Rubin,
B.
, 2000, Cosserat Theories: Shells, Rods and Points,
Springer,
Dordrecht, The Netherlands.

Antman,
S. S.
, 1995, Nonlinear Problems in Elasticity,
Springer-Verlag,
New York.

Bauchau,
O. A.
, 2010, Flexible Multibody Dynamics,
Springer,
Dordrecht, The Netherlands.

Shabana,
A. A.
, 2005, Dynamics of Multibody Systems,
Cambridge University Press,
Cambridge, UK.

Géradin,
M.
, and
Cardona,
A.
, 2001, Flexible Multibody Dynamics: A Finite Element Approach,
Wiley,
New York.

Simo,
J. C.
, and
Vu-Quoc,
L.
, 1986, “
A Three-Dimensional Finite-Strain Rod Model—Part II: Computational Aspects,” Comput. Methods Appl. Mech. Eng.,
58(1), pp. 79–116.

[CrossRef]
Simo,
J. C.
, 1985, “
A Finite Strain Beam Formulation. The Three-Dimensional Dynamic Problem—Part I,” Comput. Methods Appl. Mech. Eng.,
49(1), pp. 55–70.

[CrossRef]
Ren,
H.
, 2014, “
A Computationally Efficient and Robust Geometrically-Exact Curved Beam Formulation for Multibody Systems,” The 3rd Joint International Conference on Multibody System Dynamics and The 7th Asian Conference on Multibody Dynamics ( IMSD2014-ACMD2014), Bushan, Korea, June 30–July 3, Paper No. 0228.

Zupan,
E.
,
Saje,
M.
, and
Zupan,
D.
, 2009, “
The Quaternion-Based Three-Dimensional Beam Theory,” Comput. Methods Appl. Mech. Eng.,
198(49–52), pp. 3944–3956.

[CrossRef]
Jelenić,
G.
, and
Crisfield,
M.
, 1999, “
Geometrically Exact 3D Beam Theory: Implementation of a Strain-Invariant Finite Element for Statics and Dynamics,” Comput. Methods Appl. Mech. Eng.,
171(1), pp. 141–171.

[CrossRef]
Ibrahimbegović,
A.
, 1995, “
On Finite Element Implementation of Geometrically Nonlinear Reissner's Beam Theory: Three-Dimensional Curved Beam Elements,” Comput. Methods Appl. Mech. Eng.,
122(1), pp. 11–26.

[CrossRef]
Geradin,
M.
, and
Cardona,
A.
, 1988, “
Kinematics and Dynamics of Rigid and Flexible Mechanisms Using Finite Elements and Quaternion Algebra,” Comput. Mech.,
4(2), pp. 115–135.

[CrossRef]
Cardona,
A.
, and
Geradin,
M.
, 1988, “
A Beam Finite-Element Non-Linear Theory With Finite Rotations,” Int. J. Numer. Methods Eng.,
26(11), pp. 2403–2438.

[CrossRef]
Bauchau,
O. A.
, and
Han,
S. L.
, 2014, “
Interpolation of Rotation and Motion,” Multibody Syst. Dyn.,
31(3), pp. 339–370.

[CrossRef]
Romero,
I.
, 2004, “
The Interpolation of Rotations and Its Application to Finite Element Models of Geometrically Exact Rods,” Comput. Mech.,
34(2), pp. 121–133.

[CrossRef]
Yakoub,
R. Y.
, and
Shabana,
A. A.
, 2001, “
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications,” ASME J. Mech. Des.,
123(4), pp. 614–621.

[CrossRef]
Shabana,
A. A.
, and
Yakoub,
R. Y.
, 2001, “
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Theory,” ASME J. Mech. Des.,
123(4), pp. 606–613.

[CrossRef]
Shabana,
A. A.
, 1996, “
An Absolute Nodal Coordinate Formulation for the Large Rotation and Deformation Analysis of Flexible Bodies,” University of Illinois at Chicago, Chicago, IL, Technical Report No. MBS96-1-UIC.

Romero,
I.
, 2008, “
A Comparison of Finite Elements for Nonlinear Beams: The Absolute Nodal Coordinate and Geometrically Exact Formulations,” Multibody Syst. Dyn.,
20(1), pp. 51–68.

[CrossRef]
Shabana,
A. A.
, 2011, Computational Continuum Mechanics,
Cambridge University Press,
Cambridge, UK.

Gerstmayr,
J.
, and
Irschik,
H.
, 2008, “
On the Correct Representation of Bending and Axial Deformation in the Absolute Nodal Coordinate Formulation With an Elastic Line Approach,” J. Sound Vib.,
318(3), pp. 461–487.

[CrossRef]
Sopanen,
J. T.
, and
Mikkola,
A. M.
, 2003, “
Description of Elastic Forces in Absolute Nodal Coordinate Formulation,” Nonlinear Dyn.,
34(1–2), pp. 53–74.

