Adaptive finite elements for elastic bodies in contact

authored by

C. Carstensen, O. Scherf, Peter Wriggers

Abstract

To avoid interpenetration of matter under the small strain assumption, the linear contact condition is frequently applied where the distance of bodies is controlled only along a certain direction. The standard direction is the normal on the surface where interpenetration might occur. In this paper we allow other directions as well. We address questions such as the correct mathematical model, existence of solutions, the penalty method for regularization of the variational inequality, finite element discretization, and a priori and a posteriori error estimates, but exclude the error of penalization. The computable upper error bound leads to a criterion for automatic mesh-refinements within a finite element method. Numerical simulations of the Hertzian contact problem and a supported cantilever beam are included.

Organisation(s)

Institute of Mechanics and Computational Mechanics

External Organisation(s)

Kiel University

Type

Article

Journal

SIAM Journal of Scientific Computing

Volume

20

Pages

1605-1626

No. of pages

22

ISSN

0196-5204

Publication date

1999

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Computational Mathematics, Applied Mathematics

Electronic version(s)

https://doi.org/10.1137/S1064827595295350 (Access: Unknown)

 

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