Static Problems

  • Anca Capatina
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 31)


In this chapter we study, in an almost exhaustive way, a contact problem with friction which models the contact between an elastic body and a rigid foundation. The contact is modeled upon the well-known Signorini conditions and the friction is described by a nonlocal Coulomb friction law. The classical formulation of the model is described, and a variational formulation of the problem is derived. Under appropriate assumptions on the data, existence, uniqueness and regularity results are provided. We also derive two dual formulations of this problem. Numerical analysis is carried out and convergence results are proved. Finally, a related optimal control problem is studied.


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Anca Capatina
    • 1
  1. 1.Institute of Mathematics “Simion Stoilow” of the Romanian AcademyBucharestRomania

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