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X‐FEM in isogeometric analysis for linear fracture mechanics
Author(s) -
De Luycker E.,
Benson D. J.,
Belytschko T.,
Bazilevs Y.,
Hsu M. C.
Publication year - 2011
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.3121
Subject(s) - isogeometric analysis , finite element method , quartic function , multiplicity (mathematics) , mathematics , rate of convergence , mathematical analysis , structural engineering , computer science , engineering , pure mathematics , computer network , channel (broadcasting)
The extended finite element method (X‐FEM) has proven to be an accurate, robust method for solving problems in fracture mechanics. X‐FEM has typically been used with elements using linear basis functions, although some work has been performed using quadratics. In the current work, the X‐FEM formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics. In comparison with X‐FEM with conventional finite elements of equal degree, the NURBS‐based isogeometric analysis gives equal asymptotic convergence rates and equal accuracy with fewer degrees of freedom (DOF). Results for linear through quartic NURBS basis functions are presented for a multiplicity of one or a multiplicity equal the degree. Copyright © 2011 John Wiley & Sons, Ltd.