By means of a recursive formulation method, a generalized impulse–momentum-balance method, and a constraint violation elimination (CVE) method, we propose a new global simulation method for flexible multibody systems with kinematic structure changes. The constraint equations of a pair of adjacent bodies, considering body flexibility in Cartesian space, are derived for a recursive formulation. Constraint equations in configuration space, which are obtained from the constraints presented in this paper via recursive formulation, are very useful for modeling different kinematic structures and impacting governing equations. The novelty is that the impact governing equations, which calculate the jumps of generalized velocities, are modified by taking velocity-level CVE into consideration. Numerical examples are given to validate the presented method. Simulation results show that the new method can effectively suppress constraint drifts at the velocity level and stabilize constraint violations at the position level.

References

References
1.
Khulief
,
Y. A.
,
2013
, “
Modeling of Impact in Multibody Systems: An Overview
,”
ASME J. Comput. Nonlinear Dyn
,
8
(
2
), p.
021012
.10.1115/1.4006202
2.
Kim
,
S. S.
, and
Haug
,
E. J.
,
1988
, “
A Recursive Formulation for Flexible Multibody Dynamics, Part I: Open-Loop Systems
,”
Comput. Methods Appl. Mech. Eng.
,
71
(
3
), pp.
293
314
.10.1016/0045-7825(88)90037-0
3.
Sung-Soo
,
K.
, and
Haug
,
E. J.
,
1989
, “
A Recursive Formulation for Flexible Multibody Dynamics, Part II: Closed Loop Systems
,”
Comput. Methods Appl. Mech. Eng.
,
74
(
3
), pp.
251
269
.10.1016/0045-7825(89)90051-0
4.
Bae
,
D. S.
,
Han
,
J. M.
,
Choi
,
J. H.
, and
Yang
,
S. M.
,
2001
, “
A Generalized Recursive Formulation for Constrained Flexible Multibody Dynamics
,”
Int. J. Numer. Methods Eng.
,
50
(
8
), pp.
1841
1859
.10.1002/nme.97
5.
Saha
,
S. K.
, and
Schiehlen
,
W. O.
,
2001
, “
Recursive Kinematics and Dynamics for Parallel Structured Closed-Loop Multibody Systems
,”
Mech. Struct. Mach.
,
29
(
2
), pp.
143
175
.10.1081/SME-100104478
6.
Cuadrado
,
J.
,
Dopico
,
D.
,
Gonzalez
,
M.
, and
Naya
,
M. A.
,
2004
, “
A Combined Penalty and Recursive Real-Time Formulation for Multibody Dynamics
,”
ASME J. Mech. Des.
,
126
(
4
), pp.
602
608
.10.1115/1.1758257
7.
Qi
,
Z.
,
Xu
,
Y.
,
Luo
,
X.
, and
Yao
,
S.
,
2010
, “
Recursive Formulations for Multibody Systems With Frictional Joints Based on the Interaction Between Bodies
,”
Multibody Syst. Dyn.
,
24
(
2
), pp.
133
166
.10.1007/s11044-010-9213-z
8.
Jain
,
A.
, and
Rodriguez
,
G.
,
1992
, “
Recursive Flexible Multibody System Dynamics Using Spatial Operators
,”
J. Guid. Control Dyn.
,
15
(
6
), pp.
1453
1466
.10.2514/3.11409
9.
Arnold
,
M.
,
2013
, “
A Recursive Multibody Formalism for Systems With Small Mass and Inertia Terms
,”
Mech. Sci.
,
4
(
1
), pp.
221
231
.10.5194/ms-4-221-2013
10.
Shabana
,
A. A.
,
1997
, “
Flexible Multibody Dynamics: Review of Past and Recent Developments
,”
Multibody Syst. Dyn.
,
1
(
2
), pp.
189
222
.10.1023/A:1009773505418
11.
Khulief
,
Y. A.
,
2000
, “
Spatial Formulation of Elastic Multibody Systems With Impulsive Constraints
,”
Multibody Syst. Dyn.
