A Contact-Stabilized Newmark Method for Dynamical Contact Problems
Please always quote using this URN: urn:nbn:de:0297-zib-9361
- 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).
Author: | Peter Deuflhard, Rolf KrauseORCiD, Susanne Ertel |
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Document Type: | ZIB-Report |
Tag: | Numerical problems in dynamical systems; nonlinear stabilities |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Pxx Numerical problems in dynamical systems [See also 37Mxx] / 65P40 Nonlinear stabilities |
65-XX NUMERICAL ANALYSIS / 65Pxx Numerical problems in dynamical systems [See also 37Mxx] | |
Date of first Publication: | 2006/08/29 |
Series (Serial Number): | ZIB-Report (06-42) |
ZIB-Reportnumber: | 06-42 |
Published in: | Appeared in: International Journal for Numerical Methods in Engineering 73 (2007) 1274-1290 |