Nonlinear analysis using a reduced number of variables
type: Item
instance of: scholarly article
title: Nonlinear analysis using a reduced number of variables
zbMATH Open document ID: 0589.73077
DOI: 10.1016/0045-7825(85)90020-9
author: A. S. L. Chan
author: K. M. Hsiao
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1985-01-01T00:00:00Z
review text: This paper investigates the possibility of taking a normalized set of correction vectors, derived during the normal course of a nonlinear analysis step using an appropriate iterative scheme (the modified Newton- Raphson method was adopted here), to be the basis vectors of this transformation. These vectors correct a linear trial solution to the nonlinear one, therefore must have contained the information concerning the local characteristics of the nonlinear behavior. Indeed they can be shown to be related to the more rigorously derived path-derivatives of the generalized load-deflection curve. They can be obtained just as easily in the presence of material nonlinearity, as well as for the purely geometrical nonlinear problems, which is perhaps the greatest advantage of this simple device over the more theoretical approaches.
Mathematics Subject Classification ID: 74S30
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 3947768
zbMATH Keywords: normalized set of correction vectors
zbMATH Keywords: nonlinear analysis
zbMATH Keywords: iterative scheme
zbMATH Keywords: modified Newton-Raphson method
zbMATH Keywords: linear trial solution
MaRDI profile type: Publication
full work available at URL: 0045-7825(85)90020-9
OpenAlex ID: W1999272592
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description: scientific article; zbMATH DE number 3947768