Skip to Main content Skip to Navigation
Journal articles

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

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.
Complete list of metadatas

Cited literature [35 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01657907
Contributor : Open Archive Toulouse Archive Ouverte (oatao) <>
Submitted on : Thursday, December 7, 2017 - 11:18:02 AM
Last modification on : Wednesday, August 7, 2019 - 12:18:06 PM

File

Benson_18483.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

David J. Benson, Yuri Bazilevs, Emmanuel de Luycker, Ming Chen Hsu, Colin Scott, et al.. A generalized finite element formulation for arbitrary basis functions : from isogeometric analysis to XFEM. International Journal for Numerical Methods in Engineering, Wiley, 2010, 83 (6), pp.765-785. ⟨10.1002/nme.2864⟩. ⟨hal-01657907⟩

Share

Metrics

Record views

114

Files downloads

491