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Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements

1
Department of Mechanical Engineering, Transilvania University of Brașov, 500036 Brașov, Romania
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Technical Sciences Academy of Romania, B-dul Dacia 26, 030167 Bucharest, Romania
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Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brașov, Romania
*
Author to whom correspondence should be addressed.
Mathematics 2020, 8(3), 399; https://doi.org/10.3390/math8030399
Received: 13 February 2020 / Revised: 6 March 2020 / Accepted: 6 March 2020 / Published: 11 March 2020
The main method used to determine the equations of motion of a multibody system (MBS) with elastic elements is the method of Lagrange’s multipliers. The assembly of equations for the whole system represents an important step in the elastodynamic analysis of such a system. This paper presents a new method of approaching this stage, by applying Maggi’s equations. In this way, the links that exist between the finite elements and the connections that exist between different bodies of the MBS system are conveniently taken into account, each body having a distinct velocity and acceleration field. Although Maggi’s equations have been used, sporadically, in some applications so far, we are not aware that they have been used in the study of elastic systems using the finite element method. Finally, an algorithm is presented that uses the Maggi formalism to obtain the equations of motion for an MBS system. View Full-Text
Keywords: finite element; Lagrange; Maggi; FEA; multibody system; MBS; nonlinear system; elastic elements; analytical dynamics; robotics finite element; Lagrange; Maggi; FEA; multibody system; MBS; nonlinear system; elastic elements; analytical dynamics; robotics
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Vlase, S.; Marin, M.; Scutaru, M.L. Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements. Mathematics 2020, 8, 399.

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