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A Perturbation Result for Dynamical Contact Problems

A Perturbation Result for Dynamical Contact Problems

Year:    2009

Numerical Mathematics: Theory, Methods and Applications, Vol. 2 (2009), Iss. 3 : pp. 237–257

Abstract

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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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/nmtma.2009.m9003

Numerical Mathematics: Theory, Methods and Applications, Vol. 2 (2009), Iss. 3 : pp. 237–257

Published online:    2009-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    21

Keywords:    Dynamical contact problems stability (visco-)elasticity Signorini condition Newmark method.

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