On the Korn-type inequality in the theory of textile-type materials
type: Item
instance of: scholarly article
title: On the Korn-type inequality in the theory of textile-type materials
zbMATH Open document ID: 0655.73006
author: Z. Naniewicz
published in: Bulletin of the Polish Academy of Sciences. Technical Sciences
publication date: 1986-01-01T00:00:00Z
review text: By the ideal textile-type material we shall mean here a thin-shell which is assumed to be slender, i.e. it is not able to sustain any compressive forces, bending couples and torques. Our study will be carried on under the assumptions of the infinitesimal theory. We start with the geometrical description of thin shells following \textit{W. T. Koiter} [Nederl. Akad. Wet., Proc., Ser. B 69, 1-54 (1966)], and then introduce in the form of constraints and according to the theory of textile-type materials [the author, \textit{A. Galka} and \textit{Cz. Wozniak}, Bull. Pol. Acad. Sci. Tech. Sci. 33, 255-278 (1985; Zbl 0568.73037; Zbl 0568.73038; Zbl 0568.73039; Zbl 0568.73040)], the suitable hypotheses concerning the kinematic and kinetic fields of slender shells. This procedure leads to the governing relations in the form of a system of two variational inequalities. Such systems have been analyzed by the author in Mech. Teor. Stosov. 23, 209-222 (1985; Zbl 0596.73005), where it has been shown that from the point of view of the existence problem it is important to know, whether a certain Korn-type inequality is satisfied. The formulation of conditions under which this inequality holds is the subject of the paper.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74K15
Mathematics Subject Classification ID: 49J40
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 74B20
zbMATH DE Number: 4070423
zbMATH Keywords: thin-shell
zbMATH Keywords: infinitesimal theory
zbMATH Keywords: slender shells
zbMATH Keywords: governing relations
zbMATH Keywords: system of two variational inequalities
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4070423