Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Iterative global-local approach to consider the local effects in dynamic analysis of beams

  • Erkmen, R. Emre (School of Civil and Environmental Engineering, University of Technology) ;
  • Afnani, Ashkan (School of Civil and Environmental Engineering, University of Technology)
  • Received : 2016.11.09
  • Accepted : 2017.11.14
  • Published : 2017.12.25
⟨ Previous Next ⟩

Abstract

This paper introduces a numerical procedure to incorporate elasto-plastic local deformation effects in the dynamic analysis of beams. The appealing feature is that simple beam type finite elements can be used for the global model which needs not to be altered by the localized elasto-plastic deformations. An overlapping local sophisticated 2D membrane model replaces the internal forces of the beam elements in the predefined region where the localized deformations take place. An iterative coupling technique is used to perform this replacement. Comparisons with full membrane analysis are provided in order to illustrate the accuracy and efficiency of the method developed herein. In this study, the membrane formulation is able to capture the elasto-plastic material behaviour based on the von Misses yield criterion and the associated flow rule for plane stress. The Newmark time integration method is adopted for the step-by-step dynamic analysis.

Keywords

References

  1. Allix, O., Gendre, L., Gosselet, P. and Guguin, G. (2011), "Non-intrusive coupling: An attempt to merge industrial and research software capabilities", Rec. Develop. Innovat. Appl. Comput. Mech., 15, 125-133.
  2. Afnani, A. and Erkmen, R.E. (2016), "Iterative global-local procedure for the analysis of composite thin-walled laminates", Steel Compos. Struct., 20, 693-718. https://doi.org/10.12989/scs.2016.20.3.693
  3. Babuska, I. and Melenk, J.M. (1995), The Partition of Unity Finite Element Method (Final Report, Apr. - Jun. 1995), Vol. AD-A301760, TN-BN-1185, NIPS-96-41139.
  4. Banik, S.S., Hong, H.P. and Kopp G.A. (2010), "Assesment of capcity curves for tranmission line towers under wind loading", Wind Struct., 13(1), 1-20. https://doi.org/10.12989/was.2010.13.1.001
  5. Belytschko, T. (2001), "Arbitrary discontinuities in finite elements", J. Numer.Meth. Eng., 50(4), 993-1013. https://doi.org/10.1002/1097-0207(20010210)50:4<993::AID-NME164>3.0.CO;2-M
  6. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. (1996), "Meshless methods: An overview and recent developments", Comput. Meth. Appl.Mech. Eng., 139(1), 3-47. https://doi.org/10.1016/S0045-7825(96)01078-X
  7. Bettinotti, O., Allix, O. and Malherbe, B. (2014), "A coupling strategy for adaptive local refinement in space time with a fixed global model in explicit dynamics", Comput. Mech., 53, 561-574. https://doi.org/10.1007/s00466-013-0917-9
  8. Bozdogan, K.B. and Ozturk, D. (2016), "A method for dynamic analysis of frame-hinged shear wall structures", Earthq. Struct., 11(1), 45-61. https://doi.org/10.12989/eas.2016.11.1.045
  9. Doyle, J.F. and Farris, T.N. (1995), "Structural mechanics modeling of the impact of a double cantilever beam", J. Fract., 76(4), 311-326.
  10. Duarte, C. and Oden, J. (1996), "Hp clouds-an hp meshless method", Numer. Meth. Part. Differ. Equat., 12, 673-705. https://doi.org/10.1002/(SICI)1098-2426(199611)12:6<673::AID-NUM3>3.0.CO;2-P
  11. Duval, M., Passieux, J.C., Salaun, M. and Guinard, S. (2016), "Non-intrusive coupling: Recent advances and scalable nonlinear domain decomposition", Arch. Comput.Meth. Eng., 23(1), 17-38. https://doi.org/10.1007/s11831-014-9132-x
  12. Erkmen, E. and Bradford, M.A. (2011), "Coupling of finite element and meshfree methods for locking-free analysis of shear-deformable beams and plates", Eng. Comput., 28(8), 1003-27. https://doi.org/10.1108/02644401111179009
  13. Erkmen, R. (2013), "Bridging multi-scale approach to consider the effects of local deformations in the analysis of thin-walled members", Comput.Mech., 52(1), 65-79. https://doi.org/10.1007/s00466-012-0798-3
  14. Erkmen, R.E. (2015), "Multiple-point constraint applications for the finite element analysis of shear deformable composite beams-variational multiscale approach to enforce full composite action", Comput. Struct., 149, 17-30. https://doi.org/10.1016/j.compstruc.2014.12.001
  15. Erkmen, R.E., Saleh, A. and Afnani, A. (2016), "Incorporating local effects in the predictor step of the iterative global-local analysis of beams", J. Multisc. Comput. Eng., 14, 455-477. https://doi.org/10.1615/IntJMultCompEng.2016016592
  16. Erkmen, R.E. and Saleh, A. (2017), "Iterative global-local approach to consider the effects of local elasto-plastic deformations in the analysis of thin-walled members", J. Multisc. Comput. Eng., 15, 143-173. https://doi.org/10.1615/IntJMultCompEng.2017019767
  17. Erkmen, R.E., Mohareb, M. and Afnani, A. (2017), "Multi-scale overlapping domain decomposition to consider elasto-plastic local buckling effects in the analysis of pipes", J. Struct. Stab. Dyn., 17, 1-28.
