Asymptotic Analysis for a Mixed Boundary-Value Contact Problem |
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Authors: | C Eck S A Nazarov W L Wendland |
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Institution: | Inst. for Applied Mathematics, University of Erlangen–Nürnberg?Martensstr. 3, 91058 Erlangen, Germany?e-mail:eck@am.uni-erlangen.de, DE Lab. of Math. Modelling of Wave Phenomena, Inst. of Mech. Problems?V.O. Bolshoi pr. 61, 199178 St. Petersburg, Russia?e-mail: serna@snark.ipme.ru, RU Mathematics Institute A, University of Stuttgart?Pfaffenwaldring 57, 70569 Stuttgart, Germany?e-mail: wendland@mathematik.uni-stuttgart.de, DE
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Abstract: | The variational solution of the nonlinear Signorini contact problem determines also the active contact zone Γ
c
. If the latter is known, then the elastic field is a solution of a linear mixed boundary value problem in which on Γ
c
the normal displacement and tangential traction are given, while on the non-contact part the total traction is zero. Such
mixed boundary conditions in general generate singularities of the solution's stress field at the points P
(
k
) where the boundary conditions change. For smooth data, however, the variational solution of the Signorini contact problem
actually belongs to H
2(Ω)2, which implies the disappearance of these singularities, i.e., that the corresponding stress intensity factors vanish.
This paper is devoted to the characterization of the active contact zone Γ
c
by the vanishing stress intensity factors including their sensitivity with respect to varying Γ
c
for two-dimensional problems provided that Γ
c
consists of a finite number of intervals. We use the method of asymptotic expansions and derive an explicit formula for the
sensitivity, which is rigorously justified by employing weighted Sobolev spaces with detached asymptotics. These results can
be used to determine the points P
(
k
) with a corresponding Newton iteration.
Accepted July 6, 2000?Published online January 22, 2001 |
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Keywords: | |
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