Bifurcation indicator for geometrically nonlinear elasticity using the Method of Fundamental Solutions

Omar Askour; Abdeljalil Tri; Bouazza Braikat; Hamid Zahrouni; Michel Potier-Ferry

doi:10.1016/j.crme.2019.01.002

Bifurcation indicator for geometrically nonlinear elasticity using the Method of Fundamental Solutions

Omar Askour ¹; Abdeljalil Tri ^2,³; Bouazza Braikat ¹ ; Hamid Zahrouni ^4,⁵; Michel Potier-Ferry ^4,⁵

¹ Laboratoire d'ingénierie et matériaux (LIMAT), Faculté des sciences Ben M'Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco
² Institut supérieur des études maritimes (ISEM), Km 7, route d'El Jadida, Casablanca, Morocco
³ Laboratoire de mécanique, Faculté des sciences Aïn Chok, Hassan II University of Casablanca, Casablanca, Morocco
⁴ Université de Lorraine, CNRS, Arts et Métiers ParisTech, LEM3, 57000 Metz, France
⁵ DAMAS, Laboratory of Excellence on Design of Alloy Metals for low-mAss Structures, Université de Lorraine, 57000 Metz, France

Comptes Rendus. Mécanique, Volume 347 (2019) no. 2, pp. 91-100.

Abstract

In the present work, we propose a numerical analysis of instability and bifurcations for geometrically nonlinear elasticity problems. These latter are solved by using the Asymptotic Numerical Method (ANM) associated with the Method of Fundamental Solutions (MFS). To compute bifurcation points and to determine the critical loads, we propose three techniques. The first one is based on a geometrical indicator obtained by analyzing the Taylor series. The second one exploits the properties of the Padé approximants, and the last technique uses an analytical bifurcation indicator. Numerical examples are studied to show the efficiency and the reliability of the proposed algorithms.

Received: 2018-11-16
Accepted: 2019-01-07
Published online: 2019-01-21

DOI: 10.1016/j.crme.2019.01.002

Keywords: Bifurcation indicator, Method of Fundamental Solutions, Asymptotic Numerical Method, Nonlinear computation

Author's affiliations:

Omar Askour ¹; Abdeljalil Tri ^{2, 3}; Bouazza Braikat ¹; Hamid Zahrouni ^{4, 5}; Michel Potier-Ferry ^{4, 5}

¹ Laboratoire d'ingénierie et matériaux (LIMAT), Faculté des sciences Ben M'Sik, Hassan II University of Casablanca, BP 7955, Sidi Othman, Casablanca, Morocco
² Institut supérieur des études maritimes (ISEM), Km 7, route d'El Jadida, Casablanca, Morocco
³ Laboratoire de mécanique, Faculté des sciences Aïn Chok, Hassan II University of Casablanca, Casablanca, Morocco
⁴ Université de Lorraine, CNRS, Arts et Métiers ParisTech, LEM3, 57000 Metz, France
⁵ DAMAS, Laboratory of Excellence on Design of Alloy Metals for low-mAss Structures, Université de Lorraine, 57000 Metz, France

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     author = {Omar Askour and Abdeljalil Tri and Bouazza Braikat and Hamid Zahrouni and Michel Potier-Ferry},
     title = {Bifurcation indicator for geometrically nonlinear elasticity using the {Method} of {Fundamental} {Solutions}},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {91--100},
     publisher = {Elsevier},
     volume = {347},
     number = {2},
     year = {2019},
     doi = {10.1016/j.crme.2019.01.002},
     language = {en},
}

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Omar Askour; Abdeljalil Tri; Bouazza Braikat; Hamid Zahrouni; Michel Potier-Ferry. Bifurcation indicator for geometrically nonlinear elasticity using the Method of Fundamental Solutions. Comptes Rendus. Mécanique, Volume 347 (2019) no. 2, pp. 91-100. doi : 10.1016/j.crme.2019.01.002. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.01.002/

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