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Research Papers

Explicit and Implicit Cosimulation Methods: Stability and Convergence Analysis for Different Solver Coupling Approaches

[+] Author and Article Information
Bernhard Schweizer

Department of Mechanical Engineering,
Institute of Applied Dynamics,
Technical University Darmstadt,
Otto-Berndt-Strasse 2,
Darmstadt 64287, Germany
e-mail: schweizer@sds.tu-darmstadt.de

Pu Li, Daixing Lu

Department of Mechanical Engineering,
Institute of Applied Dynamics,
Technical University Darmstadt,
Otto-Berndt-Strasse 2,
Darmstadt 64287, Germany

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 5, 2014; final manuscript received September 3, 2014; published online April 2, 2015. Assoc. Editor: Dan Negrut.

J. Comput. Nonlinear Dynam 10(5), 051007 (Sep 01, 2015) (12 pages) Paper No: CND-14-1067; doi: 10.1115/1.4028503 History: Received March 05, 2014; Revised September 03, 2014; Online April 02, 2015

The numerical stability and the convergence behavior of cosimulation methods are analyzed in this manuscript. We investigate explicit and implicit coupling schemes with different approximation orders and discuss three decomposition techniques, namely, force/force-, force/displacement-, and displacement/displacement-decomposition. Here, we only consider cosimulation methods where the coupling is realized by applied forces/torques, i.e., the case that the coupling between the subsystems is described by constitutive laws. Solver coupling with algebraic constraint equations is not investigated. For the stability analysis, a test model has to be defined. Following the stability definition for numerical time integration schemes (Dahlquist's stability theory), a linear test model is used. The cosimulation test model applied here is a two-mass oscillator, which may be interpreted as two Dahlquist equations coupled by a linear spring/damper system. Discretizing the test model with a cosimulation method, recurrence equations can be derived, which describe the time discrete cosimulation solution. The stability of the recurrence equations system represents the numerical stability of the cosimulation approach and can easily be determined by an eigenvalue analysis.

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Figures

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Fig. 1

Linear two-mass oscillator: test model for analyzing the stability of cosimulation methods

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Fig. 2

Cosimulation test model: force/force-coupling approach

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Fig. 3

Cosimulation test model: force/displacement-coupling approach

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Fig. 4

Cosimulation test model: displacement/displacement-coupling approach

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Fig. 5

Stability plots for the implicit cosimulation approach using force/force-decomposition

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Fig. 6

Stability plots for the implicit cosimulation approach using force/displacement-decomposition

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Fig. 7

Stability plots for the implicit cosimulation approach using displacement/displacement-decomposition

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Fig. 8

Stability plots for the explicit cosimulation approach using force/force-decomposition

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Fig. 9

Stability plots for the explicit cosimulation approach using force/displacement-decomposition

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Fig. 10

Stability plots for the explicit cosimulation approach using displacement/displacement-decomposition

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Fig. 11

Convergence plots for the implicit cosimulation approach using force/force-decomposition

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Fig. 12

Convergence plots for the explicit cosimulation approach using force/force-decomposition

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