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Static Problems

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Variational Inequalities and Frictional Contact Problems

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

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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.

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  1. Institute of Mathematics “Simion Stoilow” of the Romanian Academy, Bucharest, Romania

    Anca Capatina

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  1. Anca Capatina
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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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