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Automated independent coordinates’ switching for the solution of stiff DAEs with the linearly implicit Euler method

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Abstract

The real-time (RT) integration of the equations of motion describing complex mechanical systems requires the employment of proper integration schemes which must be able to handle the time integration at each time step in less than an a priori fixed sampling time interval. The linearly implicit Euler method has been successfully employed for the RT integration of large stiff differential algebraic systems of equations (DAEs) which typically arise from the complex mechanical systems of interest in practical applications. The current industry demand is to further increase the degree of complexity of multibody models employed in RT applications, pushing researchers to improve the efficiency of the currently available integration methods. In this paper, we investigate the improvements in the efficiency of the linearly implicit Euler method coming from the conversion of the equations of motion at each time step from a dependent to an independent coordinates’ formulation. The automatic switching from dependent to independent coordinates is achieved exploiting the properties of the matrix R whose columns represent a basis of the null-space of the constraint Jacobian matrix. A non-iterative projection method is also applied in order to avoid the drift-off from the constraint conditions.

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Acknowledgements

We gratefully acknowledge the European Commission (EC) for its support of the Marie Curie IAPP project 285808 “INTERACTIVE” (“Innovative Concept Modelling Techniques for Multi-Attribute Optimization of Active Vehicles”). Furthermore, we kindly acknowledge IWT Vlaanderen for its support of the ongoing research project “Model Driven Physical Systems Operation—MODRIO”, which is part of the ITEA2 project 11004 “MODRIO” (in turn, supported by the European Commission).

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Authors and Affiliations

  1. Siemens Industry Software NV, Interleuvenlaan 68, 3001, Leuven, Belgium

    Mariano Carpinelli & Marco Gubitosa

  2. Department of Mechanical Engineering, University of Calabria, 87036, Rende, Italy

    Domenico Mundo

  3. Production Engineering, Machine Design and Automation (PMA) Section, KU Leuven, Celestijnenlaan 300, 3001, Leuven, Belgium

    Wim Desmet

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  1. Mariano Carpinelli
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  2. Marco Gubitosa
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  3. Domenico Mundo
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  4. Wim Desmet
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Correspondence to Mariano Carpinelli.

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Carpinelli, M., Gubitosa, M., Mundo, D. et al. Automated independent coordinates’ switching for the solution of stiff DAEs with the linearly implicit Euler method. Multibody Syst Dyn 36, 67–85 (2016). https://doi.org/10.1007/s11044-015-9455-x

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  • DOI: https://doi.org/10.1007/s11044-015-9455-x

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