A new analytical formula to compute the step length of Padé approximants in the ANM: Application to buckling structures

In this paper, we propose a new analytical formula to define the next branch in the Asymptotic Numerical Method (ANM) using the Padé approximants. The proposed formula is based on the computation of the relative error of two consecutive Padé approximants. This formula is obtained by developing the r...

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Bibliographic Details
Published inComptes rendus. Mecanique Vol. 347; no. 6; pp. 463 - 476
Main Authors Ayane, Rachida, Hamdaoui, Abdellah, Braikat, Bouazza, Tounsi, Noureddine, Damil, Noureddine
Format Journal Article
LanguageEnglish
Published Elsevier Masson SAS 01.06.2019
Subjects
Asymptotic Numerical Method (ANM)
Buckling
Padé approximant
Shells
Step length
Validity range
Shells
Padé approximant
Step length
Asymptotic Numerical Method (ANM)
Buckling
Validity range
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Summary:In this paper, we propose a new analytical formula to define the next branch in the Asymptotic Numerical Method (ANM) using the Padé approximants. The proposed formula is based on the computation of the relative error of two consecutive Padé approximants. This formula is obtained by developing the relative error with respect to the path parameter. An appropriate matrix formulation is adopted for the computation of this relative error. A comparison between the analytical formula proposed in this paper and the classical continuation Padé approximants using the step length computed numerically using dichotomy method is presented for examples of buckling structures.
ISSN:1631-0721
1873-7234
DOI:10.1016/j.crme.2019.04.001