A Perturbation Result for Dynamical Contact Problems
Please always quote using this URN:urn:nbn:de:0296-matheon-5499
- This paper is intended to be a first step towards the continuous dependence of dynamical contact problems on the initial data as well as the uniqueness of a solution. Moreover, it provides the basis for a proof of the convergence of popular time integration schemes as the Newmark method. We study a frictionless dynamical contact problem between both linearly elastic and viscoelastic bodies which is formulated via the Signorini contact conditions. For viscoelastic materials fulfilling the Kelvin-Voigt constitutive law, we find a characterization of the class of problems which satisfy a perturbation result in a non-trivial mix of norms in function space. This characterization is given in the form of a stability condition on the contact stresses at the contact boundaries. Furthermore, we present perturbation results for two well-established approximations of the classical Signorini condition: The Signorini condition formulated in velocities and the model of normal compliance, both satisfying even a sharper version of our stability condition.
Author: | Corinna Klapproth, Peter Deuflhard, Anton Schiela |
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URN: | urn:nbn:de:0296-matheon-5499 |
Referee: | Ralf Kornhuber |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2009/12/03 |
Release Date: | 2009/09/03 |
Tag: | |
Institute: | Freie Universität Berlin |
Zuse Institute Berlin (ZIB) | |
MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Lxx Hyperbolic equations and systems [See also 58J45] / 35L85 Linear hyperbolic unilateral problems and linear hyperbolic variational inequalities [See also 35R35, 49J40] |
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Hxx Dynamical problems / 74H55 Stability | |
74-XX MECHANICS OF DEFORMABLE SOLIDS / 74Mxx Special kinds of problems / 74M15 Contact | |
Preprint Number: | 571 |