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Non‐linear analysis of shells with arbitrary evolving cracks using XFEM
Author(s) -
Areias Pedro M. A.,
Belytschko Ted
Publication year - 2004
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.1192
Subject(s) - finite element method , shell (structure) , kinematics , plane stress , extended finite element method , logarithm , structural engineering , stress intensity factor , plane (geometry) , node (physics) , stress (linguistics) , rotation (mathematics) , stress field , mathematics , mathematical analysis , geometry , engineering , physics , classical mechanics , mechanical engineering , linguistics , philosophy
A new formulation and numerical procedures are developed for the analysis of arbitrary crack propagation in shells using the extended finite element method. The method is valid for completely non‐linear problems. Through‐the‐thickness cracks in sandwich shells are considered. An exact shell kinematics is presented, and a new enrichment of the rotation field is proposed which satisfies the director inextensibility condition. To avoid locking, an enhanced strain formulation is proposed for the 4‐node cracked shell element. A finite strain plane stress constitutive model based on the logarithmic corotational rate is employed. A cohesive zone model is introduced which embodies the special characteristics of the shell kinematics. Stress intensity factors are calculated for selected problems and crack propagation problems are solved. Copyright © 2004 John Wiley & Sons, Ltd.