An obstacle problem for Koiter's shells. (October 2019)

• Record Type: Journal Article
• Authors: Ciarlet, Philippe G; Piersanti, Paolo
• Is Part Of: Mathematics and mechanics of solids. Volume 24:Number 10(2019)
• Page Start: 3061
• Page End: 3079
• Publication Date: 2019-10
• Subjects: Linearly elastic shells -- Koiter's model -- obstacle problems -- asymptotic analysis; Materials -- Mechanical properties -- Periodicals; Solids -- Periodicals; Materials science -- Mathematics -- Periodicals; 620.11205
• DOI: 10.1177/1081286519825979
• Languages: English
• ISSNs: 1081-2865

Abstract

In this paper, we define, a priori, a natural two-dimensional Koiter's model of a 'general' linearly elastic shell subject to a confinement condition. As expected, this model takes the form of variational inequalities posed over a non-empty closed convex subset of the function space used for the 'unconstrained' Koiter's model. We then perform a rigorous asymptotic analysis as the thickness of the shell, considered a 'small' parameter, approaches zero, when the shell belongs to one of the three main classes of linearly elastic shells, namely elliptic membrane shells, generalized membrane shells and flexural shells. To illustrate the soundness of this model, we consider elliptic membrane shells to fix ideas. We then show that, in this case, the 'limit' model obtained in this fashion coincides with the two-dimensional 'limit' model obtained by means of another rigorous asymptotic analysis, but this time with the three-dimensional model of a 'general' linearly elastic shell subject to a confinement condition as a point of departure. In this fashion, our proposed Koiter's model of a linearly elastic shell subject to a confinement condition is fully justified in this case, even though it is not itself a 'limit' model.