On the use of a Pseudo-spectral method in the Asymptotic Numerical Method for the resolution of the Ginzburg–Landau envelope equation. (1st July 2022)

• Record Type: Journal Article
• Authors: Drissi, Mohamed; Mansouri, Mohamed; Mesmoudi, Said; Saadouni, Khalid
• Is Part Of: Engineering structures. Volume 262(2022)
• Publication Date: 2022-07-01
• Subjects: Buckling -- Landau–Ginzburg equation -- Bifurcation -- Pseudo-spectral; Structural engineering -- Periodicals; Structural analysis (Engineering) -- Periodicals; Construction, Technique de la -- Périodiques; Génie parasismique -- Périodiques; Pression du vent -- Périodiques; Earthquake engineering; Structural engineering; Wind-pressure; Periodicals; 624.105
• DOI: 10.1016/j.engstruct.2022.114236
• Languages: English
• ISSNs: 0141-0296

Abstract

Abstract: The present work deals with the resolution of the Ginzburg–Landau envelope equation. It is a nonlinear partial differential equation that requires a robust solver. Nowadays, Newton methods are available in many existing commercial codes. However, the computation of the associated tangent operator and its factorization at each incremental step requires a computational cost. In order to reduce this computational cost, we focus on the use of a high-order solver. This algorithm, named in this work (ANM-SM), is made by associating the Asymptotic Numerical Method (ANM) with the Spectral Method (SM). The efficiency and robustness of the used algorithm are illustrated by numerical results of a simple example of a beam resting on a non-linear Winkler foundation. Highlights: The Spectral Chebyshev was coupled with the Asymptotic Numerical Method to solve nonlinear problems. The Ginzburg–Landau envelope equation was solved by a high order solver based on the Asymptotic Numerical Method with Spectral Method. Nonlinear buckling analysis of beam was investigated. Effects of boundary conditions on the critical buckling loads of a beam were tested. Effect of boundary conditions on the buckling patterns of a beam were analyzed.