Asymptotic analysis of unilateral contact problems for linearly elastic shells: Error estimates in the membrane case

Abstract

[Abstract] We consider a family of linearly elastic shells all sharing the same middle surface and in unilateral contact with a rigid foundation on the lower face. The shells are elliptic and their lateral face is clamped. Under these conditions, when the thickness tends to zero, the solution of the three-dimensional problem converges to the solution of a two-dimensional obstacle problem for an elastic membrane shell. In this paper we provide error estimates for this convergence. The proof uses a corrector method.