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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.

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Metadaten
Author:Corinna Klapproth, Peter Deuflhard, Anton Schiela
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
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