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Sensitivity Analysis of Flexible Multibody Dynamics with Generalized-\(\upalpha \) Time Integration and Baumgarte Stabilization

A Study on Numerical Stability

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Advances in Italian Mechanism Science (IFToMM Italy 2022)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 122))

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Abstract

This paper introduces Baumgarte stabilization and generalized-\(\upalpha \) time integration to the sensitivity analysis of flexible multibody dynamics. This is done to counteract numerical drift and numerical noise in the system responses and the design sensitivities, which can lead to problems when used in concert with gradient-based optimization algorithms. Therefore, analytical direct differentiation is applied to the steps of the primal analysis: governing equation, time integration and nonlinear solver. The method is numerically validated with a slider–crank mechanism modeled with flexible multibody dynamics and three-dimensional beam elements. A parameter study is carried out by varying the values of the generalized-\(\upalpha \) integration constants and the Baumgarte stabilization constants. The results are compared and the effects on numerical drift and numerical noise are shown for both the primal analysis and the sensitivity analysis. With an appropriate choice of the examined parameters, the system responses and design sensitivities take an appropriate form for processing with gradient-based optimization algorithms.

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Authors and Affiliations

  1. Faculty of Science and Technology, Free University of Bozen-Bolzano, Universitätsplatz 1, 39100, Bozen, South Tyrol, Italy

    Veit Gufler, Erich Wehrle & Renato Vidoni

  2. Collins Aerospace, Applied Research and Technology, Munich, Germany

    Erich Wehrle

Authors
  1. Veit Gufler
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  2. Erich Wehrle
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  3. Renato Vidoni
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Corresponding author

Correspondence to Veit Gufler .

Editor information

Editors and Affiliations

  1. University of Naples Federico II, Naples, Italy

    Vincenzo Niola

  2. University of Udine, Udine, Italy

    Alessandro Gasparetto

  3. DIMEAS, Politecnico di Torino, Turin, Italy

    Giuseppe Quaglia

  4. DIMEG, University of Calabria, Rende, Italy

    Giuseppe Carbone

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Gufler, V., Wehrle, E., Vidoni, R. (2022). Sensitivity Analysis of Flexible Multibody Dynamics with Generalized-\(\upalpha \) Time Integration and Baumgarte Stabilization. In: Niola, V., Gasparetto, A., Quaglia, G., Carbone, G. (eds) Advances in Italian Mechanism Science. IFToMM Italy 2022. Mechanisms and Machine Science, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-031-10776-4_18

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