References
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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.
- 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
- 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
- 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
- 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.
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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)
- 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
- 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
- Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, (2nd Edition), CRC Press, Boca Raton, FL, USA.
- 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)
- 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
- 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
- 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
- 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
- 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
- Trahair, N.S. (2003), Flexural-Torsional Buckling of Structures, Spon Press, London, UK.
- 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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