Details
| Original language | English |
|---|---|
| Pages (from-to) | 1605-1626 |
| Number of pages | 22 |
| Journal | SIAM Journal of Scientific Computing |
| Volume | 20 |
| Issue number | 5 |
| Publication status | Published - 1999 |
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.
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal of Scientific Computing, Vol. 20, No. 5, 1999, p. 1605-1626.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Adaptive finite elements for elastic bodies in contact
AU - Carstensen, C.
AU - Scherf, O.
AU - Wriggers, Peter
PY - 1999
Y1 - 1999
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0033295419&partnerID=8YFLogxK
U2 - 10.1137/S1064827595295350
DO - 10.1137/S1064827595295350
M3 - Article
AN - SCOPUS:0033295419
VL - 20
SP - 1605
EP - 1626
JO - SIAM Journal of Scientific Computing
JF - SIAM Journal of Scientific Computing
SN - 0196-5204
IS - 5
ER -