Authors: Hamza Azzayani ¹; Hamid Zahrouni ¹; N. Mathieu ; Pascal Ventura ¹; Mickaël Brun ; M. Potier-Ferry

• 1 Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux

This paper focuses on the stability analysis of multilayer thin shells using the asymptotic numerical method (ANM) combined with Padé approximants. This technique is highly effective for solving nonlinear problems due to its high-order algorithm that ensures accurate computation of singular points along nonlinear solution branches. We present various methods for detecting bifurcation points. The first technique uses a bifurcation indicator integrated into the nonlinear problem as a scalar function. This function represents the intensity of a fictitious perturbation force, evaluated along the equilibrium branch and vanishing exactly at singular points. The second method employs Padé approximants as a bifurcation indicator by analyzing the denominator of rational fractions. The third method identifies singular points by combining buckling and linear vibrations, examining the evolution of natural frequencies along the equilibrium path. The paper evaluates these three bifurcation detection techniques for multilayer composite structures. It also analyses the impact of the solution representation by power series or Padé approximants, the truncation order, and the accuracy parameter on the solution path.