Abstract
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.
Keywords
- Related Optimal Control Problems
- Bilateral Contact Problem
- Dual Formulation
- Equilibrium Finite Element Methods
- Quasi-variational Inequalities
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Capatina, A. (2014). Static Problems. In: Variational Inequalities and Frictional Contact Problems. Advances in Mechanics and Mathematics, vol 31. Springer, Cham. https://doi.org/10.1007/978-3-319-10163-7_8
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DOI: https://doi.org/10.1007/978-3-319-10163-7_8
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