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http://dx.doi.org/10.12989/sem.2014.51.4.601

Large displacement geometrically nonlinear finite element analysis of 3D Timoshenko fiber beam element  

Hu, Zhengzhou (Department of Building Engineering, Tongji University)
Wu, Minger (Department of Building Engineering, Tongji University)
Publication Information
Structural Engineering and Mechanics / v.51, no.4, 2014 , pp. 601-625 More about this Journal
Abstract
Based on continuum mechanics and the principle of virtual displacements, incremental total Lagrangian formulation (T.L.) and incremental updated Lagrangian formulation (U.L.) were presented. Both T.L. and U.L. considered the large displacement stiffness matrix, which was modified to be symmetrical matrix. According to the incremental updated Lagrangian formulation, small strain, large displacement, finite rotation of three dimensional Timoshenko fiber beam element tangent stiffness matrix was developed. Considering large displacement and finite rotation, a new type of tangent stiffness matrix of the beam element was developed. According to the basic assumption of plane section, the displacement field of an arbitrary fiber was presented in terms of nodal displacement of centroid of cross-area. In addition, shear deformation effect was taken account. Furthermore, a nonlinear finite element method program has been developed and several examples were tested to demonstrate the accuracy and generality of the three dimensional beam element.
Keywords
3D Timoshenko fiber beam element; large displacement matrix; finite rotation; total Lagrangian formulation and updated Lagrangian formulation; incremental nonlinear finite element method;
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1 Argyris, J.H., Boni, B., Hindenlang, U. and Kleiber, M. (1982), "Finite element analysis of two- and threedimensional elasto-plastic frames- the natural approach" Comput. Meth. Appl. Mech. Eng., 35(2), 221-248.   DOI   ScienceOn
2 Bathe, K.J. (1982), Finite Element Procedures in Engineering Analysis, Prentice-Hall, New Jersey, USA.
3 Bazoune, A., Khulief, Y.A. and Stephen, N.G. (2003), "Shape functions of three-dimensional Timoshenko beam element" J. Sound. Vib., 259(2), 473-480.   DOI
4 Bathe, K.J. and Bolourch, I.S. (1979), "Large displacement analysis of three-dimensional beam structures" Int. J. Numer. Meth. Eng., 14(7), 961-986.   DOI   ScienceOn
5 Bathe, K.J., Ramm. E. and Wilson. E.L. (1975), "Finite element formulations for large deformation dynamic analysis" Int. J. Numer. Meth. Eng., 9(2), 353-386.   DOI   ScienceOn
6 Bathe, K.J. and Wilson, E.L. (1974), "Nonsap-a nonlinear structural analysis program" Nucl. Eng. Des., 29(2), 266-293.   DOI
7 Belytschko, T. and Hsieh, B.J. (1973), "Non-linear transient finite element analysis with convected coordinates" Int. J. Numer. Meth. Eng., 7(3), 255-271.   DOI   ScienceOn
8 Cai, Y.C. and Atluri, S.N. (2012), "Large rotation analyses of plate/shell structures based on the primal variational principle and a fully nonlinear theory in the updated Lagrangian co-rotational reference frame" CMES-Comp. Model. Eng., 83(3), 49-273.
9 Chu, K.H. and Rampetsreiter, R.H. (1972), "Large deflection buckling of space frames" J. Struct. Div., 98(12), 2701-2722.
10 Crisfield, M.A. (1983), "An arc-length method including line searches and accelerations" Int. J. Numer. Meth. Eng., 19(9), 1269-1289.   DOI   ScienceOn
11 Crivelli, L.A. and Felippa, C.A. (1993), "A three dimensional nonlinear Timoshenko beam based on the core-congruential formulation" Int. J. Numer. Meth. Eng., 36(21), 3647-3673.   DOI
12 Huu, T.T. and Seung, E.K. (2011a), "Second-order inelastic dynamic analysis of steel frames using fiber hinge method" J. Constr. Steel Res., 67(10), 1485-1494.   DOI
13 Eduardo, N.D., Eugenio, O. and Javier, O. (1988), "On a non-linear formulation for curved Timoshenko beam elements considering large displacement/rotation increments" Int. J. Numer. Meth. Eng., 26(7), 1597-1613.   DOI   ScienceOn
14 Griggs, H.P. (1996), "Experimental study of instability in elements of shallow space frames" Research Reprot, Dept. of Civil Eng, MIT, Cambridge, USA.
15 Hibbitt, H.D., Marcal, P.V. and Rice, J.R. (1970), "A finite element formulation for problems of large strain and large displacement" Int. J. Solid. Struct., 6(8), 1069-1086.   DOI   ScienceOn
16 Huu, T.T. and Seung, E.K. (2011b), "Nonlinear inelastic analysis of concrete-filled steel tubular frames" J. Constr. Steel Res., 67(12), 1797-1805.   DOI
17 Li, Z.X. and Izzuddin, B.A. (2011), "A mixed co-rotational curved quadrilateral shell element" Int. J. Struct. Eng., 2(2), 188-208.   DOI
18 Huu, T.T. and Seung, E.K. (2012), "Second-order inelastic analysis of cable-stayed bridges" Finite Elem. Anal. Des., 53, 48-55.   DOI
19 Li, Y., Lu, X.Z., Ye, L.P. and Ren, A.Z. (2012), "Numerical models of fire induced progressive collapse analysis for reinforced concrete frame structures" Eng. Mech., 29(4), 96-103.
