Engineering Mechanics

Proceedings Vol. 27/28 (2022)

ENGINEERING MECHANICS 2022

Copyright © 2022 Institute of Theoretical and Applied Mechanics of the Czech Academy of Sciences, Prague

 

Kolman R., González J. A., Dvořák R., Kopačka J., Park K. C.
pages 201 - 204, full text

Often, the finite element method together with direct time integration is used for modelling of contact-impact problems of bodies. For direct time integration, the implicit or explicit time stepping are generally employed. It is well known that the time step size in explicit time integration is limited by the stability limit. Further, the trouble comes with the task of impact of bodies with different critical time step sizes for each body in contact. In this case, this numerical strategy based on explicit time stepping with the same time step size for both bodies is not effective and is not accurate due to the dispersion behaviour and spurious stress oscillations. For that reason, a numerical methodology, which allows independent time stepping for each body with its time step size, is needed to develop. In this paper, we introduce the localized variant of the bipenalty method in contact-impact problems with the governing equations derived based on the Hamilton's principle. The localized bipenalty method is applied into the impact problems of bars as an one-dimensional problem. The definition of localized gaps is presented and applied into the full concept of the localized bipenalty method.

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