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Article

# New Analytical Model Used in Finite Element Analysis of Solids Mechanics

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Department of Mechanical Engineering, Transilvania University of Brașov, 500036 Brașov, Romania
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Romanian Academy of Technical Sciences, B-dul Dacia 26, 030167 Bucharest, Romania
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Faculty of Mechanical, Industrial and Maritime Engineering, Ovidius University of Constanta, 900527 Constanța, Romania
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Department of Mathematics and Computer Science, Transilvania University of Brasov, 500036 Brașov, Romania
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Authors to whom correspondence should be addressed.
Mathematics 2020, 8(9), 1401; https://doi.org/10.3390/math8091401
Received: 13 July 2020 / Revised: 15 August 2020 / Accepted: 18 August 2020 / Published: 21 August 2020
(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)
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. View Full-Text
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MDPI and ACS Style

Vlase, S.; Nicolescu, A.E.; Marin, M. New Analytical Model Used in Finite Element Analysis of Solids Mechanics. Mathematics 2020, 8, 1401. https://doi.org/10.3390/math8091401

AMA Style

Vlase S, Nicolescu AE, Marin M. New Analytical Model Used in Finite Element Analysis of Solids Mechanics. Mathematics. 2020; 8(9):1401. https://doi.org/10.3390/math8091401

Chicago/Turabian Style

Vlase, Sorin, Adrian E. Nicolescu, and Marin Marin. 2020. "New Analytical Model Used in Finite Element Analysis of Solids Mechanics" Mathematics 8, no. 9: 1401. https://doi.org/10.3390/math8091401

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