A Flow in a Thin Plastic Layer: Generalizations of the Prandtl’s Problem

Abstract

The analytical solutions of various generalizations of the classical L.Prandtl’s problem are of great interest in studying the problem of straightening plates using uniaxial stretching beyond the elastic limit. The straightening by stretching allows obtaining a high degree of flatness of thin wide strips and sheets of high-strength steels and special alloys, while the straightening by other methods does not provide satisfactory results. Based on Ilyushin’s theory of flow in a thin plastic layer, generalizations of the classical Prandtl’s problem on plastic strip compression were studied and their solutions were obtained. The planar problem of compression of a plastic strip between two parallel rough planes with accounting for the asymmetry of the conditions on the spreading ends has been solved and the upper estimate of the total compression force of the face-end areas of the plastically stretched strip has been obtained.