In extension to a former work, a detailed comparison of the absolute nodal coordinate formulation (ANCF) and the floating frame of reference formulation (FFRF) is performed for standard static and dynamic problems, both in the small and large deformation regimes. Special emphasis is laid on converged solutions and on a comparison to analytical and numerical solutions from the literature. In addition to the work of previous authors, the computational performance of both formulations is studied for the dynamic case, where detailed information is provided, concerning the different effects influencing the single parts of the computation time. In case of the ANCF finite element, a planar formulation based on the Bernoulli–Euler theory is utilized, consisting of two position and two slope coordinates in each node only. In the FFRF beam finite element, the displacements are described by the rigid body motion and a small superimposed transverse deflection. The latter is described by means of two static modes for the rotation at the boundary and a user-defined number of eigenmodes of the clamped-clamped beam. In numerical studies, the accuracy and computational costs of the two formulations are compared for a cantilever beam, a pendulum, and a slider-crank mechanism. It turns out that both formulations have comparable performance and that the choice of the optimal formulation depends on the problem configuration. Recent claims in literature that the ANCF would have deficiencies compared with the FFRF thus can be refuted.

1.
Ashley
,
H.
, 1967, “
Observation of the Dynamic Behavior of Flexible Bodies in Orbit
,”
AIAA J.
,
5
(
3
), pp.
460
469
. 0001-1452
2.
Canavin
,
J. R.
, and
Likins
,
P. W.
, 1977, “
Floating Reference Frames for Flexible Spacecrafts
,”
J. Spacecr. Rockets
,
14
(
12
), pp.
724
732
. 0022-4650
3.
De Veubeke
,
B. J.
, 1976, “
The Dynamics of Flexible Bodies
,”
Int. J. Eng. Sci.
0020-7225,
14
, pp.
895
913
.
4.
Gerstmayr
,
J.
, and
Irschik
,
H.
, 2003, “
Vibrations of the Elasto-Plastic Pendulum
,”
Int. J. Non-Linear Mech.
,
38
, pp.
111
122
. 0020-7462
5.
Dibold
,
M.
,
Gerstmayr
,
J.
, and
Irschik
,
H.
, 2003, “
Biaxial Vibrations of an Elasto-Plastic Beam With a Prescribed Rigid-Body Rotation
,”
IDETC/CIE 2003, ASME 2003 International Design Engineering Technical Conference
, Chicago, IL, ASME Paper No. DETC03/VIB-48324.
6.
Géradin
,
M.
, and
Cardona
,
A.
, 2001,
Flexible Multibody Dynamics—A Finite Element Approach
,
Wiley
,
New York
.
7.
Omar
,
M. A.
, and
Shabana
,
A. A.
, 2001, “
A Two-Dimensional Shear Deformation Beam for Large Rotation and Deformation
,”
J. Sound Vib.
0022-460X,
243
(
3
), pp.
565
576
.
8.
Berzeri
,
M.
, and
Shabana
,
A. A.
, 2000, “
Development of Simple Models for the Elastic Forces in the Absolute Nodal Coordinate Formulation
,”
J. Sound Vib.
0022-460X,
235
(
4
), pp.
539
565
.
9.
Yakoub
,
R. Y.
, and
Shabana
,
A. A.
, 2001, “
Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Application
,”
ASME J. Mech. Des.
0161-8458,
123
, pp.
614
621
.
10.
Shabana
,
A. A.
, and
Mikkola
,
A. M.
, 2003, “
Use of the Finite Element Absolute Nodal Coordinate Formulation in Modelling Slope Discontinuity
,”
ASME J. Mech. Des.
1050-0472,
125
(
2
), pp.
342
350
.
11.
Schiehlen
,
W.
, 1997, “
Multibody System Dynamics: Roots and Perspectives
,”
Multibody Syst. Dyn.
1384-5640,
1
, pp.
149
188
.
12.
Shabana
,
A. A.
, and
Schwertassek
,
R.
, 1998, “
“Equivalence of the Floating Frame of Reference Approach and Finite Element Formulations
,”
Int. J. Non-Linear Mech.
0020-7462,
33
(
3
), pp.
417
432
.
13.
Shabana
,
A. A.
,
Hussien
,
H.
, and
Escalona
,
J.
, 1998, “
Application of the Absolute Nodal Coordinate Formulation to Large Rotation and Large Deformation Problems
,”
ASME J. Mech. Des.
0161-8458,
120
, pp.
188
195
.
14.
Zander
,
R.
, and
Ulbrich
,
H.
