Steel and Composite Structures

  • 제20권3호
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  • Pages.693-718
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  • 2016
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Iterative global-local procedure for the analysis of thin-walled composite laminates

  • Afnani, Ashkan (School of Civil and Environmental Engineering, University of Technology Sydney) ;
  • Erkmen, R. Emre (School of Civil and Environmental Engineering, University of Technology Sydney)
  • 투고 : 2015.03.17
  • 심사 : 2015.12.03
  • 발행 : 2016.02.29
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents a finite element procedure based on Bridging multi-scale method (BMM) in order to incorporate the effect of local/cross-sectional deformations (e.g., flange local buckling and web crippling) on the global behaviour of thin-walled members made of fibre-reinforced polymer composite laminates. This method allows the application of local shell elements in critical regions of an existing beam-type model. Therefore, it obviates the need for using computationally expensive shell elements in the whole domain of the structure, which is otherwise necessary to capture the effect of the localized behaviour. Consequently, highly accurate analysis results can be achieved with this method by using significantly smaller finite element model, compared to the existing methods. The proposed method can be used for composite polymer laminates with arbitrary fibre orientation directions in different layers of the material, and under various loading conditions. Comparison with full shell-type finite element analysis results are made in order to illustrate the efficiency and accuracy of the proposed technique.

