# Calculs de plaques fissurées en flexion avec la méthode des éléments finis étendue (XFEM)

Abstract : This thesis is devoted to the development of numerical methods for cracked plate and shell computations. For this issue, classical methods are based on the Finite Element Method (FEM). Due to the presence of a singularity near the crack tip, the FEM has several drawbacks. Its convergence rate is not optimal. Moreover, if the crack propagates, the domain must be remeshed. A new finite element method, introduced in 1999 and called XFEM, enables to avoid these drawbacks. In this method, the finite element base is enriched by specific shape functions which represent the discontinuity of the material and the crack tip singularity. In consequence, domain and crack are independent and the rate of convergence is optimal. In this thesis, we develop two XFEM formulations adapted to thin plates. These methods have been implemented in the finite element toolbox Getfem++, and tested on benchmark problems where the exact solution is known. The measure of the error shows that XFEM has an optimal rate of convergence, whereas the FEM shows a lower convergence. The other contribution of this thesis deals with the Stress Intensity Factors (SIF) : these variables indicate the risk of propagation of a crack.We propose two original computation methods, based on our XFEM formulations. The first uses the J-integral, and the other provides a direct estimation, without post-treatment.
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https://tel.archives-ouvertes.fr/tel-00465635
Contributor : Jérémie Lasry <>
Submitted on : Saturday, March 20, 2010 - 1:34:49 PM
Last modification on : Monday, October 19, 2020 - 10:56:21 AM
Long-term archiving on: : Tuesday, June 22, 2010 - 10:54:54 AM

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• HAL Id : tel-00465635, version 1

### Citation

Jérémie Lasry. Calculs de plaques fissurées en flexion avec la méthode des éléments finis étendue (XFEM). Mathématiques [math]. INSA de Toulouse, 2009. Français. ⟨tel-00465635⟩

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