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Analysis and numerical approximation of an elastic frictional contact problem with normal compliance

100%
Han W., Sofonea M.
Applicationes Mathematicae
|
1999
|
tom 26
|
nr 4
415-435
EN
We consider the problem of frictional contact between an elastic body and an obstacle. The elastic constitutive law is assumed to be nonlinear. The contact is modeled with normal compliance and the associated version of Coulomb's law of dry friction. We present two alternative yet equivalent weak formulations of the problem, and establish existence and uniqueness results for both formulations using arguments of elliptic variational inequalities and fixed point theory. Moreover, we show the continuous dependence of the solution on the contact conditions. We also study the finite element approximations of the problem and derive error estimates. Finally, we introduce an iterative method to solve the resulting finite element system.
2
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A piezoelectric contact problem with normal compliance

100%
Sofonea M., Ouafik Y.
Applicationes Mathematicae
|
2005
|
tom 32
|
nr 4
425-442
EN
We consider a mathematical model which describes the static frictional contact between a piezoelectric body and an insulator foundation. We use a nonlinear electroelastic constitutive law to model the piezoelectric material and the normal compliance condition associated to a version of Coulomb's friction law to model the contact. We derive a variational formulation for the model which is in the form of a coupled system involving the displacement and the electric potential fields. Then we provide the existence of a weak solution to the problem and, under a smallness assumption, its uniqueness. We also study the dependence of the solution on the contact conditions and derive a convergence result.
3
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A convergence result for evolutionary variational inequalities and applications to antiplane frictional contact problems

100%
Sofonea M., Mansour M.
Applicationes Mathematicae
|
2004
|
tom 31
|
nr 1
55-67
EN
We consider a class of evolutionary variational inequalities depending on a parameter, the so-called viscosity. We recall existence and uniqueness results, both in the viscous and inviscid case. Then we prove that the solution of the inequality involving viscosity converges to the solution of the corresponding inviscid problem as the viscosity converges to zero. Finally, we apply these abstract results in the study of two antiplane quasistatic frictional contact problems with viscoelastic and elastic materials, respectively. For each of the problems we prove the existence of a unique weak solution; we also provide convergence results, together with their mechanical interpretation.
4
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Numerical analysis and simulations of quasistatic frictionless contact problems

81%
García J. R. F., Han W., Shillor M., Sofonea M.
International Journal of Applied Mathematics and Computer Science
|
2001
|
tom 11
|
nr 1
205-222
EN
A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.
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