Geometrically nonlinear analysis of 3D framed structures has focused on the treatment of the difficulties associated with finite nodal rotations. The Co-rotational formulation excludes the rigid body rotation of the element, and to account for this aspect the addition of a stability matrix is required to the natural tangent stiffness matrix. This spatial beam element stability matrix needs to fully account for the behaviour of the nodal forces and moments on the rigid body rotation. In the context of the Co-rotational formulation, the correct stability matrix is used in conjunction with the natural tangent stiffness matrix. The natural finite element concept used for the numerical analysis of nonlinear structural problems is extended to the Co-rotational formulation. It is shown through numerical examples that fully account for the rotational behaviour of nodal moments, that the Co-rotational formulation can accurately predict the flexural-torsional buckling loads for spatial structures in which the members are not connected collinearly.
ArgyrisJ.H.HilpertO.MalejannakisG.A. and ScharpfD.W. (1979). “On the geometrical stiffness of a beam in space-A consistent V.W. approach”, Computer Methods in Applied Mechanics and Engineering, Vol. 20, No. 1, pp. 105–131.
2.
ArgyrisJ.H.DunneP.C. and ScharpfD.W. (1978). “On large displacement-small strain analysis of structures with rotation DOF”, Computer Methods in Applied Mechanics and Engineering, Vol. 14, No. 3, pp. 401–451.
3.
ChanS.L. and ZhouZ.H. (1994). “Pointwise equilibrium polynomial element for nonlinear analysis of frames”, Journal of Structural Engineering, ASCE, Vol. 120, No. 6, pp. 1703–1717.
4.
ChenH. and BlandfordG.E. (1991). “Thin-walled space frames. I: Large deformation analysis theory”, Journal of Structural Engineering, ASCE, Vol. 117, No. 8, pp. 2499–2520.
5.
ChengH. and GuptaK.G. (1989). “An historical note on finite rotations”, Journal of Applied Mechanics, Vol. 56, No. 1, pp. 139–145.
6.
ConciA. and GattassM. (1990). “Natural approach for geometric non-linear analysis of thin-walled frames”, International Journal for Numerical Methods in Engineering, Vol. 30, No. 1, pp. 211–212.
7.
CrisfieldM.A. (1990). “A consistent co-rotational formulation for non-linear, three-dimensional beam elements”, Computer Methods in Applied Mechanics and Engineering, Vol. 81, No. 2, pp. 131–150.
8.
EliasZ.M. (1986). Theory and Methods of Structural Analysis, John Wiley and Sons, New York, USA.
9.
KimM.Y.ChangS.P. and ParkH.G. (2001). “Spatial postbuckling analysis of nonsymmetric thin-walled frames. I: Theoretical considerations based on semitangential property”, Journal of Engineering Mechanics, ASCE, Vol. 127, No. 8, pp. 769–778.
10.
KimM.Y.ChangS.P. and KimS.B. (2001). “Spatial postbuckling analysis of nonsymmetric thin-walled frames. II: Geometrically nonlinear FE procedures”, Journal of Engineering Mechanics, ASCE, Vol. 127, No. 8, pp. 779–790.
11.
LeungA.Y.T. and WongC.K. (2000). “Symmetry reduction of structures for large rotations”, Advances in Structural Engineering, Vol. 3, No. 1, pp. 81–102.
12.
MeekJ.L. and TanH.S. (1984). “Geometrically nonlinear analysis of space frames by an incremental iterative technique”, Computer Methods in Applied Mechanics and Engineering, Vol. 47, No. 3, pp. 261–282.
13.
MeekJ.L. and LoganathanS. (1989). “Large displacement analysis of space-frame structures”, Computer Methods in Applied Mechanics and Engineering, Vol. 72, No. 1, pp. 57–75.
14.
OranC. (1973). “Tangent stiffness in space frames”, Journal of the Structural Division, ASCE, Vol. 99, No. 6, pp. 981–1001.
15.
KuoS.R.YangY.B. and ChouJ.H. (1993). “Nonlinear analysis of space frames with finite rotations”, Journal of Structural Engineering, ASCE, Vol. 119, No. 1, pp. 1–15.
16.
TehL.H. and ClarkeM.J. (1997). “New definition of conservative internal moments in space frames”, Journal of Engineering Mechanics, ASCE, Vol. 123, No. 2, pp. 97–106.
17.
TehL.H. and ClarkeM.J. (1998). “Co-rotational and Lagrangian formulations for elastic three-dimensional beam finite elements”, Journal of Constructional Steel Research, Vol. 48, No. 2–3, pp. 123–144.
18.
TehL.H. and ClarkeM.J. (1999). “Symmetry of tangent stiffness matrices of 3Delastic frame”, Journal of Engineering Mechanics, ASCE, Vol. 125, No. 2, pp. 248–251.
19.
YangY.B. and McGuireW. (1986). “A stiffness matrix for geometric nonlinear analysis”, Journal of Structural Engineering, ASCE, Vol. 112, No. 4, pp. 853–877.
20.
YangY.B. and McGuireW. (1986). “Joint rotation and geometric nonlinear analysis”, Journal of Structural Engineering, ASCE, Vol. 112, No. 4, pp. 879–905.
21.
YangY.B. and ChiouH.T. (1987). “Rigid body motion test for nonlinear analysis with beam elements”, Journal of Engineering Mechanics, ASCE, Vol. 113, No. 9, pp. 1404–1419.
22.
YangY.B. and ShiehM.S. (1990). “Solution method for nonlinear problems with multiple critical points”, AIAA Journal, Vol. 28, No. 12, pp. 2110–2106.
23.
YangY.B. and KuoS.R. (1994). Theory and Analysis of Nonlinear Framed Structures, Prentice Hall, Englewood Cliffs, NJ, USA.
24.
YangY.B.KuoS.R. and WuY.S. (2002). “Incrementally small deformation theory for nonlinear analysis of structural frames”, Engineering Structures, Vol. 24, No. 6, pp. 783–798.
25.
YangY.B.YauJ.D. and LeuL.J. (2003). Recent Developments in Geometrically Nonlinear and Postbuckling Analysis of Framed Structures, American Society of Civil Engineers, Reston, VA, USA.
26.
YangY.B.LinS.P. and ChenC.S. (2007). “Solution strategy and rigid element for nonlinear analysis of elastically structures based on updated Lagrangian formulation”, Engineering Structures, Vol. 29, No. 6, pp. 1189–1200.
27.
YangY.B. and KuoS.R. (1991). “Consistent frame buckling analysis by finite element method”, Journal of Structural Engineering, ASCE, Vol. 117, No. 4, pp. 1053–1069.
28.
YangY.B.KuoS.R. and YauJ.D. (1991). “Use of straight-beam approach to study buckling of curved beams”, Journal of Structural Engineering, ASCE, Vol. 117, No. 7, pp. 1963–1978.
