New Analytical Model Used in Finite Element Analysis of Solids Mechanics

Sorin Vlase, Adrian Eracle Nicolescu and Marin Marin
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Sorin Vlase: Department of Mechanical Engineering, Transilvania University of Brașov, 500036 Brașov, Romania
Adrian Eracle Nicolescu: Faculty of Mechanical, Industrial and Maritime Engineering, Ovidius University of Constanta, 900527 Constanța, Romania
Marin Marin: Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brașov, Romania

Mathematics, 2020, vol. 8, issue 9, 1-17

Abstract: In classical mechanics, determining the governing equations of motion using finite element analysis (FEA) of an elastic multibody system (MBS) leads to a system of second order differential equations. To integrate this, it must be transformed into a system of first-order equations. However, this can also be achieved directly and naturally if Hamilton’s equations are used. The paper presents this useful alternative formalism used in conjunction with the finite element method for MBSs. The motion equations in the very general case of a three-dimensional motion of an elastic solid are obtained. To illustrate the method, two examples are presented. A comparison between the integration times in the two cases presents another possible advantage of applying this method.

Keywords: dynamics; vibration; finite element analysis (FEA); kinetic energy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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