Regarding constrained mechanical systems, we are faced with index-3 differential-algebraic equation (DAE) systems. Direct discretization of the index-3 DAE systems only enforces the position constraints to be fulfilled at the integration-time points, but not the hidden constraints. In addition, order reduction effects are observed in the velocity variables and the Lagrange multipliers. In literature, different numerical techniques have been suggested to reduce the index of the system and to handle the numerical integration of constrained mechanical systems. This paper deals with an alternative concept, called collocated constraints approach. We present index-2 and index-1 formulations in combination with implicit Runge–Kutta methods. Compared with the direct discretization of the index-3 DAE system, the proposed method enforces also the constraints on velocity and—in case of the index-1 formulation—the constraints on acceleration level. The proposed method may very easily be implemented in standard Runge–Kutta solvers. Here, we only discuss mechanical systems. The presented approach can, however, also be applied for solving nonmechanical higher-index DAE systems.
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July 2016
Technical Briefs
Solving Differential-Algebraic Equation Systems: Alternative Index-2 and Index-1 Approaches for Constrained Mechanical Systems
Bernhard Schweizer,
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
Institute of Applied Dynamics,
Technical University Darmstadt,
Otto-Berndt-Strasse 2,
Darmstadt 64287, Germany
e-mail: schweizer@sds.tu-darmstadt.de
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Pu Li
Pu Li
Department of Mechanical Engineering,
Institute of Applied Dynamics,
Technical University Darmstadt,
Otto-Berndt-Strasse 2,
Darmstadt 64287, Germany
Institute of Applied Dynamics,
Technical University Darmstadt,
Otto-Berndt-Strasse 2,
Darmstadt 64287, Germany
Search for other works by this author on:
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
Institute of Applied Dynamics,
Technical University Darmstadt,
Otto-Berndt-Strasse 2,
Darmstadt 64287, Germany
e-mail: schweizer@sds.tu-darmstadt.de
Pu Li
Department of Mechanical Engineering,
Institute of Applied Dynamics,
Technical University Darmstadt,
Otto-Berndt-Strasse 2,
Darmstadt 64287, Germany
Institute of Applied Dynamics,
Technical University Darmstadt,
Otto-Berndt-Strasse 2,
Darmstadt 64287, Germany
1Corresponding author.
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 23, 2014; final manuscript received August 6, 2015; published online November 13, 2015. Assoc. Editor: Dan Negrut.
J. Comput. Nonlinear Dynam. Jul 2016, 11(4): 044501 (13 pages)
Published Online: November 13, 2015
Article history
Received:
November 23, 2014
Revised:
August 6, 2015
Citation
Schweizer, B., and Li, P. (November 13, 2015). "Solving Differential-Algebraic Equation Systems: Alternative Index-2 and Index-1 Approaches for Constrained Mechanical Systems." ASME. J. Comput. Nonlinear Dynam. July 2016; 11(4): 044501. https://doi.org/10.1115/1.4031287
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