Elastic strings under vertical loads
type: Item
instance of: scholarly article
title: Elastic strings under vertical loads
zbMATH Open document ID: 0532.73051
DOI: 10.1007/BF00944593
author: Hubertus J. Weinitschke
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1983-01-01T00:00:00Z
review text: The author analyzes the nonlinear equation of an elastic string subject to a symmetrical vertical load \(p(s)=p(-s)\) and a stress strain law \(T=f(e)\) when either u (the horizontal displacement) or T (the stress) is prescribed at both ends. As the second problem, the stress problem, poses no serious problem the author concentrates on the first problem, the displacement problem. On quite general assumptions on p and T the author proves the existence and uniqueness of tensile solutions and he demonstrates that compressive solutions are not necessarily unique. Furthermore, he shows that tensile solutions are kinematically stable. The opposite, the instability of compressive solutions, is only obtained approximately.
Mathematics Subject Classification ID: 74K05
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74G30
Mathematics Subject Classification ID: 74H25
zbMATH DE Number: 3845177
zbMATH Keywords: horizontal displacement or stress prescribed at both ends
zbMATH Keywords: compressive solutions not necessarily unique
zbMATH Keywords: instability of compressive solutions obtained approximately
zbMATH Keywords: elastic string
zbMATH Keywords: symmetrical vertical load
zbMATH Keywords: stress strain law
zbMATH Keywords: displacement problem
zbMATH Keywords: existence
zbMATH Keywords: tensile solutions
zbMATH Keywords: kinematically stable
reviewed by: Friedel Hartmann
MaRDI profile type: Publication
cites work: The Nonlinear String Under a Vertical Force
cites work: Q5553187
cites work: Some static problems for the nonlinear elastic string
cites work: Formation of singularities in one-dimensional nonlinear wave propagation
cites work: Formation of singularities for wave equations including the nonlinear vibrating string
description: scientific article; zbMATH DE number 3845177