Explicit bipenalty finite element contact-impact algorithm

0518660 - ÚT 2020 RIV CZ eng A - Abstract
Gabriel, Dušan - Kopačka, Ján - Kolman, Radek
Explicit bipenalty finite element contact-impact algorithm.
Modelling 2019. Ostrava: Institute of Geonics of the Czech Academy of Sciences, 2019 - (Blaheta, R.; Starý, J.; Sysala, S.). s. 137. ISBN 978-80-86407-79-1.
[Modelling 2019: International conference on mathematical modelling and computational methods in applied sciences and engineering. 16.09.2019-20.09.2019, Olomouc]
R&D Projects: GA AV ČR(CZ) GA19-04956S; GA MŠMT(CZ) EF15_003/0000493
Institutional support: RVO:61388998
Keywords : contact-impact algorithm * penalty methods * conditionally stable time integration schemes
OECD category: Applied mechanics

It is well known that standard stiffness penalty methods can significantly decrease the critical time step in explicit conditionally stable time integration schemes in transient dynamic finite element analysis. This is due to the fact that the stiffness penalty can greatly enlarge the maximum eigenfrequency of a system. One of the possibility to remedy this shortcoming is use the bipenalty method which utilizes both sti ness and mass penalties to impose constraints that have a minimal effect on the eigenfrequencies of the nite element system including its maximum eigenfrequency. The stability of the bipenalty method has been studied for one-dimensional contact-impact problems. The main attention has been paid on an upper bound estimation of the stable Courant number for the bipenalty method with respect to sti ness penalty and mass penalty parameters. In this work, use of the bipenalty method is extended for the solution of two-dimensional contact-impact problems. To this end, present symmetry preserving explicit contact algorithm has been modi ed to consider bipenalty treatment of contact constraints. Several numerical examples are presented including the longitudinal impact of two thick plates/cylindrical rods, for which analytical solutions are available. In all the cases the superiority of the bipenalty method over the standard sti ness penalty method is demonstrated.
Permanent Link: http://hdl.handle.net/11104/0304501