International Journal of Concrete Structures and Materials

  • 제2권2호
  • /
  • Pages.153-160
  • /
  • 2008
  • /
  • 1976-0485(pISSN)
  • /
  • 2234-1315(eISSN)
한국콘크리트학회 (Korea Concrete Institute)
권호 표지
DOI QR코드

DOI QR Code

Numerical Fracture analysis of prestressed concrete beams

  • Rabczuk, Timon (University of Canterbury, Dept. of Mechanical Engineering) ;
  • Zi, Goangseup (Korea University, Department of Civil & Environmental Engineering)
  • 발행 : 2008.12.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

Fracture of prestressed concrete beams is studied with a novel and robust three-dimensional meshfree method. The meshfree method describes the crack as a set of cohesive crack segments and avoids the representation of the crack surface. It is ideally suited for a large number of cracks. The crack is modeled by splitting particles into two particles on opposite sides of the crack segment and the shape functions of neighboring particles are modified in a way the discontinuous displacement field is captured appropriately. A simple, robust and efficient way to determine, on which side adjacent particles of the corresponding crack segment lies, is proposed. We will show that the method does not show any "mesh" orientation bias and captures complicated failure patterns of experimental data well.

키워드

참고문헌

  1. F. Armero and K. Garikipati, "An analysis of Strong Discontinuities in Multiplicative Finite Strain Plasticity and Their Relation with the Numerical Simulation of Strain Localization in Solids," International Journal of Solids and Structures, Vol.33, No.20-22,:1996, pp. 2863-2885 https://doi.org/10.1016/0020-7683(95)00257-X
  2. T. Belytschko and T. Black, "Elastic Crack Growth in Finite Elements with Minimal Remeshing," International Journal for Numerical Methods in Engineering, Vol. 45, No. 5. 1999, pp. 601-620 https://doi.org/10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
  3. T. Belytschko, J. Fish, and B. Englemann, "A Finite Element Method with Embedded Localization Zones," Computer Methods in Applied Mechanics and Engineering, Vol. 70, 1988, pp. 59-89 https://doi.org/10.1016/0045-7825(88)90180-6
  4. T. Belytschko, M. Fleming, D. Organ, Y. Krongauz, and W.K. Liu, "Smoothing and Accelerated Computations in the Element Free Galerkin Method". Journal of Computational and Applied Mathematics, Vol 74, 1996, pp. 111-126 https://doi.org/10.1016/0377-0427(96)00020-9
  5. T. Belytschko and Y.Y. Lu, "Element-Free Galerkin Methods for Static and Dynamic Fracture," International Journal of Solids and Structures, Vol. 32, 1995, pp. 2547-2570 https://doi.org/10.1016/0020-7683(94)00282-2
  6. T. Belytschko, Y.Y. Lu, and L. Gu, "Crack Propagation by Element-Free Galerkin Methods," Engineering Fracture Mechanics, Vol. 51, No. 2, 1995, pp. 295-315 https://doi.org/10.1016/0013-7944(94)00153-9
  7. T. Belytschko, N. Moes, S. Usui, and C. Parimi, "Arbitrary Discontinuities in Finite Elements," International Journal for Numerical Methods in Engineering, Vol 50, No. 4, pp. 993-1013 https://doi.org/10.1002/1097-0207(20010210)50:4<993::AID-NME164>3.0.CO;2-M
  8. T. Belytschko, D. Organ, and M. Tabbara, "Numerical Simulations of Mixed Mode Dynamic Fracture in Concrete Using Element-free Galerkin Methods," ICES Conference Proceedings, 1995
