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Finite Element Analysis of the Longitudinal Impact of a Rod with Various Support Conditions

Ragab M. Etiwa, Hanaa M. Elabsy, and Hesham A. Elkaranshawy
Department of Engineering Mathematics and Physics, Alexandria University, Engineering Mechanics Division, Alexandria, Egypt

Abstract— In this paper, a finite element formulation is developed to analyze the stress wave propagation in an elastic rod struck by a rigid body. The rod has either rigid, free, or deformable support conditions. The formulation is based upon Saint-Venant’s contact theory. Accordingly, the equations of motion are introduced, and the equivalent finite element formulation is obtained. Hence, the dynamic responses are illustrated, and contact forces are evaluated. Certain simulation results are compared to the corresponding published analytical results. Results demonstrate the influence of the support condition on the propagated stress wave and consequently on the velocities, the displacements, and the contact forces. A simulated visualization for the reflection and transmission of the stress wave at the constraint end is presented to improve the perception of the phenomenon.

Index Terms—wave propagation, longitudinal impact, newmark integration method, finite element method, longitudinal vibration

Cite: Ragab M. Etiwa, Hanaa M. Elabsy, and Hesham A. Elkaranshawy, "Finite Element Analysis of the Longitudinal Impact of a Rod with Various Support Conditions," International Journal of Mechanical Engineering and Robotics Research, Vol. 10, No.11, pp. 626-632, November 2021. DOI: 10.18178/ijmerr.10.11.626-632

Copyright © 2021 by the authors. This is an open access article distributed under the Creative Commons Attribution License (CC BY-NC-ND 4.0), which permits use, distribution and reproduction in any medium, provided that the article is properly cited, the use is non-commercial and no modifications or adaptations are made.