Adaptive Finite Elements for Elastic Bodies in Contact

Authors:
C. Carstensen;O. Scherf;P. Wriggers
Affiliations:
-;-;-
Venue:
SIAM Journal on Scientific Computing
Year:
1999

Citing 0
Cited 8

Implementation of the fixed point method in contact problems with Coulomb friction based on a dual splitting type technique

Journal of Computational and Applied Mathematics - Special issue: Proceedings of the 9th International Congress on computational and applied mathematics
A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems

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An a Posteriori Error Estimator for Two-Body Contact Problems on Non-Matching Meshes

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A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems

Applied Numerical Mathematics - Selected papers from the 16th Chemnitz finite element symposium 2003
A posteriori error analysis for the normal compliance problem

Applied Numerical Mathematics
An adaptive NS/ES-FEM approach for 2D contact problems using triangular elements

Finite Elements in Analysis and Design
A Posteriori Error Estimator for Obstacle Problems

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Adaptive finite elements for a certain class of variational inequalities of second kind

Calcolo: a quarterly on numerical analysis and theory of computation

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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.