  18. Farris, T.N. and Doyle, J.F. (1993), "A global/local approach to lengthwise cracked beams-dynamic analysis", J. Fract., 60(2), 147-156. https://doi.org/10.1007/BF00012442
  19. Feyel, F. (2003), "A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua", Comput.Meth. Appl.Mech. Eng., 192, 3233-3244. https://doi.org/10.1016/S0045-7825(03)00348-7
  20. Fish, J., Markolefas, S., Guttal, R. and Nayak, P. (1994), "On adaptive multilevel superposition of finite element meshes for linear elastostatics", Appl. Numer.Math., 14, 135-164. https://doi.org/10.1016/0168-9274(94)90023-X
  21. Gendre, L., Allix, O., Gosselet, P. and Comte, F. (2009), "Non-intrusive and exact global/local techniques for structural problems with local plasticity", Comput. Mech., 44(2), 233-245. https://doi.org/10.1007/s00466-009-0372-9
  22. Hadianfard, M.A., Farahani, A. and B-Jahromi, A. (2012), "On the effect of steel column cross-sectional properties on the behaviours when subjected to blast loading", Struct. Eng. Mech., 44(4), 449-463. https://doi.org/10.12989/sem.2012.44.4.449
  23. Hughes, T.J.R., Feijoo, G.R., Mazzei, L. and Quincy, J.B. (1998), "Variational multiscale method-a paradigm for computational mechanics", Comput. Meth. Appl. Mech. Eng., 166(1), 3-24. https://doi.org/10.1016/S0045-7825(98)00079-6
  24. Hughes, T.J.R. and Sangalli, G. (2007), "Variational multiscale analysis: The fine-scale green's function, projection, optimization, localization, and stabilized methods", SIAM J. Numer. Analy., 45(2), 539-519. https://doi.org/10.1137/050645646
  25. Ibrahimbegovic, A., Taylor, R.L. and Wilson, E.L. (1990), "A robust quadrilateral membrane finite element with drilling degrees of freedom", J. Numer. Meth. Eng., 30(3), 445-457. https://doi.org/10.1002/nme.1620300305
  26. Kerfriden, P., Passieux, J.C. and Bordas, S.P.A. (2012), "Local/global model order reduction strategy for the simulation of quasi-brittle fracture", J. Numer. Meth. Eng., 89(2), 154-179. https://doi.org/10.1002/nme.3234
  27. Knight, N.O.R.M.A.N.F.J.R., Ransom, J., Griffin, O.H.J.R. and Thompson, D. (1991), "Global/local methods research using a common structural analysis framework", Fin. Elem. Analy. Des., 9, 91-112. https://doi.org/10.1016/0168-874X(91)90053-2
  28. Lim, H.K., Kang, J.W., Lee, Y.G. and Chi, H.S. (2016), "Seismic performance evaluation of a three-dimensional unsymmetrical reinforced concrete beams", Multisc. Multiphys. Mech., 1(2), 143-156. https://doi.org/10.12989/mmm.2016.1.2.143
  29. Liu, W., Hao, S., Belytschko, T., Li, S. and Chang, C. (2000), "Multi-scale methods", J. Numer. Meth. Eng., 50, 993-1013.
  30. Mao, K.M. and Sun, C.T. (1991), "A refined global-local finite element analysis method", J. Numer. Meth. Eng., 32(1), 29-43. https://doi.org/10.1002/nme.1620320103
  31. McConnell, J.R. and Brown, H. (2011), "Evaluation of progressive collapse alternate load path analyses in designing for blast resistance of steel columns", Eng. Struct., 33(10), 2899-2909. https://doi.org/10.1016/j.engstruct.2011.06.014
  32. Mote, C.D.J.R. (1971), "Global-local finite element (global-local finite element combined ritz methods for beam and plate vibration analysis)", J. Numer. Meth. Eng., 3, 565-574. https://doi.org/10.1002/nme.1620030410
  33. Newmark, N. (1959), "A method of computational for structural dynamics", J. Eng. Mech. Div., 85, 67-94.
  34. Noor, A. (1986), "Global-local methodologies and their application to nonlinear analysis", Fin. Elem. Analy. Des., 2, 333-346. https://doi.org/10.1016/0168-874X(86)90020-X
  35. Simo, J.C. and Hughes, T.J.R. (1998), Computational Inelasticity, Springer-Verlag (Interdisciplinary Applied Mathematics, New York, U.S.A.
  36. Strouboulis, T., Copps, K. and Babuska, I. (2001), "The generalized finite element method", Comput. Meth. Appl. Mech. Eng., 190, 4081-4193. https://doi.org/10.1016/S0045-7825(01)00188-8
  37. Sun, C.T. and Mao, K.M. (1988), "A global-local finite element method suitable for parallel computations", Comput. Struct., 29(2), 309-315. https://doi.org/10.1016/0045-7949(88)90264-7
  38. Voleti, S.R., Chandra, N. and Miller, J.R. (1996), "Global-local analysis of large-scale composite structures using finite element method", Comput. Struct., 58(2), 453-464. https://doi.org/10.1016/0045-7949(95)00172-D
  39. Whitcomb, J.D. (1991), "Iterative global/local finite element analysis", Comput. Struct., 40, 1027-1031. https://doi.org/10.1016/0045-7949(91)90334-I
  40. Whitcomb, J. and Woo, K. (1993a), "Application of iterative global/local finite-element analysis. Part 1: Linear analysis", J. Numer. Meth. Eng., 9(9), 745-756. https://doi.org/10.1002/cnm.1640090905
  41. Whitcomb, J. and Woo, K. (1993b), "Application of iterative global/local finite element analysis. Part 2: Geometrically nonlinear analysis", J. Numer. Meth. Eng., 9, 757-766. https://doi.org/10.1002/cnm.1640090906