Updated Lagrangian Co-rotational Formulation for Geometrically Nonlinear FE Analysis of 3-D Beam Element

BATHE K J,RAMM E,WILSON E L.Finite element formulations for large deformation dynamic analysis[J]. International Journal of Numerical Methods and Engineering,1975,9(2):353-386.[2] BATHE K J.An assessment of current finite element analysis of nonlinear problems in solid mechanics[C] // Numerical Solution of Partial Differential Equations.Maryland:University of Maryland,1975.[3] BATHE K J,BOLOURCHI S.Large displacement analysis of three-dimensional beam structures[J]. International Journal of Numerical Methods and Engineering,1979,14 (7):961-986.[4] 陈政清,曾庆元,颜全胜.空间杆系结构大挠度问题内力分析的UL列式法[J]. 土木工程学报,1992,25(5):34-44.[5] WEMPNER G A.Finite elements,finite rotations and small strains of flexible shells[J]. International Journal of Solids and Structures,1969,5:117-153.[6] BELYTSCHKO T,SCHWER L.Non-linear transient finite element analysis with convected co-ordinates[J]. International Journal of Numerical Methods and Engineering,1973,7(9):255-271.[7] HUGHERS T,WINGET J.Finite rotation effects in numerical integration of rate constitutive equations arising in largedeformation analysis[J]. International Journal of Numerical Methods and Engineering,1980,15 (12):1 862-1 867.[8] ARGYRIS J H.An excursion into large rotations[J]. Computer Methods in Applied Mechanics and Engineering,1982,32(5):85-155.[9] RANKIN C C,BROGAN F A.An element independent corotational procedure for the treatment of large rotations[J]. Journal of Pressure Vessel Technology,1986,108:165-174.[10] CRISFIELD M A,MOITA G F.A unified co-rotational framework for solids,shells and beams[J]. International Journal of Solids and Structures,1996,33(24):2 969-2 992.[11] HSIAO K,LIN W Y.Co-rotational finite element formulation for buckling and post buckling analyses of spatial beams[J]. Computer Methods in Applied Mechanics and Engineering,2000,188 (3):567-594.[12] FELIPPA C A,HAUGEN B.A unified formulation of small-strain corotational finite elements[J]. Theory Computer Methods in Applied Mechanics and Engineering,2005,194(19):2 285-2 335.