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

• Published in: Continuum mechanics and thermodynamics Vol. 36; no. 1; pp. 197 - 215
• Main Authors: Vlase, Sorin, Marin, Marin, Öchsner, Andreas, El Moutea, Omar
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2024; Springer Nature B.V
• Subjects: Classical and Continuum Physics; Classical mechanics; Dimensional analysis; Elastic analysis; Elastic systems; Engineering Thermodynamics; Finite element method; Heat and Mass Transfer; Kinematics; Literature reviews; Mathematical analysis; Mathematical models; Mechanics; Multibody systems; Original Article; Physics; Physics and Astronomy; Structural Materials; Systems analysis; Theoretical and Applied Mechanics; Hamilton equations; Gibbs–Appell’s equations; MBS with elastic elements; Maggi’s formalism; Energy of acceleration; Analytical mechanics; Kane’s equation; Finite element analysis (FEA); Lagrange’s equations
• ISSN: 0935-1175; 1432-0959
• DOI: 10.1007/s00161-023-01270-4

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.