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Local Parameterization and the Asymptotic NumericalMethod

Published online by Cambridge University Press:  26 August 2010

A. Taik ,
H. Mottaqui ,
B. Braikat  and
N. Damil
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Abstract

The Asymptotic Numerical Method (ANM) is a family of algorithms, based on computation oftruncated vectorial series, for path following problems [2]. In this paper, we present anddiscuss some techniques to define local parameterization [4, 6, 7] in the ANM. We givesome numerical comparisons of pseudo arc-length parameterization and localparameterization on non-linear elastic shells problems

Keywords

asymptotic numerical methodcontinuation methodslocal parameterization
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 7: JANO9 – The 9thInternational Conference on Numerical Analysis and Optimization , 2010 , pp. 16 - 22
Copyright
© EDP Sciences, 2010

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References

Cochelin, B.. A path-following technique via an asymptotic-numerical method . Computers Structures, 53 (1994), No. 5, 1181–1192.CrossRefGoogle Scholar
B. Cochelin, N. Damil, M. Potier-Ferry. Méthode asymptotique numérique. Hermès-Lavoisier, Paris, 2007.
Elhage-Hussein, A., Potier-Ferry, M., Damil, N.. A numerical continuation method based on Padé approximants . Int.J. Solids and Structures, 37 (2000), 6981–7001.CrossRefGoogle Scholar
Gervais, J. J., Sadiky, H.. A new steplength control for continuation with the asymptotic numerical method . IAM, J. Nomer. Anal., 22 (2000), No. 2, 207–229.CrossRefGoogle Scholar
H. Mottaqui, B. Braikat, N. Damil.Influence de la paramétrisation dans la méthode asymptotique numérique : Application au calcul de structures. Premier congrès Tunisien de mécanique, (2008), 173–174.
Rheinboldt, W. C., Burkadt, J. V.. A Localy parameterized continuation . Acm Transaction on Mathmatical Software, 9 (1983), No. 2, 215–235.CrossRefGoogle Scholar
R. Seydel. World of bifurcation, online collection and tutorials of nonlinear phenomena, (www.bifurcation.de) (1999).