Hierarchical enrichment for bridging scales and mesh-free boundary conditions

International Journal for Numerical Methods in Engineering

Volumn 50, Issue 3, 2001, Pages 507-524

  Wagner, Gregory J ^a   Liu, Wing Kam ^a,b  

^a Northwestern University   (United States)

^b Dept of Mech and Civil Engineering ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL MESH; MESH-FREE BOUNDARY CONDITIONS;

BOUNDARY CONDITIONS; ERROR ANALYSIS; FUNCTIONS; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS; STIFFNESS MATRIX;

FINITE ELEMENT METHOD;

EID: 0035127997     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/1097-0207(20010130)50:3<507::AID-NME33>3.0.CO;2-B     Document Type: Article

References (17)

1. Liu WK, Zhang YF, Ramirez MR. Multiple scale finite element methods. International Journal for Numerical Methods in Fluids 1991; 32:969-990.
2. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45:601-620.
3. Liu WK, Belytschko T, Oden JT. (eds). Special Issue on Meshless Methods, Computer Methods in Applied Mechanics and Engineering, vol. 139, 1996.
4. Liu WK, Chen Y, Uras RA, Chang CT. Generalized multiple scale reproducing kernel particle methods. Computer Methods in Applied Mechanics and Engineering 1996; 139:91-157.
5. Liu WK, Uras RA, Chen Y. Enrichment of the finite element method with the reproducing kernel particle method. Journal of Applied Mechanics 1997; 64:861-870.
6. Liu WK, Chen Y, Chang CT, Belytschko T. Advances in multiple scale kernel particle methods. Computational Mechanics 1996; 18:73-111.
7. Li S, Liu WK. Reproducing kernel hierarchical partition of unity. International Journal for Numerical Methods in Engineering 1999; 45:251-317.
8. Hao S, Liu WK, Qian D. Localization-induced band and cohesive model. ASME Journal of Applied Mechanics 2000, accepted for publication.
9. Babuška I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
10. Strouboulis T, Babuska I, Copps K. The design and analysis of the generalized finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 181:43-69.
11. Dolbow J, Moës N, Belytschko T. Discontinuous enrichment in finite elements with a partition of unity method. Finite Elements in Analysis and Design 2000, to appear.
12. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46:131-150.
13. Belytschko T, Organ D, Krongauz Y. A coupled finite element - element free galerkin method. Computational Mechanics 1995; 17:186-195.
14. Melenk JM, Babuška I. The partition of unity finite element method: basic theory and applications. Computer Methods in Applied Mechanics and Engineering 1996; 139:289-314.
15. Brezzi F, Franca LP, Hughes TJR, Russo A. b = (Latin small letter esh sign) g. Computer Methods in Applied Mechanics and Engineering 1997; 145:329-339.
16. Wagner GJ, Liu WK. Application of essential boundary conditions in mesh-free methods: a corrected collocation method. International Journal for Numerical Methods in Engineering 2000; 47:1367-1379.
17. Li S, Hao W, Liu WK. Meshfree simulations of shear banding in large deformation. International Journal of Solids and Structures, 2000, accepted for publication.