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A generalized finite element formulation for arbitrary basis functions : from isogeometric analysis to XFEM

Benson, David J. and Bazilevs, Yuri and De Luycker, Emmanuel and Hsu, Ming Chen and Scott, Colin and Hughe, Thomas Joseph Robert and Belytschko, Ted A generalized finite element formulation for arbitrary basis functions : from isogeometric analysis to XFEM. (2010) International Journal for Numerical Methods in Engineering, 83 (6). 765-785. ISSN 1097-0207

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/nme.2864/abstract

Abstract

Many of the formulations of cm-rent 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 clement 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.

Item Type:Article
Additional Information:Thanks to Wiley Online Library editor. The definitive version is available at : http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0207
HAL Id:hal-01657907
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:Other partners > Northwestern University (USA)
Other partners > University of Texas at Austin (USA)
Other partners > University of California - UC San Diego (USA)
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Deposited By: Emmanuel DE LUYCKER
Deposited On:15 Nov 2017 15:41

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