Direct computation of paths of limit points using the Asymptotic Numerical Method

Sébastien Baguet (1) , Bruno Cochelin (2)

1 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
2 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

This paper is concerned with parameter dependent problems for structural instability. The aim is the direct determination of the so called fold curve connecting the limit points of the equilibrium path for a structure subjected to a variable imperfection. This is traditionally achieved by adding a well-chosen constraint equation requiring the criticality of the equilibrium. The crucial feature of the paper lies in the numerical resolution of the obtained augmented system. Indeed, it is solved using the Asymptotic Numerical Method (A.N.M.) which is well-known for its robustness. The theoretical framework upon which the A.N.M. and the extended system are based are presented. From a numerical point of view, it leads to an efficient treatment which takes the singularity of the tangent stiffness matrix into account. Emphasis is given on two specific types of geometrical imperfections. Eventually, the numerical isolation of an initial starting limit point is discussed.

Mots clés: Instabilities; Fold curve; Turning points; Asymptotic Numerical Method; Extend- ed system; Finite elements; Path following

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

Sébastien Baguet, Bruno Cochelin. Direct computation of paths of limit points using the Asymptotic Numerical Method. IASS-IACM 2000, 4th International Colloquium on Computation of Shell & Spatial Structures, Jun 2000, Chania - Crete, Greece. 20pp. ⟨hal-00623488⟩