Stability of thin-shell structures and imperfection sensitivity analysis with the Asymptotic Numerical Method

Sébastien Baguet (1) , Bruno Cochelin (2)

1 DCS - Dynamique et Contrôle des Structures
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

This paper is concerned with stability behaviour and imperfection sensitivity of thin elastic shells. The aim is to determine the reduction of the critical buckling load as a function of the imperfection amplitude. For this purpose, the direct calculation of the so-called fold line connecting all the limit points of the equilibrium branches when the imperfection varies is performed. This fold line is the solution of an extended system demanding the criticality of the equilibrium. The Asymptotic Numerical Method is used as an alternative to Newton-like incremental-iterative procedures for solving this extended system. It results in a very robust and efficient path-following algorithm that takes the singularity of the tangent stiffness matrix into account. Two specific types of imperfections are detailed and several numerical examples are discussed.

Mots clés: Imperfection sensitivity; Thin shells; Buckling; Fold line; Extended system; Asymptotic Numerical Method; Finite elements; Stability and bifurcation analysis; Continuation methods

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Sébastien Baguet, Bruno Cochelin. Stability of thin-shell structures and imperfection sensitivity analysis with the Asymptotic Numerical Method. Revue Européenne des Éléments Finis, 2002, 11/2-3-4, pp.493-509. ⟨10.3166/reef.11.493-509⟩. ⟨hal-00623497⟩