65Pxx Numerical problems in dynamical systems [See also 37Mxx]
Refine
Year of publication
- 2006 (1)
Document Type
- ZIB-Report (1)
Language
- English (1)
Has Fulltext
- yes (1)
Is part of the Bibliography
- no (1)
Keywords
Institute
- ZIB Allgemein (1)
The numerical integration of dynamical contact problems often leads to instabilities at contact boundaries caused by the non-penetration condition between bodies in contact. Even a recent energy dissipative modification due to Kane et al. (1999), which discretizes the non-penetration constraints implicitly, is not able to circumvent artificial oscillations. For this reason, the present paper suggests a contact stabilization which avoids artificial oscillations at contact interfaces and is also energy dissipative. The key idea of this contact stabilization is an additional $L^2$-projection at contact interfaces, which can easily be added to any existing time integration scheme. In case of a lumped mass matrix, this projection can be carried out completely locally, thus creating only negligible additional numerical cost. For the new scheme, an elementary analysis is given, which is confirmed by numerical findings in an illustrative test example (Hertzian two body contact).