A numerical method based on Taylor series for bifurcation analyses within Föppl–von Karman plate theory. (October 2018)

• Record Type: Journal Article
• Authors: Tian, H.; Potier-Ferry, M.; Abed-Meraim, F.
• Is Part Of: Mechanics research communications. Volume 93(2018)
• Page Start: 154
• Page End: 158
• Publication Date: 2018-10
• Subjects: Taylor meshless -- Trefftz method -- Asymptotic numerical method -- Bifurcation -- Buckling; Mechanics, Applied -- Periodicals; Mécanique appliquée -- Périodiques; Mechanics, Applied; Periodicals; 530
• DOI: 10.1016/j.mechrescom.2017.12.006
• Languages: English
• ISSNs: 0093-6413

Abstract

Highlights: A new numerical method is proposed for bifurcation analysis. Taylor series with respect to loading are combined with Taylor series with respect to space variables. The adaptive step length allows to compute post-bifurcation paths with very small perturbations. Abstract: A new numerical technique for post-buckling analysis is presented by combining the asymptotic numerical method (ANM) and the Taylor meshless method (TMM). These two methods are based on Taylor series, with respect to a scalar load parameter for ANM, and with respect to the space variables for TMM. The advantage of ANM is an adaptive step length, which is very efficient near bifurcation points. The specificity of TMM is a quasi-exact solution of the partial differential equations inside the domain, which leads to a strong reduction of the number of degrees of freedom.