Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements
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 presen...
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| Format: | Article |
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MDPI AG
2020-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/3/399 |
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| author | Sorin Vlase Marin Marin Maria Luminița Scutaru |
| author_facet | Sorin Vlase Marin Marin Maria Luminița Scutaru |
| author_sort | Sorin Vlase |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T03:53:18Z |
| format | Article |
| id | doaj.art-cc53e664d6a84252b246ed829ff7e0e0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-14T03:53:18Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
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| spelling | doaj.art-cc53e664d6a84252b246ed829ff7e0e02022-12-21T23:18:09ZengMDPI AGMathematics2227-73902020-03-018339910.3390/math8030399math8030399Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic ElementsSorin Vlase0Marin Marin1Maria Luminița Scutaru2Department of Mechanical Engineering, Transilvania University of Brașov, 500036 Brașov, RomaniaDepartment of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brașov, RomaniaDepartment of Mechanical Engineering, Transilvania University of Brașov, 500036 Brașov, RomaniaThe 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.https://www.mdpi.com/2227-7390/8/3/399finite elementlagrangemaggifeamultibody systemmbsnonlinear systemelastic elementsanalytical dynamicsrobotics |
| spellingShingle | Sorin Vlase Marin Marin Maria Luminița Scutaru Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements Mathematics finite element lagrange maggi fea multibody system mbs nonlinear system elastic elements analytical dynamics robotics |
| title | Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements |
| title_full | Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements |
| title_fullStr | Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements |
| title_full_unstemmed | Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements |
| title_short | Maggi’s Equations Used in the Finite Element Analysis of the Multibody Systems with Elastic Elements |
| title_sort | maggi s equations used in the finite element analysis of the multibody systems with elastic elements |
| topic | finite element lagrange maggi fea multibody system mbs nonlinear system elastic elements analytical dynamics robotics |
| url | https://www.mdpi.com/2227-7390/8/3/399 |
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