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Dynamic frictional contact of a viscoelastic beam
Published online by Cambridge University Press: 21 June 2006
Abstract
In this paper, we study the dynamic frictional contact of a viscoelastic beam with a deformableobstacle. The beam is assumed to be situated horizontally and to move, in both horizontal andtangential directions, by the effect of applied forces. The left end of the beam is clampedand the right one is free. Its horizontal displacement is constrained because of the presenceof a deformable obstacle, the so-called foundation, which is modelled by a normal compliance contact condition.The effect of the friction is included in the vertical motion ofthe free end, by using Tresca's law or Coulomb's law. In both cases, the variationalformulation leads to a nonlinear variational equation for the horizontal displacement coupledwith a nonlinear variational inequality for the vertical displacement. We recall an existenceand uniqueness result. Then, by using the finite element method to approximate the spatial variableand an Euler scheme to discretize the time derivatives, a numerical scheme is proposed. Error estimates on the approximative solutions are derived. Numerical results demonstrate the application of the proposed algorithm.
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 2 , March 2006 , pp. 295 - 310
- Copyright
- © EDP Sciences, SMAI, 2006
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