Formulations of the problems of the theory of an ideally elastic-plastic body
type: Item
instance of: scholarly article
title: Formulations of the problems of the theory of an ideally elastic-plastic body
zbMATH Open document ID: 0627.73032
DOI: 10.1016/0021-8928(85)90087-5
published in: Journal of Applied Mathematics and Mechanics
publication date: 1985-01-01T00:00:00Z
review text: The mathematical correctness of the problem of ideally plastic materials has been studied previously by many authors. In the present paper, various functional formulations are given for the problems of the theory of quasi-static equilibrium of ideally elastic-plastic media. Three problems are considered. The problem A follows from the classical formulations. It is shown that the problem A is equivalent to two partial problems (problems B and C). Problem B represents an evolutionary variational inequality for the stress tensor, which has a unique solution. In problem C, the known stress field is used to determine the velocity field. It is shown that problems A and C have no solution. However, a modified form of each of the problems has a unique solution. An example is given in which problem A has no solution, but its modified form has a unique solution. The paper is much mathematical. Practical engineers may not find interest in it.
Mathematics Subject Classification ID: 74C99
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74A20
Mathematics Subject Classification ID: 74G30
Mathematics Subject Classification ID: 74H25
Mathematics Subject Classification ID: 46N99
zbMATH DE Number: 4020574
zbMATH Keywords: classical boundary value problem
zbMATH Keywords: Radon measure
zbMATH Keywords: load parameters
zbMATH Keywords: quasi- static equilibrium
zbMATH Keywords: ideally elastic-plastic media
zbMATH Keywords: evolutionary variational inequality
zbMATH Keywords: stress tensor
zbMATH Keywords: stress field
zbMATH Keywords: velocity field
zbMATH Keywords: unique solution
author: G. Seregin
MaRDI profile type: Publication
full work available at URL: 0021-8928(85)90087-5
OpenAlex ID: W1966511609
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description: scientific article; zbMATH DE number 4020574