Gibbs-Appell Equations used in Finite Element Analysis of Elastic Materials with Voids having a Plane Motion

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Iulia Cristina MARE
Iuliu NEGREAN
Sorin VLASE
Arina MODREA

Abstract

The paper aims to use the Gibbs-Appell equations to obtain the evolution equations of a finite element (FE) to solve a problem that is becoming more and more current in the context of the accelerated use of composite materials in engineering. It is the problem of modeling materials with voids, which appear accidentally or are intentionally introduced into a material. In general, Lagrange's equations represent the most used mathematical tool for solving such cases. The complexity of current engineering applications, in which numerous parameters must be taken into account and numerous steps must be completed in the modeling activity, make some of the classical methods of Analytical Mechanics to be reconsidered, in order to take advantage of the particularities offered by them. This can reduce the number of procedures to follow in modeling the system and also reduce the amount of computation required (and costs). In this context the Gibbs-Appell method is used to finally obtain the equations of motion for a material with voids. For example, it can be noted that for a concentration of voids of 4% the stresses increase by 12%.

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How to Cite
[1]
2024. Gibbs-Appell Equations used in Finite Element Analysis of Elastic Materials with Voids having a Plane Motion. Romanian Journal of Acoustics and Vibration. 20, 1 (Jun. 2024), 83–90.
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How to Cite

[1]
2024. Gibbs-Appell Equations used in Finite Element Analysis of Elastic Materials with Voids having a Plane Motion. Romanian Journal of Acoustics and Vibration. 20, 1 (Jun. 2024), 83–90.

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