[CrossRef]
Sugiyama,
H.
, and
Suda,
Y.
, 2007, “
A Curved Beam Element in the Analysis of Flexible Multi-Body Systems Using the Absolute Nodal Coordinates,” Proc. Inst. Mech. Eng. Part K,
221(2), pp. 219–231.

[CrossRef]
Ren,
H.
, 2015, “
A Simple Absolute Nodal Coordinate Formulation for Thin Beams With Large Deformations and Large Rotations,” ASME J. Comput. Nonlinear Dyn.,
10(6), p. 061005.

[CrossRef]
Von Dombrowski,
S.
, 2002, “
Analysis of Large Flexible Body Deformation in Multibody Systems Using Absolute Coordinates,” Multibody Syst. Dyn.,
8(4), pp. 409–432.

[CrossRef]
Zhao,
Z. H.
, and
Ren,
G. X.
, 2012, “
A Quaternion-Based Formulation of Euler–Bernoulli Beam Without Singularity,” Nonlinear Dyn.,
67(3), pp. 1825–1835.

[CrossRef]
Gerstmayr,
J.
,
Sugiyama,
H.
, and
Mikkola,
A.
, 2013, “
Review on the Absolute Nodal Coordinate Formulation for Large Deformation Analysis of Multibody Systems,” ASME J. Comput. Nonlinear Dyn.,
8(3), p. 031016.

[CrossRef]
Bauchau,
O. A.
,
Han,
S. L.
,
Mikkola,
A.
, and
Matikainen,
M. K.
, 2014, “
Comparison of the Absolute Nodal Coordinate and Geometrically Exact Formulations for Beams,” Multibody Syst. Dyn.,
32(1), pp. 67–85.

[CrossRef]
Zhu,
W. D.
,
Ren,
H.
, and
Xiao,
C.
, 2011, “
A Nonlinear Model of a Slack Cable With Bending Stiffness and Moving Ends With Application to Elevator Traveling and Compensation Cables,” ASME J. Appl. Mech.,
78(4), p. 041017.

[CrossRef]
Huang,
J. L.
, and
Zhu,
W. D.
, 2014, “
Nonlinear Dynamics of a High-Dimensional Model of a Rotating Euler–Bernoulli Beam Under the Gravity Load,” ASME J. Appl. Mech.,
81(10), p. 101007.

[CrossRef]
Li,
L.
,
Zhu,
W. D.
,
Zhang,
D. G.
, and
Du,
C. F.
, 2015, “
A New Dynamic Model of a Planar Rotating Hub-Beam System Based on a Description Using the Slope Angle and Stretch Strain of the Beam,” J. Sound Vib.,
345, pp. 214–232.

[CrossRef]
Fan,
W.
,
Zhu,
W. D.
, and
Ren,
H.
, 2016, “
A New Singularity-Free Formulation of a Three-Dimensional Euler–Bernoulli Beam Using Euler Parameters,” ASME J. Comput. Nonlinear Dyn.,
11(4), p. 041013.

[CrossRef]
Timoshenko,
S. P.
, and
Goodier,
J.
, 1970, Theory of Elasticity,
McGraw-Hill,
New York.

Arnold,
M.
, and
Brüls,
O.
, 2007, “
Convergence of the Generalized-α Scheme for Constrained Mechanical Systems,” Multibody Syst. Dyn.,
18(2), pp. 185–202.

[CrossRef]
Chung,
J.
, and
Hulbert,
G.
, 1993, “
A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method,” ASME J. Appl. Mech.,
60(2), pp. 371–375.

[CrossRef]
Gerstmayr,
J.
, and
Shabana,
A.
, 2005, “
Efficient Integration of the Elastic Forces and Thin Three-Dimensional Beam Elements in the Absolute Nodal Coordinate Formulation,” Multibody Dynamics of ECCOMAS Thematic Conference, Madrid, Spain, June 21–24.

Kelley,
C. T.
, 2003, Solving Nonlinear Equations With Newton's Method,
SIAM,
Philadelphia.

Bathe,
K. J.
, and
Bolourchi,
S.
, 1979, “
Large Displacement Analysis of Three-Dimensional Beam Structures,” Int. J. Numer. Methods Eng.,
14(7), pp. 961–986.

[CrossRef]
Shigley,
J. E.
,
Budynas,
R. G.
, and
Mischke,
C. R.
, 2004, Mechanical Engineering Design,
McGraw-Hill,
New York.

Gerstmayr,
J.
, and
Shabana,
A. A.
, 2006, “
Analysis of Thin Beams and Cables Using the Absolute Nodal Co-Ordinate Formulation,” Nonlinear Dyn.,
45(1–2), pp. 109–130.

[CrossRef]
Kramer,
E.
, 1993, Dynamics of Rotors and Foundations,
Springer-Verlag,
London.