On the Korn-type inequality in the theory of textile-type materials
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.
scientific article; zbMATH DE number 4070423