A numerical method based on Taylor series for bifurcation analyses within Föppl-von Karman plate theory

Haitao Tian (1) , Michel Potier-Ferry (1) , Farid Abed-Meraim (1)

1 LEM3 - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux

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 and this is very efficient near bifurcation points. The specificity of TMM is a quasi-exact solution of the PDEs inside the domain, which leads to a strong reduction of the number of degrees of freedom (DOFs).

Mots clés: Taylor meshless; Trefftz method; Asymptotic numerical method; Bifurcation; Buckling

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des structures [physics.class-ph]; Sciences de l'ingénieur [physics]; Mécanique [physics.med-ph]; Modélisation et simulation

Haitao Tian, Michel Potier-Ferry, Farid Abed-Meraim. A numerical method based on Taylor series for bifurcation analyses within Föppl-von Karman plate theory. Mechanics Research Communications, 2018, 93, pp.154-158. ⟨10.1016/j.mechrescom.2017.12.006⟩. ⟨hal-02386528⟩