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On finite element uniqueness studies for Coulombs frictional contact model

100%
Hild P.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 1
41-50
EN
We are interested in the finite element approximation of Coulomb's frictional unilateral contact problem in linear elasticity. Using a mixed finite element method and an appropriate regularization, it becomes possible to prove existence and uniqueness when the friction coefficient is less than Cε^{2}|log(h)|^{-1}, where h and ε denote the discretization and regularization parameters, respectively. This bound converging very slowly towards 0 when h decreases (in comparison with the already known results of the non-regularized case) suggests a minor dependence of the mesh size on the uniqueness conditions, at least for practical engineering computations. Then we study the solutions of a simple finite element example in the non-regularized case. It can be shown that one, multiple or an infinity of solutions may occur and that, for a given loading, the number of solutions may eventually decrease when the friction coefficient increases.
2
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Penalties, Lagrange multipliers and Nitsche mortaring

88%
Grossmann C.
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
|
2010
|
tom 30
|
nr 2
205-220
EN
Penalty methods, augmented Lagrangian methods and Nitsche mortaring are well known numerical methods among the specialists in the related areas optimization and finite elements, respectively, but common aspects are rarely available. The aim of the present paper is to describe these methods from a unifying optimization perspective and to highlight some common features of them.
3
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Error estimation and adaptivity for nonlinear FE analysis

75%
Huerta A., Rodríguez-Ferran A., Díez P.
International Journal of Applied Mathematics and Computer Science
|
2002
|
tom 12
|
nr 1
59-70
EN
An adaptive strategy for nonlinear finite-element analysis, based on the combination of error estimation and h-remeshing, is presented. Its two main ingredients are a residual-type error estimator and an unstructured quadrilateral mesh generator. The error estimator is based on simple local computations over the elements and the so-called patches. In contrast to other residual estimators, no flux splitting is required. The adaptive strategy is illustrated by means of a complex nonlinear problem: the failure analysis of a single-edge notched beam. The quasi-brittle response of concrete is modelled by means of a nonlocal damage model.
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