Integration of singular enrichment functions in the generalized/extended finite element method for three-dimensional problems

Kyoungsoo Park; Jeronymo P. Pereira; C. Armando Duarte; Glaucio H. Paulino

doi:10.1002/nme.2530

Integration of singular enrichment functions in the generalized/extended finite element method for three-dimensional problems

Kyoungsoo Park, Jeronymo P. Pereira, C. Armando Duarte, Glaucio H. Paulino

Research output: Contribution to journal › Article › peer-review

79 Scopus citations

Abstract

A mapping method is developed to integrate weak singularities, which result from enrichment functions in the generalized/extended finite element method. The integration scheme is applicable to 2D and 3D problems including arbitrarily shaped triangles and tetrahedra. Implementation of the proposed scheme in existing codes is straightforward. Numerical examples for 2D and 3D problems demonstrate the accuracy and convergence properties of the technique.

Original language	English (US)
Pages (from-to)	1220-1257
Number of pages	38
Journal	International Journal for Numerical Methods in Engineering
Volume	78
Issue number	10
DOIs	https://doi.org/10.1002/nme.2530
State	Published - Jun 4 2009
Externally published	Yes

All Science Journal Classification (ASJC) codes

Numerical Analysis
General Engineering
Applied Mathematics

Keywords

BEM
Boundary element method
Branch functions
Extended FEM
Fracture
GFEM/X-FEM
Generalized FEM
Mapping method
Singular enrichment functions
Weakly singular integration

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10.1002/nme.2530

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abstract = "A mapping method is developed to integrate weak singularities, which result from enrichment functions in the generalized/extended finite element method. The integration scheme is applicable to 2D and 3D problems including arbitrarily shaped triangles and tetrahedra. Implementation of the proposed scheme in existing codes is straightforward. Numerical examples for 2D and 3D problems demonstrate the accuracy and convergence properties of the technique.",

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AU - Park, Kyoungsoo

AU - Pereira, Jeronymo P.

AU - Duarte, C. Armando

AU - Paulino, Glaucio H.

PY - 2009/6/4

Y1 - 2009/6/4

N2 - A mapping method is developed to integrate weak singularities, which result from enrichment functions in the generalized/extended finite element method. The integration scheme is applicable to 2D and 3D problems including arbitrarily shaped triangles and tetrahedra. Implementation of the proposed scheme in existing codes is straightforward. Numerical examples for 2D and 3D problems demonstrate the accuracy and convergence properties of the technique.

AB - A mapping method is developed to integrate weak singularities, which result from enrichment functions in the generalized/extended finite element method. The integration scheme is applicable to 2D and 3D problems including arbitrarily shaped triangles and tetrahedra. Implementation of the proposed scheme in existing codes is straightforward. Numerical examples for 2D and 3D problems demonstrate the accuracy and convergence properties of the technique.

KW - BEM

KW - Boundary element method

KW - Branch functions

KW - Extended FEM

KW - Fracture

KW - GFEM/X-FEM

KW - Generalized FEM

KW - Mapping method

KW - Singular enrichment functions

KW - Weakly singular integration

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JO - International Journal for Numerical Methods in Engineering

JF - International Journal for Numerical Methods in Engineering

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Integration of singular enrichment functions in the generalized/extended finite element method for three-dimensional problems

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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