  9. T. Belytschko and M. Tabbara, "Dynamic Fracture Using Element-free Galerkin Methods," International Journal for Numerical Methods in Engineering, Vol 39, No. 6, 1996, pp. 923-938 https://doi.org/10.1002/(SICI)1097-0207(19960330)39:6<923::AID-NME887>3.0.CO;2-W
  10. G. T. Camacho and M. Ortiz, "Computational Modeling of Impact Damage in Brittle Materials," International Journal of Solids and Structures, Vol. 33, 1996, pp.2899-2938 https://doi.org/10.1016/0020-7683(95)00255-3
  11. C. Daux, N. Moes, J. Dolbow, N. Sukumar, and T. Belytschko, "Arbitrary Branched and Intersection Cracks with the Extended Finite Element Method," International Journal for Numerical Methods in Engineering, Vol. 48, 2000, pp. 1731-1760
  12. N. Hermann. Experimentelle Erfassung des Betonverhaltens unter Schockwellen. PhD thesis, Institut fuer Massivbau und Baustofftechnologie, Universitaet Karlsruhe, 2002
  13. P. Krysl and T. Belytschko, "The Element Free Galerkin Method for Dynamic Propagation of Arbitrary 3-D Cracks," International Journal for Numerical Methods in Engineering, Vol. 44, No. 6, 1999, pp. 767-800 https://doi.org/10.1002/(SICI)1097-0207(19990228)44:6<767::AID-NME524>3.0.CO;2-G
  14. J. Lemaitre, "Evaluation of Dissipation and Damage in Metal Submitted to Dynamic Loading," Proceedings ICM 1, 1971
  15. N. Moes, J. Dolbow, and T. Belytschko, "A Finite Element Method for Crack Growth without Remeshing," International Journal for Numerical Methods in Engineering, Vol.46, No. 1, 1999, pp. 133-150
  16. J. Oliver, "Modelling Strong Discontinuities in Solid Mechanics via Strain Softening Constituitive Equations, Part 1: Fundamentals. Part 2: Numerical Simulation," International Journal for Numerical Methods in Engineering, Vol. 39, 1996, pp. 3575-3624 https://doi.org/10.1002/(SICI)1097-0207(19961115)39:21<3575::AID-NME65>3.0.CO;2-E
  17. J. Oliver, M. Cervera, and O. Manzoli, "Strong Discontinuities and Continuum Plasticity Models: the Strong Discontinuity Approach," International Journal of Plasticity, Vol 15, 1999, pp. 319-351 https://doi.org/10.1016/S0749-6419(98)00073-4
  18. J. Oliver, A.E. Huespe, and P.J. Snchez, "A Comparative Study on Finite Elements for Capturing Strong Discontinuities: EFem vs. x-Fem," Computer Methods in Applied Mechanics and Engineering, in press, 2006
  19. D. Organ, M. Fleming, T. Terry, and T. Belytschko, "Continuous Meshless Approximations for Nonconvex Bodies by Diffraction and Transparency," Computational Mechanics, Vol 18, 1996, pp. 225-235 https://doi.org/10.1007/BF00369940
  20. M. Ortiz, Y. Leroy, and A. Needleman, "Finite Element Method for Localized Failure Analysis," Computer Methods in Applied Mechanics and Engineering, Vol. 61, No. 2, 1987, pp. 189-214 https://doi.org/10.1016/0045-7825(87)90004-1
  21. T. Rabczuk, J. Akkermann, and J. Eibl, "A Numerical Model for Reinforced Concrete Structures," International Journal of Solids and Structures, 5-6, 2005, pp. 1327-1354, 42
  22. T. Rabczuk, P.M.A. Areias, and T. Belytschko, "A Meshfree Thin Shell for Large Deformation, Finite Strain and Arbitrary Evolving Cracks," International Journal for Numerical Methods in Engineering, Vol. 72, No. 5, 2007, pp. 524-548 https://doi.org/10.1002/nme.2013
  23. T. Rabczuk and T. Belytschko, "Cracking Particles: A Simplified Meshfree Method for Arbitrary Evolving Cracks," International Journal for Numerical Methods in Engineering, Vol. 61, No. 13, 2004, pp. 2316-2343 https://doi.org/10.1002/nme.1151
