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Discrete adjoint variable method for the sensitivity analysis of ALI3-P formulations

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Abstract

The sensitivity analysis of the dynamics of multibody systems is a topic that has been attracting the attention of several researchers for years, particularly due to its value in optimal control and design problems. Depending on the dynamic formulation and the sensitivity method considered, different sets of sensitivity systems of equations would be reached involving diverse complexity levels. In this work, the analytical sensitivity analysis of the augmented Lagrangian index-3 formulation with velocity and acceleration projections (ALI3-P) is developed using the discrete adjoint variable method, considering a Newmark’s family integrator for the numerical integration of the forward dynamics, adjoint sensitivity and gradient equations, and a penalty formulation for the initial acceleration problem. The accuracy and efficiency of the new sensitivity formulation are tested in a five-bar mechanism benchmark problem and in the multibody model of a real-life four-wheeled vehicle. The method has been implemented in the MBSLIM multibody library as two general sensitivity formulations over the already existing global and topological forward dynamics formulations in natural and joint coordinates respectively.

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Notes

  1. For simplicity, only holonomic constraints will be considered in this work, although the ALI3-P formulation presented in [11] supports also nonholonomic constraints.

  2. The reader is referred to those works for a more detailed description of the mechanism.

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Acknowledgements

The support of the Spanish Ministry of Economy and Competitiveness (MINECO) under project DPI2016-81005-P and the support of Spanish Ministry of Science and Innovation (MICINN) under project PID2020-120270GB-C21 are greatly acknowledged. Furthermore, the first author would like to emphasize the acknowledgment for the support of MINECO by means of the doctoral research contract BES-2017-080727, co-financed by the European Union through the ESF program.

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Authors and Affiliations

  1. Laboratorio de Ingeniería Mecánica (LIM), CITENI, Campus Industrial de Ferrol, Universidade da Coruña, Mendizábal s/n, Ferrol, Spain

    Álvaro López Varela & Daniel Dopico Dopico

  2. Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, USA

    Corina Sandu & Adrian Sandu

Authors
  1. Álvaro López Varela
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  2. Corina Sandu
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  3. Adrian Sandu
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  4. Daniel Dopico Dopico
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Contributions

Alvaro Lopez Varela, M.D. (Conceptualization: Equal; Investigation: Lead; Software:Lead; Validation: Lead; Writing – original draft: Lead) Corina Sandu (Supervision: Supporting; Writing – review & editing: Supporting) Adrian Sandu (Supervision: Supporting; Writing – review & editing: Supporting) Daniel Dopico (Conceptualization: Equal; Formal analysis: Lead; Investigation: Equal; Methodology: Lead; Software: Equal; Supervision: Lead; Validation: Supporting; Writing – review & editing: Lead)

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Correspondence to Corina Sandu.

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López Varela, Á., Sandu, C., Sandu, A. et al. Discrete adjoint variable method for the sensitivity analysis of ALI3-P formulations. Multibody Syst Dyn (2023). https://doi.org/10.1007/s11044-023-09911-x

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