Asymptotic justification of the intrinsic equations of Koiter's model of a linearly elastic shell

Philippe G. Ciarlet; Cristinel Mardare

doi:10.1016/j.crma.2018.10.008

Author(s)

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	99-110
Journal / Publication	Comptes Rendus Mathematique
Volume	357
Issue number	1
Online published	14 Nov 2018
Publication status	Published - Jan 2019

Link(s)

DOI	DOI https://doi.org/10.1016/j.crma.2018.10.008 Final Published version
	Check@CityULib
Attachment(s)	Documents 26739659.pdf Final Published version, 353 KB, PDF Publisher's Copyright Statement This full text is made available under CC-BY-NC-ND 4.0. https://creativecommons.org/licenses/by-nc-nd/4.0/
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-85056505787&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(7bc70c31-f46e-4654-8242-fd82079449be).html

Abstract

We show that the intrinsic equations of Koiter's model of a linearly elastic shell can be derived from the intrinsic formulation of the three-dimensional equations of a linearly elastic shell, by using an appropriate a priori assumption regarding the three-dimensional strain tensor fields appearing in these equations. To this end, we recast in particular the Dirichlet boundary conditions satisfied by any admissible displacement field as boundary conditions satisfied by the covariant components of the corresponding strain tensor field expressed in the natural curvilinear coordinates of the shell. Then we show that, when restricted to strain tensor fields satisfying a specific a priori assumption, these new boundary conditions reduce to those of the intrinsic equations of Koiter's model of a linearly elastic shell.