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A Perturbation Result for Dynamical Contact Problems

机译:动态接触问题的摄动结果

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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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