## Á. Arós, G. Castiñeira, J.M. Viaño, Viscoelastic elliptic membrane shells on bilateral frictional contact: An asymptotic approach

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DOI: 10.23952/jnva.6.2022.5.02

Volume 6, Issue 5, 1 October 2022, Pages 441-460

Abstract. We consider a family of linearly viscoelastic shells, all sharing the same middle surface, with thickness $2\epsilon$, clamped along their entire lateral face and on frictional, and bilateral contact with an obstacle along its lower face. Friction is modeled with a Tresca condition and tractions may act on the upper face of the shell. We prove that, if the shell is an elliptic membrane, the solution of the three-dimensional scaled variational contact problem, in curvilinear coordinates, $u(\epsilon)$, converges to a limit function, $u$, which is independent of the transverse variable and can be identified with the solution of a limit two-dimensional variational problem, describing tangential deformations of the middle surface, and giving us a two-dimensional model (obstacle problem) for viscoelastic shells with bilateral frictional contact.