키워드

참고문헌

  1. Babuska, I. and Melenk, J.M. (1997), "The partition of unity method", Int. J. Numer. Method. Eng., 40(4), 727-758. https://doi.org/10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N
  2. Babuska, I., Banerjee, U. and Osborn, J.E. (2003), "Survey of meshless and generalized finite element methods: A unified approach", Acta Numer., 12, 1-125. https://doi.org/10.1017/S0962492902000090
  3. Back, S.Y. and Will, K.M. (2008), "Shear-flexible thin-walled element for composite I-beams", Eng. Struct., 30(5), 1447-1458. https://doi.org/10.1016/j.engstruct.2007.08.002
  4. Batoz, J.L. and Tahar, M.B. (1982), "Evaluation of a new quadrilateral thin plate bending element", Int. J. Numer. Method. Eng., 18(11), 1655-1677. https://doi.org/10.1002/nme.1620181106
  5. Bauld, N.R. and Tzeng, L.S. (1984), "A Vlasov theory for fiber-reinforced beams with thin-walled open cross sections", Int. J. Solid. Struct., 20(3), 277-297. https://doi.org/10.1016/0020-7683(84)90039-8
  6. Belytschko, T., Krongauz, Y., Organ, D., Fleming, M. and Krysl, P. (1996), "Meshless methods: An overview and recent developments", Comput. Method. Appl. Mech. Eng., 139(1-4), 3-47. https://doi.org/10.1016/S0045-7825(96)01078-X
  7. Belytschko, T., Moes, N., Usui, S. and Parimi, C. (2001), "Arbitrary discontinuities in finite elements", Int. J. Numer. Method. Eng., 50(4), 993-1013. https://doi.org/10.1002/1097-0207(20010210)50:4<993::AID-NME164>3.0.CO;2-M
  8. Bradford, M.A. (1992), "Lateral-distortional buckling of steel I-section members", J. Construct. Steel Res., 23(1-3), 97-116. https://doi.org/10.1016/0143-974X(92)90038-G
  9. Bradford, M.A. and Hancock, G.J. (1984), "Elastic interaction of local and lateral buckling in beams", Thin-Wall. Struct., 2(1), 1-25. https://doi.org/10.1016/0263-8231(84)90013-2
  10. Cardoso, J.E.B., Benedito, N.M.B. and Valido, A.J.J. (2009), "Finite element analysis of thin-walled composite laminated beams with geometrically nonlinear behavior including warping deformation", Thin-Wall. Struct., 47(11), 1363-1372.
  11. Davies, J.M., Leach, P. and Heinz, D. (1994), "Second-order generalised beam theory", J. Construct. Steel Res., 31(2-3), 221-241. https://doi.org/10.1016/0143-974X(94)90011-6
  12. Erkmen, R.E. (2013), "Bridging multi-scale approach to consider the effects of local deformations in the analysis of thin-walled members", Computat. Mech., 52(1), 65-79. https://doi.org/10.1007/s00466-012-0798-3
  13. Erkmen, E. and Bradford, M.A. (2011), "Coupling of finite element and meshfree methods be for lockingfree analysis of shear-deformable beams and plates", Eng. Computat., 28(8), 1003-1027. https://doi.org/10.1108/02644401111179009
  14. Feyel, F. (2003), "A multilevel finite element method (FE2) to describe the response of highly non-linear structures using generalized continua", Comput. Method. Appl. Mech. Eng., 192(28-30), 32-44.
  15. 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(1-3), 135-164. https://doi.org/10.1016/0168-9274(94)90023-X
  16. Geers, M.G.D., Kouznetsova, V.G. and Brekelmans, W.A.M. (2010), "Multi-scale computational homogenization: Trends and challenges", J. Computat. Appl. Math., 234(7), 2175-2182. https://doi.org/10.1016/j.cam.2009.08.077
  17. 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. Anal., 45(2), 539-557. https://doi.org/10.1137/050645646
  18. Hughes, T.J.R., Feijoo, G.R., Mazzei, L. and Quincy, J.B. (1998), "The variational multiscale method - A paradigm for computational mechanics", Comput. Method. Appl. Mech. Eng., 166(1-2), 3-24. https://doi.org/10.1016/S0045-7825(98)00079-6
  19. Ibrahimbegovic, A., Taylor, R.L. and Wilson, E.L. (1990), "Robust quadrilateral membrane finite element with drilling degrees of freedom", Int. J. Numer. Method. Eng., 30(3), 445-457. https://doi.org/10.1002/nme.1620300305
  20. Kadowaki, H. and Liu, W.K. (2004), "Bridging multi-scale method for localization problems", Comput. Method. Appl. Mech. Eng., 193(30-32), 3267-3302. https://doi.org/10.1016/j.cma.2003.11.014
  21. Kim, N.I., Shin, D.K. and Kim, M.Y. (2007), "Exact lateral buckling analysis for thin-walled composite beam under end moment", Eng. Struct., 29(8), 1739-1751. https://doi.org/10.1016/j.engstruct.2006.09.017
  22. Kollar, L.P. (1991), "Mechanics of laminated composite plates and shells", Int. J. Solid. Struct., 38(42), 7525-7541. https://doi.org/10.1016/S0020-7683(01)00024-5
  23. Lee, J. (2006), "Lateral buckling analysis of thin-walled laminated composite beams with monosymmetric sections", Eng. Struct., 28(14), 1997-2009. https://doi.org/10.1016/j.engstruct.2006.03.024
  24. Lee, J., Kim, S.E. and Hong, K. (2002), "Lateral buckling of I-section composite beams", Eng. Struct., 24(7), 955-964. https://doi.org/10.1016/S0141-0296(02)00016-0
  25. Li, S. and Liu, W.K. (2002), "Meshfree and particle methods and their applications", Appl. Mech. Rev., 55(1), 1-34. https://doi.org/10.1115/1.1431547
  26. Liu, W.K., Li, S. and Belytschko, T. (1997), "Moving least-square reproducing kernel methods (I) methodology and convergence", Comput. Method. Appl. Mech. Eng., 143(1-2), 113-154. https://doi.org/10.1016/S0045-7825(96)01132-2
  27. Liu, W.K., Hao, S., Belytschko, T., Li, S. and Chang, C.T. (2000), "Multi-scale methods", Int. J. Numer. Method. Eng., 47(7), 1343-1361. https://doi.org/10.1002/(SICI)1097-0207(20000310)47:7<1343::AID-NME828>3.0.CO;2-W
  28. Machado, S.P. (2010), "Interaction of combined loads on the lateral stability of thin-walled composite beams", Eng. Struct., 32(11), 3516-3527. https://doi.org/10.1016/j.engstruct.2010.07.020
  29. Mittelstedt, C. (2007), "Local buckling of wide-flange thin-walled anisotropic composite beams", Arch. Appl. Mech., 77(7), 439-452. https://doi.org/10.1007/s00419-006-0102-0
  30. Oden, J.T., Prudhomme, S., Romkes, A. and Bauman, P.T. (2006), "Multiscale modeling of physical phenomena: Adaptive control of models", SIAM J. Scientif. Comput., 28(6), 2359-2389. https://doi.org/10.1137/050632488
  31. Omidvar, B. and Ghorbanpoor, A. (1996), "Nonlinear FE solution for thin-walled open-section composite beams", J. Struct. Eng., 122(11), 1369-1377. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:11(1369)
  32. Pandey, M.D., Kabir, M.Z. and Sherbourne, A.N. (1995), "Flexural-torsional stability of thin-walled composite I-section beams", Compos. Eng., 5(3), 321-342. https://doi.org/10.1016/0961-9526(94)00101-E
  33. Qian, D., Wagner, G.J. and Liu, W.K. (2004), "A multi-scale projection method for the analysis of carbon nanotubes", Comput. Method. Appl. Mech. Eng. Computat., 193(17-20), 1603-1632. https://doi.org/10.1016/j.cma.2003.12.016
  34. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, (2nd Edition), CRC Press, Boca Raton, FL, USA.
  35. Roberts, T.M. (2002), "Influence of shear deformation on buckling of pultruded fiber reinforced plastic profiles", J. Compos. Construct., 6(4), 241-248. https://doi.org/10.1061/(ASCE)1090-0268(2002)6:4(241)
  36. Roberts, T.M. and Masri, H.M.K.J.A.H. (2003), "Section properties and buckling behavior of pultruded FRP profiles", J. Reinf. Plast. Compos., 22(14), 1305-1317. https://doi.org/10.1177/0731684403035584
  37. Ronagh, H.R. and Bradford, M.A. (1996), "A rational model for the distortional buckling of tapered members", Comput. Method. Appl. Mech. Eng., 130(3-4), 263-277. https://doi.org/10.1016/0045-7825(95)00930-2
  38. Sapkas, A. and Kollar, L.P. (2002), "Lateral-torsional buckling of composite beams", Int. J Solid. Struct., 39(1), 2939-2963. https://doi.org/10.1016/S0020-7683(02)00236-6
  39. Schafer, B.W. (2008), "Review: The direct strength method of cold-formed steel member design", J. Construct. Steel Res., 64(7-8), 766-778. https://doi.org/10.1016/j.jcsr.2008.01.022
  40. Strouboulis, T., Copps, K. and Babuska, I. (2001), "Computational mechanics advances. The generalized finite element method", Comput. Method. Appl. Mech. Eng., 190(32-33), 4081-4193. https://doi.org/10.1016/S0045-7825(01)00188-8
  41. Trahair, N.S. (2003), Flexural-Torsional Buckling of Structures, Spon Press, London, UK.
  42. Zienkiewicz, O.C. and Taylor, R.L. (2000), The Finite Element Method for Solid and Structural Mechanics, (6th Edition), Butterworth-Heinemann, Oxford, UK.

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