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.
Accepted:
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Rachida Ayane 1; Abdellah Hamdaoui 1; Bouazza Braikat 1; Noureddine Tounsi 1; Noureddine Damil 1
@article{CRMECA_2019__347_6_463_0,
author = {Rachida Ayane and Abdellah Hamdaoui and Bouazza Braikat and Noureddine Tounsi and Noureddine Damil},
title = {A new analytical formula to compute the step length of {Pad\'e} approximants in the {ANM:} {Application} to buckling structures},
journal = {Comptes Rendus. M\'ecanique},
pages = {463--476},
publisher = {Elsevier},
volume = {347},
number = {6},
year = {2019},
doi = {10.1016/j.crme.2019.04.001},
language = {en},
}
TY - JOUR AU - Rachida Ayane AU - Abdellah Hamdaoui AU - Bouazza Braikat AU - Noureddine Tounsi AU - Noureddine Damil TI - A new analytical formula to compute the step length of Padé approximants in the ANM: Application to buckling structures JO - Comptes Rendus. Mécanique PY - 2019 SP - 463 EP - 476 VL - 347 IS - 6 PB - Elsevier DO - 10.1016/j.crme.2019.04.001 LA - en ID - CRMECA_2019__347_6_463_0 ER -
%0 Journal Article %A Rachida Ayane %A Abdellah Hamdaoui %A Bouazza Braikat %A Noureddine Tounsi %A Noureddine Damil %T A new analytical formula to compute the step length of Padé approximants in the ANM: Application to buckling structures %J Comptes Rendus. Mécanique %D 2019 %P 463-476 %V 347 %N 6 %I Elsevier %R 10.1016/j.crme.2019.04.001 %G en %F CRMECA_2019__347_6_463_0
Rachida Ayane; Abdellah Hamdaoui; Bouazza Braikat; Noureddine Tounsi; Noureddine Damil. A new analytical formula to compute the step length of Padé approximants in the ANM: Application to buckling structures. Comptes Rendus. Mécanique, Volume 347 (2019) no. 6, pp. 463-476. doi : 10.1016/j.crme.2019.04.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.04.001/
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