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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 , 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, , converges to a limit function, , 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.
How to Cite this Article:
Á. Arós, G. Castiñeira, J.M. Viaño, Viscoelastic elliptic membrane shells on bilateral frictional contact: An asymptotic approach, J. Nonlinear Var. Anal. 6 (2022), 441-460.