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http://dx.doi.org/10.12989/csm.2017.6.4.501

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)
Publication Information
Coupled systems mechanics / v.6, no.4, 2017 , pp. 501-522 More about this Journal
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
iterative global-local method; multi-scale analysis; finite elements; elasto-plastic behavior; structural dynamics;
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Times Cited By KSCI : 4  (Citation Analysis)
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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.   DOI
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.   DOI
5 Belytschko, T. (2001), "Arbitrary discontinuities in finite elements", J. Numer.Meth. Eng., 50(4), 993-1013.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
17 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.   DOI
18 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.
19 Farris, T.N. and Doyle, J.F. (1993), "A global/local approach to lengthwise cracked beams-dynamic analysis", J. Fract., 60(2), 147-156.   DOI
20 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.   DOI
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.   DOI
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.   DOI
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.   DOI
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.   DOI
25 Mao, K.M. and Sun, C.T. (1991), "A refined global-local finite element analysis method", J. Numer. Meth. Eng., 32(1), 29-43.   DOI
26 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.   DOI
27 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.   DOI
28 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.   DOI
29 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.   DOI
30 Liu, W., Hao, S., Belytschko, T., Li, S. and Chang, C. (2000), "Multi-scale methods", J. Numer. Meth. Eng., 50, 993-1013.
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.   DOI
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.   DOI
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.   DOI
35 Simo, J.C. and Hughes, T.J.R. (1998), Computational Inelasticity, Springer-Verlag (Interdisciplinary Applied Mathematics, New York, U.S.A.
36 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.   DOI
37 Strouboulis, T., Copps, K. and Babuska, I. (2001), "The generalized finite element method", Comput. Meth. Appl. Mech. Eng., 190, 4081-4193.   DOI
38 Sun, C.T. and Mao, K.M. (1988), "A global-local finite element method suitable for parallel computations", Comput. Struct., 29(2), 309-315.   DOI
39 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.   DOI
40 Whitcomb, J.D. (1991), "Iterative global/local finite element analysis", Comput. Struct., 40, 1027-1031.   DOI
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.   DOI