On stability and reflection-transmission analysis of the bipenalty method in contact-impact problems: A one-dimensional, homogeneous case study

0488825 - ÚT 2019 RIV GB eng J - Journal Article
Kopačka, Ján - Tkachuk, A. - Gabriel, Dušan - Kolman, Radek - Bischoff, M. - Plešek, Jiří
On stability and reflection-transmission analysis of the bipenalty method in contact-impact problems: A one-dimensional, homogeneous case study.
International Journal for Numerical Methods in Engineering. Roč. 113, č. 10 (2018), s. 1607-1629. ISSN 0029-5981. E-ISSN 1097-0207
R&D Projects: GA MŠMT(CZ) EF15_003/0000493; GA ČR(CZ) GA17-22615S; GA ČR GA17-12925S; GA ČR(CZ) GA16-03823S
Grant - others:AV ČR(CZ) DAAD-16-12
Program: Bilaterální spolupráce
Institutional support: RVO:61388998
Keywords : bipenalty method * explicit time integration * finite element method * penalty method * reflection-transmission analysis * stability analysis
OECD category: Applied mechanics
Impact factor: 2.746, year: 2018
http://onlinelibrary.wiley.com/doi/10.1002/nme.5712/full

The stability and reflection-transmission properties of the bipenalty method are studied in application to explicit finite element analysis of one-dimensional contact-impact problems. It is known that the standard penalty method, where an additional stiffness term corresponding to contact boundary conditions is applied, attacks the stability limit of finite element model. Generally, the critical time step size rapidly decreases with increasing penalty stiffness. Recent comprehensive studies have shown that the so-called bipenalty technique, using mass penalty together with standard stiffness penalty, preserves the critical time step size associated to contact-free bodies. In this paper, the influence of the penalty ratio (ratio of stiffness and mass penalty parameters) on stability and reflection-transmission properties in one-dimensional contact-impact problems using the same material and mesh size for both domains is studied. The paper closes with numerical
examples, which demonstrate the stability and reflection-transmission behavior of the bipenalty method in one-dimensional contact-impact and wave propagation problems of homogeneous materials.
Permanent Link: http://hdl.handle.net/11104/0283554