Material-dependent stability conditions in the buckling of nonlinear elastic bars
type: Item
instance of: scholarly article
title: Material-dependent stability conditions in the buckling of nonlinear elastic bars
zbMATH Open document ID: 0611.73063
DOI: 10.1007/BF01182133
published in: Acta Mechanica
publication date: 1987-01-01T00:00:00Z
review text: A thorough study of the critical and post-critical large displacement response of simple discrete and continuous systems made from a nonlinear elastic material, is presented. Simple material-dependent stability conditions are established, whose application does not require the solution of the intractable nonlinear differential equations of equilibrium. The predominent role of the nonlinear component of the curvature on the buckling mechanism of the foregoing systems, is revealed. Moreover, it is found that elastic systems which were considered as exhibiting post-buckling strength might be imperfection sensitive, if the effect of material nonlinearity is taken into account. An approximate but very efficient analytical approach leading to very reliable results is derived for establishing the large displacement behavior of a nonlinear elastic cantilever bar. The degree of accuracy of this approach is checked by comparing it with the ''exact'' numerical solution of Runge Kutta. The numerical results presented herein contribute to our understanding of this problem and at the same time show the efficiency, reliability and range of applicability of the proposed approach.
Mathematics Subject Classification ID: 74G60
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 3988838
zbMATH Keywords: critical
zbMATH Keywords: post-critical large displacement response
zbMATH Keywords: simple discrete
zbMATH Keywords: continuous systems
zbMATH Keywords: material-dependent stability conditions
zbMATH Keywords: post- buckling strength
zbMATH Keywords: imperfection sensitive
zbMATH Keywords: large displacement behavior
zbMATH Keywords: cantilever bar
author: A. N. Kounadis
MaRDI profile type: Publication
cites work: Large deflection collapse analysis of an inelastic inextensional ring under external pressure
cites work: Global Behavior of Buckled States of Nonlinearly Elastic Rods
cites work: Q4121475
cites work: Q4160117
cites work: Q3863485
description: scientific article; zbMATH DE number 3988838