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A path following method for identifying static equilibrium in multi-body-dynamic systems

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Abstract

Determining states of static equilibrium for multi-body-dynamic (MBD) systems can be challenging and may result in convergence failure for nonlinear static solvers. Analysts are often faced with uncertainty in regards to the values of candidate equilibrium states or whether a state of minimum potential energy was found. In the event of static solver failure or uncertainty with regards to a candidate solution, equilibrium could be obtained through a dynamic simulation which may require the addition of artificial damping. However, this method can have significant computational expense as compared to static solution procedures. Using MBD systems representing a pendulum, two variations of a spring supported arch, and a seven-body mechanism, arc-length solvers were found suitable for identifying equilibrium states through a robust production of static solution curves thereby avoiding dynamic simulation. Using these examples, a procedure for finding the correct equilibrium state for general systems is proposed.

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Acknowledgements

This work was funded by the Advanced Degree Program at NASA Langley Research Center.

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Authors and Affiliations

  1. Structural Dynamics Branch, NASA Langley Research Center, 4 West Taylor Street, MS 230, Hampton, VA, 23681, USA

    Geoffrey K. Rose

  2. Department of Mechanical and Aerospace Engineering, Old Dominion University, 1317 Engineering & Computational Sciences Building, Norfolk, VA, 23529, USA

    Brett A. Newman

  3. Department of Civil and Environmental Engineering, Old Dominion University, 1319 Engineering & Computational Sciences Building, Norfolk, VA, 23529, USA

    Duc T. Nguyen

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  1. Geoffrey K. Rose
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  2. Brett A. Newman
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  3. Duc T. Nguyen
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Correspondence to Geoffrey K. Rose.

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Rose, G.K., Newman, B.A. & Nguyen, D.T. A path following method for identifying static equilibrium in multi-body-dynamic systems. Multibody Syst Dyn 45, 315–359 (2019). https://doi.org/10.1007/s11044-018-9618-7

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  • DOI: https://doi.org/10.1007/s11044-018-9618-7

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