Asymptotic analysis of unilateral contact problems for linearly elastic shells: Error estimates in the membrane case. (August 2019)

• Record Type: Journal Article
• Authors: Cao-Rial, M.T.; Rodríguez-Arós, Á.
• Is Part Of: Nonlinear analysis. Volume 48(2019)
• Page Start: 40
• Page End: 53
• Publication Date: 2019-08
• Subjects: Shells -- Unilateral contact -- Asymptotic analysis -- Elasticity -- Membrane -- Error estimates; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.01.009
• Languages: English
• ISSNs: 1468-1218

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.