Finite Element Method-Based Elastic Analysis of Multibody Systems: A Review

Sorin Vlase, Marin Marin and Negrean Iuliu
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Sorin Vlase: Department of Mechanical Engineering, Transilvania University of Brașov, 500036 Brașov, Romania
Marin Marin: Department of Mathematics and Informatics, Transilvania University of Brașov, B-dul Eroilor 20, 500036 Brașov, Romania
Negrean Iuliu: Romanian Academy of Technical Sciences, B-dul Dacia 26, 030167 Bucharest, Romania

Mathematics, 2022, vol. 10, issue 2, 1-15

Abstract: This paper presents the main analytical methods, in the context of current developments in the study of complex multibody systems, to obtain evolution equations for a multibody system with deformable elements. The method used for analysis is the finite element method. To write the equations of motion, the most used methods are presented, namely the Lagrange equations method, the Gibbs–Appell equations, Maggi’s formalism and Hamilton’s equations. While the method of Lagrange’s equations is well documented, other methods have only begun to show their potential in recent times, when complex technical applications have revealed some of their advantages. This paper aims to present, in parallel, all these methods, which are more often used together with some of their engineering applications. The main advantages and disadvantages are comparatively presented. For a mechanical system that has certain peculiarities, it is possible that the alternative methods offered by analytical mechanics such as Lagrange’s equations have some advantages. These advantages can lead to computer time savings for concrete engineering applications. All these methods are alternative ways to obtain the equations of motion and response time of the studied systems. The difference between them consists only in the way of describing the systems and the application of the fundamental theorems of mechanics. However, this difference can be used to save time in modeling and analyzing systems, which is important in designing current engineering complex systems. The specifics of the analyzed mechanical system can guide us to use one of the methods presented in order to benefit from the advantages offered.

Keywords: Maggi’s equations; Lagrange method; Gibbs–Appell equations; Hamilton formalism; analytical mechanics (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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