The interacting components of complex technical systems are often described by coupled systems of differential equations. In dynamical simulation, these coupled differential equations have to be solved numerically. Cosimulation techniques, multirate methods, and other approaches that exploit the modular structure of coupled systems are frequently used as alternatives to classical time integration methods. The numerical stability and convergence of such modular time integration methods is studied for a class of sequential modular methods for coupled multibody system models. Theoretical investigations and numerical test results show that the stability of these sequential modular methods may be characterized by a contractivity condition. A linearly implicit stabilization of coupling terms is proposed to guarantee numerical stability and convergence.

1.
M.
Arnold
, and
W.
Schiehlen
, eds., 2008, “
Simulation Techniques for Applied Dynamics
,”
CISM Courses and Lectures
,
Springer
,
New York
, Vol.
507
.
2.
Bichet
,
F.
,
Chombart
,
P.
,
Relovsky
,
B.
, and
Otter
,
M.
, 2009, “
MODELISAR (Modelica–AUTOSAR Interoperability and Vehicle Functional Mock-up)
,” Modelica Newsletter 2009–1, http://www.modelica.org/publications/newsletters/2009-1/http://www.modelica.org/publications/newsletters/2009-1/
3.
Kübler
,
R.
, and
Schiehlen
,
W.
, 2000, “
Two Methods of Simulator Coupling
,”
Math. Comput. Model. Dyn. Syst.
,
6
, pp.
93
113
.
4.
Jackson
,
K.
, 1991, “
A Survey of Parallel Numerical Methods for Initial Value Problems for Ordinary Differential Equations
,”
IEEE Trans. Magn.
0018-9464,
27
, pp.
3792
3797
.
5.
Arnold
,
M.
, 2007, “
Multi-Rate Time Integration for Large Scale Multibody System Models
,”
Multiscale Problems in Multibody System Contacts
,
P.
Eberhard
, ed.,
Springer
,
New York
, pp.
1
10
.
6.
Arnold
,
M.
, and
Günther
,
M.
, 2001, “
Preconditioned Dynamic Iteration for Coupled Differential-Algebraic Systems
,”
BIT
0006-3835,
41
, pp.
1
25
.
7.
Tseng
,
F.
, and
Hulbert
,
G.
, 1999, “
Network-Distributed Multibody Dynamics Simulation—Gluing Algorithm
,”
Advances in Computational Multibody Dynamics
,
J.
Ambrósio
and
W.
Schiehlen
, eds.,
IDMEC/IST Lisbon
,
Portugal
, pp.
521
540
.
8.
Arnold
,
M.
, and
Simeon
,
B.
, 2000, “
Pantograph and Catenary Dynamics: A Benchmark Problem and Its Numerical Solution
,”
Appl. Numer. Math.
0168-9274,
34
, pp.
345
362
.
9.
Veitl
,
A.
, and
Arnold
,
M.
, 1999, “
Coupled Simulation of Multibody Systems and Elastic Structures
,”
Advances in Computational Multibody Dynamics
,
J.
Ambrósio
and
W.
Schiehlen
, eds.,
IDMEC/IST Lisbon
,
Portugal
, pp.
635
644
.
10.
Poetsch
,
G.
,
Evans
,
J.
,
Meisinger
,
R.
,
Kortüm
,
W.
,
Baldauf
,
W.
,
Veitl
,
A.
, and
Wallaschek
,
J.
, 1997, “
Pantograph/Catenary Dynamics and Control
,”
Veh. Syst. Dyn.
0042-3114,
28
, pp.
159
195
.
11.
Collina
,
A.
, and
Bruni
,
S.
, 2002, “
Numerical Simulation of Pantograph–Overhead Equipment Interaction
,”
Veh. Syst. Dyn.
0042-3114,
38
, pp.
261
291
.
12.
Hairer
,
E.
, and
Wanner
,
G.
, 1996,
Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems
,
2nd ed.
,
Springer-Verlag
,
Berlin
.
13.
Walter
,
W.
, 1998, “
Ordinary Differential Equations
,”
Graduate Texts in Mathematics
,
Springer
,
New York
.
14.
Deuflhard
,
P.
,
Hairer
,
E.
, and
Zugck
,
J.
, 1987, “
One-Step and Extrapolation Methods for Differential-Algebraic Systems
,”
Numer. Math.
0029-599X,
51
, pp.
501
516
.
15.
Möller
,
B.
, 2003, “
Multirate–Verfahren für gekoppelte differentiell-algebraische Systeme
,” MS thesis, Munich University of Technology, Department of Mathematics, Germany.
16.
Deuflhard
,
P.
, and
Hohmann
,
A.
, 2003, “
Numerical Analysis in Modern Scientific Computing: An Introduction
,”
Texts in Applied Mathematics
,
2nd ed.
,
Springer
,
New York
.
17.
Hippmann
,
G.
,
Arnold
,
M.
, and
Schittenhelm
,
M.
, 2005, “
Efficient Simulation of Bush and Roller Chain Drives
,”
Proceedings of Multibody Dynamics 2005 (ECCOMAS Thematic Conference)
,
J.
Goicolea
,
J.
Cuadrado
, and
J.
García Orden
, eds.,
Universidad Politecnica de Madrid
,
Madrid, Spain
.
You do not currently have access to this content.