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eXtended finite element methods for thin cracked plates with Kirchhoff–Love theory
Author(s) -
Lasry Jérémie,
Pommier Julien,
Renard Yves,
Salaün Michel
Publication year - 2010
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2939
Subject(s) - discretization , finite element method , convergence (economics) , extended finite element method , displacement (psychology) , bending , matching (statistics) , mathematics , degrees of freedom (physics and chemistry) , degree (music) , mathematical analysis , structural engineering , geometry , physics , engineering , acoustics , psychology , statistics , quantum mechanics , economics , psychotherapist , economic growth
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 1 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. Copyright © 2010 John Wiley & Sons, Ltd.