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Equivalent analytical formulation-based multibody elastic system analysis using one-dimensional finite elements

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Abstract

For the particular case of an elastic multibody system (MBS) that can be modeled using one-dimensional finite elements, the main methods offered by analytical mechanics in its classical form for analysis are presented in a unitary description. The aim of the work is to present in a unitary form the main methods offered by classical mechanics for the analysis of solid systems. There is also a review of the literature that uses and highlights these methods, which need to be reconsidered considering the progress of the industry and the complexity of the studied systems. Thus, the kinematics of a finite element is described for the calculation of the main quantities used in the modeling of multibody systems and in analytical mechanics. The main methods used in the research of MBS systems are presented and analyzed. Thus, Lagrange’s equations, Gibbs–Appell equations, Maggi’s formalism, Kane’s equations and Hamilton’s equations are studied in turn. This presentation is determined by the advantages that alternatives to Lagrange’s equations can offer, which currently represent the method most used by researchers.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Transilvania University of Braşov, 500036, Braşov, Romania

    Sorin Vlase

  2. Technical Sciences Academy of Romania, B-dul Dacia 26, 030167, Bucharest, Romania

    Sorin Vlase

  3. Department of Mathematics and Computer Science, Transilvania University of Braşov, B-dul Eroilor 20, 500036, Braşov, Romania

    Marin Marin

  4. Academy of Romanian Scientists, Ilfov Street, No. 3, 050045, Bucharest, Romania

    Marin Marin

  5. Faculty of Mechanical and Systems Engineering, Esslingen University of Applied Sciences, 73728, Esslingen, Germany

    Andreas Öchsner

  6. Laboratory of Mathematics and Applications-ENS, Hassan II University, 20000, Casablanca, Morocco

    Omar El Moutea

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  1. Sorin Vlase
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  2. Marin Marin
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  3. Andreas Öchsner
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  4. Omar El Moutea
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Correspondence to Marin Marin.

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Communicated by Andreas Öchsner.

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Vlase, S., Marin, M., Öchsner, A. et al. Equivalent analytical formulation-based multibody elastic system analysis using one-dimensional finite elements. Continuum Mech. Thermodyn. 36, 197–215 (2024). https://doi.org/10.1007/s00161-023-01270-4

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