Numerical analysis of a bilateral frictional contact problem for linearly elastic materials |
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Authors: | Barboteu, Mikael Han, Weimin Sofonea, Mircea |
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Affiliation: | 1 Laboratoire de Théorie des Systèmes, Université de Perpignan, 52 Avenue de Villeneuve, 66860 Perpignan, France 2 Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA |
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Abstract: | We consider a mathematical model which describes the contactbetween a linearly elastic body and an obstacle, the so-calledfoundation. The process is quasistatic and the contact is bilateral,i.e. there is no loss of contact during the process. The frictionis modelled with Tresca's law. The variational formulation ofthe problem is a nonlinear evolutionary inequality for the displacementfield which has a unique solution under certain assumptionson the given data. We study spatially semi-discrete and fullydiscrete schemes for the problem with finite-difference discretizationin time and finite-element discretization in space. The numericalschemes have unique solutions. We show the convergence of thescheme under the basic solution regularity. Under appropriateregularity assumptions on the solution, we derive optimal ordererror estimates. Finally, we present numerical results in thestudy of two-dimensional test problems. |
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Keywords: | linearly elastic material bilateral contact Tresca's friction law weak solution semi-discrete approximation fully discrete approximation finite element method error estimates convergence numerical experiments |
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