20 Li, Z.X., Liu, Y.F., Izzuddin, B.A. and Vu-Quoc, L.A. (2011), "Stabilized co-rotational curved quadrilateral composite shell element" Int. J. Numer. Meth. Eng., 86(8), 975-999.   DOI
21 Meek, J.L. and Tan, H.S. (1984), "Geometrically nonlinear analysis of space frames by an incremental iterative technique" Comput. Meth. Appl. Mech. Eng., 47(3), 261-282.   DOI   ScienceOn
22 Papadrakakis, M. (1981), "Post-buckling analysis of spatial structures by vector iteration methods" Comput. Struct., 14(5-6), 393-402.   DOI   ScienceOn
23 Nie, J.G. and Wang, Y.H. (2012), "Development and application of steel-concrete composite fiber beam model in ABAQUS platform" Eng. Mech., 29(1), 70-80.
24 Nour-Omid, B. and Rankin, C.C. (1991), "Finite rotation analysis and consistent linearization using projectors" Comput. Meth. Appl. Mech. Eng., 93(3), 353-384.   DOI
25 Oran, C. (1973), "Tangent stiffness in space frames" J. Struct. Div., 99(6), 987-1001.
26 Park, M.S. and Lee, B.C. (1998), "Geometrically non-linear and elastoplastic three dimensional shear flexible beam element of von-mises-type hardending material" Int. J. Numer. Meth. Eng., 39(3), 383-408.
27 Shi, G. and Atluri, S.N. (1988), "Elasto-plastic large deformation analysis of space-frames: a plastic-hinge and stress-based explicit derivation of tangent stiffnesses" Int. J. Numer. Meth. Eng., 26(3), 589-615.   DOI   ScienceOn
28 Pramin, N., Songsak, S. and Ki, K. (2012), "A co-rotational 8-node degenerated thin-walled element with assumed natural strain and enhanced assumed strain" Finite Elem. Anal. Des., 50, 70-85.   DOI
29 Riks, E. (1979), "An incremental approach to the solution of snapping and buckling problems" Int. J. Solid. Struct., 15(7), 529-551.   DOI   ScienceOn
30 Schulz, M. and Filippou, F.C. (2001), "Non-linear spatial Timoshenko beam element with curvature interpolation" Int. J. Numer. Meth. Eng., 50(4), 761-785.   DOI
31 Spacone, E., Filippou, F.C. and Taucer, F.F. (1996a), "Fiber beam-column model for nonlinear analysis of R/C frames: part I. Formulation" Earthq. Eng. Struct., 25(7), 711-725.   DOI
32 Spacone, E., Filippou, F.C. and Taucer, F.F. (1996b), "Fiber beam-column model for nonlinear analysis of R/C frames: part II. Applications" Earthq. Eng Struct, 25(7), 727-742.   DOI
33 Taucer, F.F., Spacone, E. and Filippou, F.C. (1991), "A Fiber Beam-Column Element for Seismic Response Analysis of Reinforced Concrete Structures" EERC Report 91/17, Earthquake Engineering Research Center, University of California.
34 Tort, C. and Hajjar, J. (2010), "Mixed finite element for three-dimensional nonlinear dynamic analysis of rectangular concrete-filled steel tube beam-columns" J. Eng. Mech., 136(11), 1329-1339.   DOI   ScienceOn
35 Zeris, C.A. and Mahin, S.A. (1991), "Behavior of reinforced concrete structures subjected to biaxial excitation" J. Struct. Eng., 117(9), 2657-2673.   DOI
36 Yang, Y.B. (1994), Theory and Analysis of Nonlinear Framed Structures, Prentice-Hall, New Jersey, USA.
37 Watson, L.T. and Holzer, S.M. (1984), "Quadratic convergence of crisfield's method" Comput. Struct., 17(1), 69-72.
38 William, F.W. (1964), "An approach to the non-linear behaviour of the members of a rigid jointed plane framework with finite deflections" Q. J. Mech. Appl. Math., 17(4), 451-469.   DOI
39 Zhang, L.X., Xu, G.L. and Bai, Y.S. (2011), "Fiber model based on Timoshenko beam theory and its application" Adv. Sci. Lett., 4(4-5), 1886-1888.   DOI
40 Zubydan, A.H. and ElSabbagh, A.I. (2011), "Monotonic and cyclic behavior of concrete-filled steel-tube beam-columns considering local buckling effect" Thin Wall. Struct., 49(4), 465-481.   DOI
41 Zeris, C.A. and Mahin, S.A. (1988), "Analysis of reinforced concrete beam-columns under uniaxial excitation" J. Struct. Eng., 114(4), 804-820.   DOI
42 Crisfield, M.A. and Moita. G.F. (1996), "A unified co-rotational frame work for solids, shells and beams" Int. J. Solid. Struct., 33(20-22), 2969-2992.   DOI