10.1016/S0045-7949(98)00188-6
  5. Askes, H., and Sluys, L.J. (1999), "Adaptive ALE analyses of crack propagation with a continuum material model", Europ. Conf. on Computational Mechanics-Solids, Structures and Coupled Problems in Engineering, Wunderlich W., ed., TU Munchen.
  6. Askes, H., and Sluys, L.J. (2000), "Remeshing strategies for adaptive ALE analysis of strain localisation", European J. Mechanics A/Solids, 19, 447-467. https://doi.org/10.1016/S0997-7538(00)00176-5
  7. Bode, L. (1994), "Stratégies numeriques pour la prévision de la ruine des structures du génie civil", Dissertation, E.N.S. de Cachan/CNRS/Universite Paris 6.
  8. Bode, L., Pijaudier-Cabot, G., and Huerta, A. (1995), "ALE finite element analysis of strain localisation- consistent computational strategy and remeshing issues", Computational Plasticity IV, Owen D.R.J., Onate, E., Hinton, E., eds., Pineridge Press, Swansea, UK. 587-598.
  9. de Borst, R. (1987), "Computation of post-bifurcation and post-failure behavior of strain-softening solids", Comput. and Struct., 25, 211-224. https://doi.org/10.1016/0045-7949(87)90144-1
  10. Diez, P., and Huerta, A. (1999), "A unified approach to remeshing strategies for finite element h-adaptivity", Comput. Meth. in Appl. Mech. and Eng., 176, 215-229. https://doi.org/10.1016/S0045-7825(98)00338-7
  11. Donea, J. (1983), "Arbitrary Lagrangian-Eulerian finite element methods", Comput. for Transient Analysis, Belytschko, T., Hughes, T.J.R., eds., Elsevier, chapter 10, 474-516.
  12. Huerta, A., and Casadei, F. (1994), "New ALE applications in non-linear fast-transient solid dynamics", Eng. Comput., 11, 317-345. https://doi.org/10.1108/02644409410799317
  13. Huerta, A., Casadei, F., and Donea, J. (1995), "ALE stress update in transient plasticity problems", Computational Plasticity IV, Owen, D.R.J., Onate, E., Hinton, E., eds., Pineridge Press, Swansea, UK, 1865- 1876.
  14. Huerta, A., and Pijaudier-Cabot, G. (1994), "Discretization influence on the regularization by two localization limiters", J. Eng. Mech., ASCE, 120, 1198-1218. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:6(1198)
  15. Huerta, A., Rodríguez-Ferran, A., Díez, P., and Sarrate, J. (1999), "Adaptive finite element strategies based on error assessment", Int. J. Numer. Meth. in Eng., 46, 1803-1818. https://doi.org/10.1002/(SICI)1097-0207(19991210)46:10<1803::AID-NME725>3.0.CO;2-3
  16. Hughes, T.J.R., Liu, W.K., and Zimmermann, T.K. (1981), "Lagrangian-Eulerian finite element formulation for incompressible viscous flows", Comput. Meth. Appl. Mech. and Eng., 29, 329-349. https://doi.org/10.1016/0045-7825(81)90049-9
  17. Ortiz, M., and Quigley, J.J. (1991), "Adaptive mesh refinement in strain localization problems", Comput. Meth. in Appl. Mech. and Eng., 90, 781-804. https://doi.org/10.1016/0045-7825(91)90184-8
  18. Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M., de Vree, J.H.P., and Spee, I. (1996), "Some observations on localisation in non-local and gradient damage models", Europ. J. of Mech., A/Solids, 15, 937-953.
  19. Peerlings, R.H.J., de Borst, R., Brekelmans, W.A.M., and Geers, M.G.D. (1998), "Gradient-enhanced damage modelling of concrete fracture", Mechanics of Cohesive-Frictional Materials, 3, 323-342. https://doi.org/10.1002/(SICI)1099-1484(1998100)3:4<323::AID-CFM51>3.0.CO;2-Z
  20. Pijaudier-Cabot G., and Bazant,  Z.P. (1987), "Nonlocal damage theory", ASCE J. Eng. Mech., 113, 1512-1533. https://doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1512)
  21. Pijaudier-Cabot, G., Bode, L., and Huerta, A. (1995), "Arbitrary Lagrangian-Eulerian finite element analysis of strain localization in transient problems", Int. J. Numer. Meth. in Eng., 38, 4171-4191. https://doi.org/10.1002/nme.1620382406
  22. Rodriguez-Ferran, A., Casadei, F., and Huerta, A. (1998), "ALE stress update for transient and quasistatic processes", Int. J. Numer. Meth. in Eng., 43, 241-262. https://doi.org/10.1002/(SICI)1097-0207(19980930)43:2<241::AID-NME389>3.0.CO;2-D
  23. Sluys, J.J. (1992), "Wave propagation, localisation and dispersion in softening solids", Dissertation, Delft University of Technology.
  24. Sluys, L.J., Cauvern, M., and de Borst, R. (1995), "Discretization influence in strain-softening problems", Eng. Comput., 12, 209-228. https://doi.org/10.1108/02644409510799569
  25. Zienkiewicz, O.C., and Zhu, J.Z. (1991), "Adaptivity and mesh generation", Int. J. Numer. Meth. in Eng., 32, 783-810. https://doi.org/10.1002/nme.1620320409

Cited by

  1. Automatic LEFM crack propagation method based on local Lepp–Delaunay mesh refinement vol.41, pp.2, 2010, https://doi.org/10.1016/j.advengsoft.2009.10.004
  2. Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture vol.45, pp.1, 2009, https://doi.org/10.1007/s00466-009-0417-0
  3. A conforming to interface structured adaptive mesh refinement technique for modeling fracture problems vol.59, pp.4, 2001, https://doi.org/10.1007/s00466-016-1366-z