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A generalized finite element formulation for arbitrary basis functions: From isogeometric analysis to XFEM
Author(s) -
Benson D. J.,
Bazilevs Y.,
De Luycker E.,
Hsu M.C.,
Scott M.,
Hughes T. J. R.,
Belytschko T.
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.2864
Subject(s) - isogeometric analysis , basis (linear algebra) , finite element method , extended finite element method , basis function , mathematics , tetrahedron , computer science , subdivision , element (criminal law) , mathematical optimization , geometry , mathematical analysis , structural engineering , engineering , civil engineering , political science , law
Many of the formulations of current research interest, including iosogeometric methods and the extended finite element method, use nontraditional basis functions. Some, such as subdivision surfaces, may not have convenient analytical representations. The concept of an element, if appropriate at all, no longer coincides with the traditional definition. Developing a new software for each new class of basis functions is a large research burden, especially, if the problems involve large deformations, non‐linear materials, and contact. The objective of this paper is to present a method that separates as much as possible the generation and evaluation of the basis functions from the analysis, resulting in a formulation that can be implemented within the traditional structure of a finite element program but that permits the use of arbitrary sets of basis functions that are defined only through the input file. Elements ranging from a traditional linear four‐node tetrahedron through a higher‐order element combining XFEM and isogeometric analysis may be specified entirely through an input file without any additional programming. Examples of this framework to applications with Lagrange elements, isogeometric elements, and XFEM basis functions for fracture are presented. Copyright © 2010 John Wiley & Sons, Ltd.