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A Dynamic Frictional Contact Problem of a Viscoelastic Beam

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • M. Campo

    (Universidade de Santiago de Compostela. Facultade de Matemáticas, Departamento de Matemática Aplicada)

  • J.R. Fernández

    (Universidade de Santiago de Compostela. Facultade de Matemáticas, Departamento de Matemática Aplicada)

  • G.E. Stavroulakis

    (Technical University of Crete, Department of Production Engineering and Management
    Technical University of Braunschweig, Greece and Department of Civil Engineering)

  • J.M. Viaño

    (Universidade de Santiago de Compostela. Facultade de Matemáticas, Departamento de Matemática Aplicada)

Abstract

We study the dynamic frictional contact of a viscoelastic beam with a deformable obstacle. The left end of the beam is rigidly attached and the horizontal movement of the right one is constrained because of the presence of a deformable obstacle. The effect of the friction is included in the vertical motion of the free end, by using Tresca’s law or Coulomb’s law.We recall an existence and uniqueness result. Then, by using the finite element method to approximate the spatial variable and an Euler scheme to discretize the time derivatives, a numerical scheme is proposed. Error estimates are derived on the approximative solutions. Finally, some numerical results are shown.

Suggested Citation

  • M. Campo & J.R. Fernández & G.E. Stavroulakis & J.M. Viaño, 2006. "A Dynamic Frictional Contact Problem of a Viscoelastic Beam," Springer Books, in: Alfredo Bermúdez de Castro & Dolores Gómez & Peregrina Quintela & Pilar Salgado (ed.), Numerical Mathematics and Advanced Applications, pages 1091-1098, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-34288-5_109
    DOI: 10.1007/978-3-540-34288-5_109
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