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Research Papers

Stability of Sequential Modular Time Integration Methods for Coupled Multibody System Models

[+] Author and Article Information
Martin Arnold

NWF III—Institute of Mathematics, Martin Luther University Halle-Wittenberg, D-06099 Halle (Saale), Germanymartin.arnold@mathematik.uni-halle.de

J. Comput. Nonlinear Dynam 5(3), 031003 (May 14, 2010) (9 pages) doi:10.1115/1.4001389 History: Received April 09, 2009; Revised March 04, 2010; Published May 14, 2010; Online May 14, 2010

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.

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Figures

Grahic Jump Location
Figure 1

System pantograph/catenary (9)

Grahic Jump Location
Figure 2

Modular time integration according to Eqs. 5,8 starting with the catenary equations (see Eq. 4, “○”) or with the pantograph equations (see Eq. 4, “◻”): error of q̃(t) (left plot) and λ̃(t) (right plot) for H=5.0×10−5 (solid lines) and H=1.0×10−5 (dotted lines) (6)

Grahic Jump Location
Figure 3

Sequential modular time integration according to Eq. 12 applied to the test problem in Eq. 25. Comparison of constant (left plot) and linear (right plot) extrapolation of coupling terms, see Eqs. 13,23.

Grahic Jump Location
Figure 4

Stabilized modular time integration starting with the catenary equations (see Eq. 4, “◇”) or with the pantograph equations (see Eq. 4, “◻”): error of q¯(t) (left plot) and λ¯(t) (right plot) for H=5.0×10−5 (solid lines) and H=1.0×10−5 (dotted lines) (6)

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