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http://dx.doi.org/10.12989/csm.2019.8.6.537

Geometrically exact initially curved Kirchhoff's planar elasto-plastic beam  

Imamovic, Ismar (Faculty of Civil Engineering, University of Sarajevo)
Ibrahimbegovic, Adnan (University of Technology of Compiegne/Sorbonne University Alliance)
Hajdo, Emina (Faculty of Civil Engineering, University of Sarajevo)
Publication Information
Coupled systems mechanics / v.8, no.6, 2019 , pp. 537-553 More about this Journal
Abstract
In this paper we present geometrically exact Kirchhoff's initially curved planar beam model. The theoretical formulation of the proposed model is based upon Reissner's geometrically exact beam formulation presented in classical works as a starting point, but with imposed Kirchhoff's constraint in the rotated strain measure. Such constraint imposes that shear deformation becomes negligible, and as a result, curvature depends on the second derivative of displacements. The constitutive law is plasticity with linear hardening, defined separately for axial and bending response. We construct discrete approximation by using Hermite's polynomials, for both position vector and displacements, and present the finite element arrays and details of numerical implementation. Several numerical examples are presented in order to illustrate an excellent performance of the proposed beam model.
Keywords
Kirchhoff beam; rotated strain measure; Hermite's polynomials; elasto-plastic response;
Citations & Related Records
Times Cited By KSCI : 6  (Citation Analysis)
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1 Ibrahimbegovic, A. and Frey, F. (1993a), "Finite element analysis of linear and non-linear planar deformations of elastic initially curved beam", Int. J. Numer. Meth. Eng., 36, 3239-3258. https://doi.org/10.1002/nme.1620361903.   DOI
2 Ibrahimbegovic, A., Hajdo, E. and Dolarevic, S. (2013), "Linear instability or buckling problems for mechanical and coupled thermomechanical extreme conditions", Coupled Syst. Mech., 2(4), 349-374. https://doi.org/10.12989/csm.2013.2.4.349.   DOI
3 Imamovic, I., Ibrahimbegovic, A. and Mesic, E. (2017), "Nonlinear kinematics Reissner's beam with combined hardening/softening elastoplasticity", Comput. Struct., 189, 17-20. https://doi.org/10.1016/j.compstruc.2017.04.011.
4 Meier, C., Grill, M.J., Wall, W. and Popp, A. (2018), "Geometrically exact beam elements and smooth contact schemes for the modeling of fiber-based materials and structures", Int. J. Solids Struct., 154, 124-46. https://doi.org/10.1016/j.ijsolstr.2017.07.020.   DOI
5 Meier, C., Popp, A. and Wall, W. (2019), "Geometrically exact finite element formulations for slender beams: Kirchhoff-love theory versus Simo-Reissner theory", Arch. Comput. Meth. Eng., 26(1), 163-243. https://doi.org/10.1007/s11831-017-9232-5.   DOI
6 Reissner, E. (1981), "On finite deformations of space-curved beams", Zeitschrift fur angewandte Mathematik und Physik ZAMP, 32(6), 734-44. https://doi.org/10.1007/BF00946983.   DOI
7 Ngo, V.M., Ibrahimbegovic, A. and Hajdo, E. (2014), "Nonlinear instability problems including localized plastic failure and large deformations for extreme thermo-mechanical conditions", Coupled Syst. Mech., 3(1) ,89-110. https://doi.org/10.12989/csm.2014.3.1.089.   DOI
8 Pirmansek, K., Cesarek, P., Zupan, D. and Saje, M. (2017), "Material softening and strain localization in spatial geometrically exact beam finite element method with embedded discontinuity", Comput. Struct., 182, 267-283. https://doi.org/10.1016/j.compstruc.2016.12.009.   DOI
9 Reissner, E. (1972), "On one-dimensional finite-strain beam theory: The plane problem", Zeitschrift fur angewandte Mathematik und Physik ZAMP, 23(5), 795-804. https://doi.org/10.1007/BF01602645.   DOI
10 Simo, J.C. (1985), "A finite strain beam formulation. The three-dimensional dynamic problem. Part I. Computer", Meth. Appl. Mech. Eng., 49(1), 55-70. https://doi.org/10.1016/0045-7825(85)90050-7.   DOI
11 Simo, J.C., Hjelmstad, K.D. and Taylor, R.L. (1984), "Numerical formulations of elasto-viscoplastic response of beams accounting for the effect of shear", Comput. Meth. Appl. Mech. Eng., 42(3), 301-330. https://doi.org/10.1016/0045-7825(84)90011-2.   DOI
