A unified enrichment approach addressing blending and conditioning issues in enriched finite elements

被引：34
作者：
Agathos, Konstantinos [1 ]
Chatzi, Eleni [1 ]
Bordas, Stephane P. A. [2 ,3 ,4 ]
机构：
[1] Swiss Fed Inst Technol, Dept Civil Environm & Geomat Engn, Stefano Franscini Pl 5, CH-8093 Zurich, Switzerland
[2] Luxembourg Univ, Res Unit Engn Sci, 6 Rue Richard Coudenhove Kalergi, L-1359 Luxembourg, Luxembourg
[3] Cardiff Univ, Inst Theoret Appl & Computat Mech, Cardiff CF24 3AA, S Glam, Wales
[4] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan
来源：
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING | 2019年 / 349卷
基金：
瑞士国家科学基金会;
关键词：
XFEM; GFEM; PU-FEM; Higher-order; Conditioning; CRACK-TIP ENRICHMENT; GENERALIZED FEM; X-FEM; XFEM; INTEGRATION; PARTITION; DISCONTINUITIES; IMPLEMENTATION; APPROXIMATION; INTERPOLATION;
D O I：
10.1016/j.cma.2019.02.005
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
We present a combination of techniques to improve the convergence and conditioning properties of partition of unity (PU) enriched finite element methods. By applying these techniques to different types of enrichment functions, namely polynomial, discontinuous and singular, higher order convergence rates can be obtained while keeping condition number growth rates similar to the ones corresponding to standard finite elements. (C) 2019 Elsevier B.V. All rights reserved.
引用
收藏
页码：673 / 700
页数：28
相关论文
共 69 条
[51]  
Moës N, 1999, INT J NUMER METH ENG, V46, P131, DOI 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO
[52]  
2-J
[53]   Generalized Gaussian quadrature rules for discontinuities and crack singularities in the extended finite element method [J].
Mousavi, S. E. ;
Sukumar, N. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2010, 199 (49-52) :3237-3249
[54]  
Ndeffo M., 2017, Adv. Model. Simul. Eng. Sci., V4, DOI [10.1186/s40323-017-0090-3, DOI 10.1186/S40323-017-0090-3]
[55]   A new cloud-based hp finite element method [J].
Oden, JT ;
Duarte, CAM ;
Zienkiewicz, OC .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 1998, 153 (1-2) :117-126
[56]   An integration technique for 3D curved cracks and branched discontinuities within the extended Finite Element Method [J].
Paul, B. ;
Ndeffo, M. ;
Massin, P. ;
Moes, N. .
FINITE ELEMENTS IN ANALYSIS AND DESIGN, 2017, 123 :19-50
[57]   The Orthonormalized Generalized Finite Element Method - OGFEM: Efficient and stable reduction of approximation errors through multiple orthonormalized enriched basis functions [J].
Sillem, A. ;
Simone, A. ;
Sluys, L. J. .
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2015, 287 :112-149
[58]   An extended finite element method with higher-order elements for curved cracks [J].
Stazi, FL ;
Budyn, E ;
Chessa, J ;
Belytschko, T .
COMPUTATIONAL MECHANICS, 2003, 31 (1-2) :38-48
[59]  
Strouboulis T, 2000, INT J NUMER METH ENG, V47, P1401, DOI 10.1002/(SICI)1097-0207(20000320)47:8<1401::AID-NME835>3.0.CO
[60]  
2-8
1234567