The solution of multi-parameter systems of equations with application to problems in nonlinear elasticity
type: Item
instance of: scholarly article
title: The solution of multi-parameter systems of equations with application to problems in nonlinear elasticity
zbMATH Open document ID: 0588.73022
DOI: 10.1016/0045-7825(86)90101-5
author: G. A. Duffett
author: B. D. Reddy
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1986-01-01T00:00:00Z
review text: Systems of nonlinear equations governed by more than one parameter are discussed with particular attention to bifurcation behaviour. The procedure adopted is to add to the original system of n equations (m-1) further equations, in the case of m parameters, and to seek solution curves in \({\mathbb{R}}^{n+m}\) to this augmented system. Two types of additional equations are considered: one describes a piecewise linear path in the space of parameters, and the second constrains the solution curve to be a locus of singular points. These ideas are all subsequently applied to the systems of equations arising from finite element approximations of boundary value problems in nonlinear elasticity. The behaviour of a nonlinear elastic thick-walled cylinder subjected to internal pressure and axial extension is discussed.
Mathematics Subject Classification ID: 74B20
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 3945427
zbMATH Keywords: multi-parameter systems of equations
zbMATH Keywords: bifurcation
zbMATH Keywords: additional equations
zbMATH Keywords: thick-walled cylinder
zbMATH Keywords: internal pressure
zbMATH Keywords: axial extension
zbMATH Keywords: incompressible bodies
zbMATH Keywords: static, isothermal problems
zbMATH Keywords: determination of all solutions
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MaRDI profile type: Publication
full work available at URL: 0045-7825(86)90101-5
OpenAlex ID: W2036331842
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description: scientific article; zbMATH DE number 3945427