, 2006, “
Free Plain Motion of Flexible Beams in MBS—A Comparison of Models
,”
Mech. Based Des. Struct. Mach.
1539-7734,
34
(
4
), pp.
365
387
.
15.
Rodrıguez
,
J. I.
,
Jimenez
,
J. M.
,
Funes
,
F. M.
, and
Garcıa de Jalon
,
J.
, 2004, “
Recursive and Residual Algorithms for the Efficient Numerical Integration of Multi-Body Systems
,”
Multibody Syst. Dyn.
,
11
, pp.
295
320
. 1384-5640
16.
Shabana
,
A. A.
, 1998,
Dynamics of Multibody Systems
,
2nd ed.
,
Cambridge University Press
,
Cambridge, England
.
17.
Gerstmayr
,
J.
, and
Shabana
,
A. A.
, 2006, “
Analysis of Thin Beams and Cables Using the Absolute Nodal Coordinate Formulation
,”
Nonlinear Dyn.
0924-090X,
45
(
1–2
), pp.
109
130
.
18.
Schwab
,
A. L.
, and
Meijaard
,
J. P.
, 2005,
Proceedings of the IDETC/CIE 2005, ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2005
, Long Beach, CA, ASME Paper No. DETC2005-85104.
19.
Sopanen
,
J. T.
, and
Mikkola
,
A. M.
, 2003, “
Studies on the Stiffness Properties of the Absolute Nodal Coordinate Formulation for Three-Dimensional Beams
,”
Nonlinear Dyn.
0924-090X,
34
, pp.
53
74
.
20.
Gerstmayr
,
J.
, and
Shabana
,
A. A.
, 2005, “
Efficient Integration of the Elastic Forces and Thin Three-Dimensional Beam Elements in the Absolute Nodal Coordinate Formulation
,”
Multibody Dynamics 2005, ECCOMAS Thematic Conference
,
G.
Cuadrado
and
G.
Orden
, eds., Madrid, Spain, CD-ROM.
21.
Gerstmayr
,
J.
, and
Matikainen
,
M.
, 2006, “
Improvement of the Accuracy of Stress and Strain in the Absolute Nodal Coordinate Formulation
,”
Mech. Based Des. Struct. Mach.
1539-7734,
34
(
4
), pp.
409
430
.
22.
Gerstmayr
,
J.
, and
Schöberl
,
J.
, 2006, “
A 3D Finite Element Method for Flexible Multibody Systems
,”
Multibody Syst. Dyn.
,
15
, pp.
305
324
. 1384-5640
23.
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.
0022-460X,
318
, pp.
359
384
.
24.
Simo
,
J. C.
, and
Vu-Quoc
,
L.
, 1986, “
On the Dynamics of Flexible Beams Under Large Overall Motion—The Plane Case: Part I
,”
ASME J. Appl. Mech.
,
53
, pp.
849
855
. 0021-8936
25.
Reissner
,
E.
, 1972, “
On One-Dimensional Finite-Strain Beam Theory: The Plane Problem
,”
Z. Angew. Math. Phys.
0044-2275,
23
, pp.
795
804
.
26.
Dibold
,
M.
,
Gerstmayr
,
J.
, and
Irschik
,
H.
, 2007, “
On the Accuracy and Computational Costs of the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation in Deformable Multibody Systems
,”
Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/MSNDC 2007
, Las Vegas, NV, Sept. 4–7, ASME Paper No. DETC2007-34756.
27.
1991,
Hütte, Die Grundlagen der Ingenieurwissenschaften
,
29th ed.
,
H.
Czichos
, ed.,
Springer-Verlag
,
Berlin
.
28.
Ziegler
,
F.
, 1991,
Mechanics of Solids and Fluids
,
Springer-Verlag
,
New York
.
29.
Dmitrochenko
,
O. N.
, and
Pogorelov
,
D. Y.
, 2003, “
Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation
,”
Multibody Syst. Dyn.
1384-5640,
10
, pp.
17
43
.
30.
Dufva
,
K. E.
,
Sopanen
,
J. T.
, and
Mikkola
,
A. M.
, 2005, “
A Two-Dimensional Shear Deformable Beam Element Based on the Absolute Nodal Coordinate Formulation
,”
J. Sound Vib.
0022-460X,
280
, pp.
719
738
.
31.
Hjelmstad
,
K. D.
, 1997,
Fundamentals of Structural Mechanics
,
Prentice-Hall
,
Englewood Cliffs, NJ.
You do not currently have access to this content.