,
4
(
4
), pp.
383
406
.10.1023/A:1009801322539
12.
Mukherjee
,
R. M.
, and
Anderson
,
K. S.
,
2007
, “
Efficient Methodology for Multibody Simulations With Discontinuous Changes in System Definition
,”
Multibody Syst. Dyn.
,
18
(
2
), pp.
145
168
.10.1007/s11044-007-9075-1
13.
Kane
,
T. R.
,
1962
, “
Impulsive Motions
,”
ASME J. Appl. Mech.
,
29
(
4
), pp.
715
718
.10.1115/1.3640659
14.
Wehage
,
R. A.
, and
Haug
,
E. J.
,
1982
, “
Dynamic Analysis of Mechanical Systems With Intermittent Motion
,”
ASME J. Mech. Des.
,
104
(
4
), pp.
778
784
.10.1115/1.3256436
15.
Khulief
,
Y. A.
,
1986
, “
Dynamic Analysis of Constrained Systems of Rigid and Flexible Bodies With Intermittent Motion
,”
ASME J. Mech. Des.
,
108
(
1
), pp.
38
45
.10.1115/1.3260781
16.
Galin
,
L. A.
, and
Gladwell
,
G. M. L.
,
2008
,
Contact Problems: The Legacy of LA Galin
, Vol.
155
,
Springer
,
NY
.
17.
Popov
,
V. L.
,
2010
,
Contact Mechanics and Friction: Physical Principles and Applications
,
Springer
,
Berlin, Germany
.
18.
Haug
,
E. J.
,
1989
,
Computer Aided Kinematics and Dynamics of Mechanical Systems
, Vol.
1
,
Allyn and Bacon
,
Boston, MA
, pp.
48
104
.
19.
Khulief
,
Y. A.
,
2010
, “
Numerical Modelling of Impulsive Events in Mechanical Systems
,”
Int. J. Modell. Simul.
,
30
(
1
), pp.
80
86
.10.2316/Journal.205.2010.1.205-5090
20.
Canavin
,
J. R.
, and
Likins
,
P. W.
,
1977
, “
Floating Reference Frames for Flexible Spacecraft
,”
J. Spacecr. Rockets
,
14
(
12
), pp.
724
732
.10.2514/3.57256
21.
Shabana
,
A. A.
, and
Schwertassek
,
R.
,
1998
, “
Equivalence of the Floating Frame of Reference Approach and Finite Element Formulations
,”
Int. J. Nonlinear Mech.
,
33
(
3
), pp.
417
432
.10.1016/S0020-7462(97)00024-3
22.
Berzeri
,
M.
,
Campanelli
,
M.
, and
Shabana
,
A. A.
,
2001
, “
Definition of the Elastic Forces in the Finite-Element Absolute Nodal Co-Ordinate Formulation and the Floating Frame of Reference Formulation
,”
Multibody Syst. Dyn.
,
5
(
1
), pp.
21
54
.10.1023/A:1026465001946
23.
Xu
,
W.
,
Meng
,
D.
,
Chen
,
Y.
,
Qian
,
H.
, and
Xu
,
Y.
,
2013
, “
Dynamics Modeling and Analysis of a Flexible-Base Space Robot for Capturing Large Flexible Spacecraft
,”
Multibody Syst. Dyn.
,
185
(
2
), pp.
1149
1159
.10.1007/s11044-013-9389-0
24.
Braun
,
D. J.
, and
Goldfarb
,
M.
,
2009
, “
Eliminating Constraint Drift in the Numerical Simulation of Constrained Dynamical Systems
,”
Comput. Methods Appl. Mech. Eng.
,
198
(
37
), pp.
3151
3160
.10.1016/j.cma.2009.05.013
25.
Blajer
,
W.
,
2011
, “
Methods for Constraint Violation Suppression in the Numerical Simulation of Constrained Multibody Systems–A Comparative Study
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
13
), pp.
1568
1576
.10.1016/j.cma.2011.01.007
You do not currently have access to this content.