  24. T. Rabczuk and T. Belytschko, "Adaptivity for Structured Meshfree Particle Methods in 2D and 3D," International Journal for Numerical Methods in Engineering, Vol. 63, No. 11, 2005, pp. 1559-1582 https://doi.org/10.1002/nme.1326
  25. T. Rabczuk and T. Belytschko, "Application of Meshfree Particle Methods to Static Fracture of Reinforced Concrete Structures," International Journal of Fracture, 137(1-4), 2006, pp. 19-49 https://doi.org/10.1007/s10704-005-3075-z
  26. T. Rabczuk and T. Belytschko, "A Three Dimensional Large Deformation Meshfree Method for Arbitrary Evolving Cracks," Computer Methods in Applied Mechanics and Engineering, 196 (29-30), 2007, pp. 2777-2799 https://doi.org/10.1016/j.cma.2006.06.020
  27. T. Rabczuk, T. Belytschko, and S.P. Xiao, "Stable Particle Methods Based on Lagrangian Kernels," Computer Methods in Applied Mechanics and Engineering, 193:1035-1063, 2004 https://doi.org/10.1016/j.cma.2003.12.005
  28. J. J. C. Remmers, R. de Borst, and A. Needleman, "A Cohesive Segments Method for the Simulation of Crack Growth," Computational Mechanics, Vol. 31, 2003, pp. 69-77 https://doi.org/10.1007/s00466-002-0394-z
  29. X.-P. Xu and A. Needleman, "Void Nucleation by Inclusion Debonding in a Crystal Matrix," Modell. Simul. Mater. Sci. Engng., Vol. 1, 1993, pp. 111-132 https://doi.org/10.1088/0965-0393/1/2/001
  30. X.-P. Xu and A. Needleman, "Numerical Simulations of Fast Crack Growth in Brittle Solids," Journal of the Mechanics and Physics of Solids, Vol. 42, 1994, pp. 1397-1434 https://doi.org/10.1016/0022-5096(94)90003-5
  31. F. Zhou and J.F. Molinari, "Dynamic Crack Propagation with Cohesive Elements: a Methodolgy to Address Mesh Dependence," International Journal for Numerical Methods in Engineering, Vol. 59, No. 1, 2004, pp. 1-24 https://doi.org/10.1002/nme.857
  32. S. Bordas and B. Moran, "Enriched Finite Elements and Level Sets for Damage Tolerance Assessment of Complex Structures," Engineering Fracture Mechanics, Vol 73, 2006, pp. 1176-1201 https://doi.org/10.1016/j.engfracmech.2006.01.006
  33. R. Duddu and S. Bordas and B. Moran, "A Combined Extended Finite Element and Level set Method for Biofilm Growth," International Journal for Numerical Methods in Engineering, Vol. 74, No. 5, 2008, pp. 848-870 https://doi.org/10.1002/nme.2200
  34. S. Bordas and V.P. Nguyen and C. Dunant and H. Nguyen-Dang and A. Guidoum, "An Extended Finite Element Library," International Journal for Numerical Methods in Engineering, Vol. 71, No. 6, 2007, pp. 703-732 https://doi.org/10.1002/nme.1966
  35. S. Bordas and J.G. Conley and B. Moran and J. Gray and E. Nichols, "A Simulation-Based Design Paradigm for Complex Cast Components," Engineering with Computers, Vol. 23, No. 1, 2007, pp. 25-37 https://doi.org/10.1007/s00366-006-0030-1
  36. L. Stempniewski and J. Eibl and T. Rabczuk, Der Endbereich von im Werk vorgespannten Fertigteiltraegern-Hohlplatten, Final report, University of Karlsruhe, Institut fuer Massivbau und Baustofftechnologie, 2001

피인용 문헌

  1. Modeling of post-tensioned one-way and two-way slabs with unbonded tendons vol.13, pp.5, 2014, https://doi.org/10.12989/cac.2014.13.5.587
  2. Effect of Concrete Strength and Reinforcement on Time-Dependent Deflection of Posttensioned Slabs vol.23, pp.1, 2018, https://doi.org/10.1061/(ASCE)SC.1943-5576.0000353