In this technical brief, a consistent rotation-based formulation is proposed using the absolute nodal coordinate formulation (ANCF) kinematic description. The proposed formulation defines a unique rotation field, employs one interpolation, captures shear deformations, does not suffer from the redundancy problem encountered when using large rotation vector formulations, allows for systematically describing curved geometry, and leads to elastic force definitions that eliminate high-frequency modes associated with the deformation of the cross section. The drawback of this formulation, as it is the case with the large rotation vector formulations, is the nonlinearity of the inertia forces including nonzero Coriolis and centrifugal forces. Furthermore, the formulation does not capture deformation modes that can be captured using the more general ANCF finite elements. Nonetheless, the proposed method is consistent with the continuum mechanics general description, can be related to computational geometry methods, and can be used to develop beam, plate, and shell models without violation of basic mechanics principles.

References

References
1.
Simo
,
J. C.
, and
Vu-Quoc
,
L.
,
1986
, “
On the Dynamics of Flexible Beams Under Large Overall Motions-The Plane Case: Parts I and II
,”
ASME J. Appl. Mech.
,
53
(
4
), pp.
849
863
.
2.
Ding
,
J.
,
Wallin
,
M.
,
Wei
,
C.
,
Recuero
,
A. M.
, and
Shabana
,
A. A.
,
2014
, “
Use of Independent Rotation Field in the Large Displacement Analysis of Beams
,”
Nonlinear Dyn.
,
76
(
3
), pp.
1829
1843
.
3.
Cottrell
,
J. A.
,
Hughes
,
T. J. R.
, and
Bazilevs
,
Y.
,
2009
,
Isogeometric Analysis
,
Wiley
,
Chichester, UK
.
4.
Nachbagauer
,
K.
,
2013
, “
Development of Shear and Cross Section Deformable Beam Finite Elements Applied to Large Deformation and Dynamics Problems
,” Ph.D. dissertation, Johannes Kepler University, Linz, Austria.
5.
Dmitrochenko
,
O.
, and
Mikkola
,
A.
,
2011
, “
Digital Nomenclature Code for Topology and Kinematics of Finite Elements Based on the Absolute Nodal Co-Ordinate Formulation
,”
IMechE J. Multibody Dyn.
,
225
(
1
), pp.
34
51
.
6.
Hamed
,
A. M.
,
Jayakumar
,
P.
,
Letherwood
,
M. D.
,
Gorsich
,
D. J.
,
Recuero
,
A. M.
, and
Shabana
,
A. A.
,
2015
, “
Ideal Compliant Joints and Integration of Computer Aided Design and Analysis
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
2
), p.
021015
.
7.
Hu
,
W.
,
Tian
,
Q.
, and
Hu
,
H. Y.
,
2014
, “
Dynamics Simulation of the Liquid-Filled Flexible Multibody System Via the Absolute Nodal Coordinate Formulation and SPH Method
,”
Nonlinear Dyn.
,
75
(
4
), pp.
653
671
.
8.
Liu
,
C.
,
Tian
,
Q.
, and
Hu
,
H. Y.
,
2011
, “
Dynamics of Large Scale Rigid-Flexible Multibody System Composed of Composite Laminated Plates
,”
Multibody Syst. Dyn.
,
26
(
3
), pp.
283
305
.
9.
Shabana
,
A. A.
,
2012
,
2nd ed.
,
Cambridge University Press
,
Cambridge, UK
.
10.
Shabana
,
A. A.
,
2015
, “
ANCF Tire Assembly Model for Multibody System Applications
,”
ASME J. Comput. Nonlinear Dyn.
,
10
(
2
), p.
024504
.
11.
Tian
,
Q.
,
Chen
,
L. P.
,
Zhang
,
Y. Q.
, and
Yang
,
J. Z.
,
2009
, “
An Efficient Hybrid Method for Multibody Dynamics Simulation Based on Absolute Nodal Coordinate Formulation
,”
ASME J. Comput. Nonlinear Dyn.
,
4
(
2
), p.
021009
.
12.
Tian
,
Q.
,
Sun
,
Y. L.
,
Liu
,
C.
,
Hu
,
H. Y.
, and
Paulo
,
F.
,
2013
, “
Elasto-Hydro-Dynamic Lubricated Cylindrical Joints for Rigid-Flexible Multibody Dynamics
,”
Comput. Struct.
,
114–115
, pp.
106
120
.
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