Gibbs–Appell Equations in Finite Element Analysis of Mechanical Systems with Elements Having Micro-Structure and Voids

In this paper, the authors propose the application of the Gibbs–Appell equations to obtain the equations of motion in the case of a mechanical system that has elements with a micro-polar structure, containing voids. Voids can appear as a result of the processing or manufacturing of the parts, or can...

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Bibliographic Details
Published inMathematics (Basel) Vol. 12; no. 2; p. 178
Main Authors Vlase, Sorin, Marin, Marin, Itu, Calin
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.01.2024
Subjects
Analysis
analytical dynamics
Composite materials
Engineering
Equations of motion
Evolution
FEM
Finite element method
Hypotheses
Manufacturing
Mathematical analysis
MBS
Mechanical properties
Mechanical systems
Mechanics
Methods
micropolar
micropolar media
Multibody systems
Numerical analysis
Physical properties
Robot arms
Voids
Romania
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Summary:In this paper, the authors propose the application of the Gibbs–Appell equations to obtain the equations of motion in the case of a mechanical system that has elements with a micro-polar structure, containing voids. Voids can appear as a result of the processing or manufacturing of the parts, or can be intentionally introduced. This research involves a model of the considered solid material containing voids. To determine the dynamic behavior of such a system, the Gibbs–Appell (GA) method is used to obtain the evolution equations, as an alternative to Lagrange’s classical description. The proposed method can be applied to any mechanical system consisting of materials with a micro-polar structure and voids. The study of such systems is interesting because the literature shows that even a reduce number of small voids can produce significant variations in physical behavior. The proposed method requires a smaller number of mathematical operations. To apply this method, the acceleration energy is calculated, which is then used to derive the equations. The method comes with advantages in the application to multibody systems having the mentioned properties and, in particular, in the study of robots and manipulators. Using the GA method, it is necessary to do a fewer differentiation operations than applying the Lagrange’s equations. This leads to a reduced amount of computation for obtaining the evolution equations.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12020178