12 Hill, R. (1950), The Mathematical Theory of Plasticity, Clarendon Press, Oxford, U.K.
13 Sonneville, V., Bruls, O. and Bauchau, O. (2017), "Interpolation schemes for geometrically exact beams: A motion approach", Int. J. Numer. Meth. Eng., 112(9), 1129-53. https://doi.org/10.1002/nme.5548.   DOI
14 Taylor, R.L. (2008), FEAP - A Finite Element Analysis Program, Berkeley, California, U.S.A.
15 Williams, F.W. (1964), "An approach to the non-linear beahviour of the members of a rigid jointed plane framework with finite deflection", Quart. J. Mech. Appl. Math., 17(4), 451-469. https://doi.org/10.1093/qjmam/17.4.451.   DOI
16 Armero, F. and Valverde, J. (2012), "Invariant Hermitian finite elements for thin Kirchhoff rods. II: The linear three-dimensional case", Comput. Meth. Appl. Mech. Eng., 213-216, 458-85. https://doi.org/10.1016/j.cma.2011.05.014.   DOI
17 Boyer, F. and Primault, D. (2004), "Finite element of slender beams in finite transformations: A geometrically exact approach", Int. J. Numer. Meth. Eng., 59, 669-702. https://doi.org/10.1002/nme.879.   DOI
18 DaDeppo, D.A. and Schmidt, R. (1975), "Instability of clamped-hinged circular arches subjected to a point load", J. Appl. Mech., 42(4), 894-96. https://doi.org/10.1115/1.3423734.   DOI
19 Hadzalic, E., Ibrahimbegovic, A. and Dolarevic, S. (2018), "Failure mechanisms in coupled soil-foundation systems", Coupled Syst. Mech., 7(1), 27-42. https://doi.org/10.12989/csm.2018.7.1.027.   DOI
20 Hadzalic, E., Ibrahimbegovic, A. and Nikolic, M. (2018), "Failure mechanisms in coupled poro-plastic medium", Coupled Syst. Mech., 7(1), 43-59. https://doi.org/10.12989/csm.2018.7.1.043.   DOI
21 Ibrahimbegovic, A. (1992), "A consistent finite-element formulation of non-linear elastic cables", Commun. Appl. Numer. Meth., 8(8), 547-556. https://doi.org/10.1002/cnm.1630080809.   DOI
22 Ibrahimbegovic, A. (1995), "On finite element implementation of geometrically nonlinear Reissner's beam theory: Three-dimensional curved beam elements", Comput. Meth. Appl. Mech. Eng., 122(1-2), 11-26. https://doi.org/10.1016/0045-7825(95)00724-F.   DOI
23 Ibrahimbegovic, A. (2009), Nonlinear Solid Mechanics, Springer, Dordrecht, Germany.
24 Maassen, S., Pimenta, P. and Schroeder, J. (2018), "A geometrically exact euler-bernoulli beam formulation for nonlinear 3d material laws", Proceedings of the 39th Ibero-Latin American Congress on Computational Methods in Engineering, Paris/Compiegne, France, November.
25 Imamovic, I., Ibrahimbegovic, A. and Mesic, E. (2018), "Coupled testing-modeling approach to ultimate state computation of steel structure with connections for statics and dynamics", Coupled Syst. Mech., 7(5), 555-581. https://doi.org/10.12989/csm.2018.7.5.555   DOI
26 Imamovic, I., Ibrahimbegovic, A., Knopf-Lenoir, C. and Mesic, E. (2015), "Plasticity-damage model parameters identification for structural connections", Coupled Syst. Mech., 4(4), 337-364. https://doi.org/10.12989/csm.2015.4.4.337.   DOI
27 Kitarovic, S. (2014) "Nonlinear Euler-Bernoulli beam kinematics in progressive collapse analysis based on the Smith's approach", Mar. Struct., 39, 118-130. https://doi.org/10.1016/j.marstruc.2014.07.001.   DOI
28 Maurin, F., Greco, F., Dedoncker, S. and Desmet, W. (2018), "Isogeometric analysis for nonlinear planar Kirchhoff rods: Weighted residual formulation and collocation of the strong form", Comput. Meth. Appl. Mech. Eng., 340, 1023-1043. https://doi.org/10.1016/j.cma.2018.05.025.   DOI