Extended finite element methods for thin cracked plates with Kirchhoff-Love theory

Jérémie Lasry (1) , Julien Pommier , Yves Renard (2, 3) , Michel Salaün (4)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
3 ICJ - Institut Camille Jordan
4 ICA - Institut Clément Ader

A modelization of cracked plates under bending loads in the XFEM framework is addressed. The Kirchhoff–Love model is considered. It is well suited for very thin plates commonly used for instance in aircraft structures. Reduced HCT and FVS elements are used for the numerical discretization. Two kinds of strategies are proposed for the enrichment around the crack tip with, for both of them, an enrichment area of fixed size (i.e. independant of the mesh size parameter). In the first one, each degree of freedom inside this area is enriched with the nonsmooth functions that describe the asymptotic displacement near the crack tip. The second strategy consists in introducing these functions in the finite element basis with a single degree of freedom for each one. An integral matching is then used in order to ensure the C1 continuity of the solution at the interface between the enriched and the non-enriched areas. Finally, numerical convergence results for these strategies are presented and discussed.

Mots clés: Structures; Fracture; EXtended finite element method; Plates; Kirchhoff–Love; Rate of convergence

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

Jérémie Lasry, Julien Pommier, Yves Renard, Michel Salaün. Extended finite element methods for thin cracked plates with Kirchhoff-Love theory. International Journal for Numerical Methods in Engineering, 2010, 84 (9), pp.1115-1138. ⟨10.1002/nme.2939⟩. ⟨hal-00629684⟩