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Regularity of solutions to a dynamic frictionless contact problem with normal compliance

✍ Scribed by K.L. Kuttler; M. Shillor

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
206 KB
Volume
59
Category
Article
ISSN
0362-546X

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✦ Synopsis

The regularity in time of solutions to a problem of frictionless dynamic contact between a viscoelastic body and a reactive foundation is established. Contact is modeled with the normal compliance condition. It is shown that the differentiability of the normal compliance function, its behavior at the onset of contact, determines the regularity of the solution, and additional differentiability of the data and appropriate compatibility on the initial conditions yield higher solutions' differentiability. Unlike the case when the Signorini condition is used, in this problem there is no intrinsic regularity ceiling. A simple example shows that these results are close to being optimal.

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## Abstract The present paper deals with the theoretical and numerical treatment of dynamic unilateral problems. The governing equations are formulated as an equivalent variational inequality expressing D' Alembert's principle in its inequality form. The discretization with respect to time and spac