Reproducing kernel element method. Part III: Generalized enrichment and applications

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 12-14, 2004, Pages 989-1011

  Lu, Hongsheng ^a   Li, Shaofan ^b   Simkins Jr , Daniel C ^b   Liu, Wing Kam ^a   Cao, Jian ^a  

^a Northwestern University   (United States)

^b Berkeley   (United States)

Author keywords

Enrichment; Finite element methods; Kirchhoff plates; Meshfree method

Indexed keywords

FUNCTIONS; HIERARCHICAL SYSTEMS; MATHEMATICAL MODELS; POLYNOMIALS; PROBLEM SOLVING;

PARTITION POLYNOMIALS; TRIANGULAR MESH;

FINITE ELEMENT METHOD;

FINITE ELEMENT METHOD;

EID: 1842575616     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2003.12.003     Document Type: Article

References (40)

1. Argyris J.H. Fried I. Scharpf D.W. The TUBA family of plate elements for the matrix displacement method Aeronaut. Royal Aeronaut. Soc. 72 1968 701-709
2. G.P. Bazeley, Y.K. Cheung, B.M. Irons, O.C. Zienkiewicz, Triangle elements in bending: conforming and nonconforming solutions, in: Proc. 1st Conference on Matrix Methods in Structural Mechanics, Wright-Patterson, AFB, Ohio, 1965
3. Bell K. A refined triangular plate bending finite element Int. J. Numer. Methods Engrg. 1 1969 101-122
4. Belytschko T. Fleming M. Smoothing, enrichment and contact in the element-free Galerkin method Comput. Struct. 71 1999 173-195
5. Belytschko T. Liu W.K. Moran B. Nonlinear Finite Elements for Continua and Structures 2000 Wiley England
6. Belytschko T. Moes N. Usui S. Parimi C. Arbitrary discontinuities infinite elements Int. J. Numer. Methods Engrg. 50 2001 993-1013
7. Belytschko T. Lu Y.Y. Gu L. Element-free Galerkin methods Int. J. Numer. Methods Engrg. 37 1994 229-256
8. Birkhoff G. de Boor C. Piecewise polynomial interpolation and approximation Garabedian H.L. Approximation of Functions 1965 Elsevier New York
9. Birkhoff G. Schultz M.H. Varga R.S. Piecewise Hermite interpolation in one and two variables with applications to partial differential equations Numer. Math. 11 1968 232-256
10. Brenner S.C. Scott L.R. The Mathematical Theory of Finite Element Methods 1994 Springer-Verlag New York
11. Chen J.S. Han W. You Y. Meng X. A reproducing kernel method with nodal interpolation property Int. J. Numer. Methods Engrg. 56 2003 935-960
12. Chen J.S. Wu C.T. Yoon S. You Y. A stabilized conforming nodal integration for Galerkin meshfree methods Int. J. Numer. Methods Engrg. 50 2001 435-466
13. Chen J.S. Pan C. Wu C.T. Liu W.K. Reproducing kernel particle methods for large deformation analysis of nonlinear structures Comput. Methods Appl. Mech. Engrg. 139 1996 195-229
14. R.W. Clough, J. Tocher, Finite element stiffness matrices for the analysis of plate bending, in: Proc. 1st Conference on Matrix Methods in Structural Mechanics, Wright-Patterson, AFB, Ohio, 1965
15. Donning B. Liu W.K. Meshless methods for shear-deformable beams and plates Comput. Methods Appl. Mech. Engrg. 152 1998 47-72
16. Duarte C.A.M. Oden J.T. A hp adaptive method using clouds Comput. Methods Appl. Mech. Engrg. 139 1996 237-262
17. Ergatoudis I. Irons B.M. Zienkiewicz O.C. Curved, isoparametric, "quadrilateral" elements for finite element analysis Int. J. Solids Struct. 4 1968 31-42
18. Felippa C. Clough R.W. The finite element in solid mechanics SIAM-AMS Proceedings vol. 2 1970 210-252 Amer. Math. Soc Providence, RI
19. de Veubeke, B. Fraeijs, Bending and stretching of plates--special models for upper and lower bounds, in: Proc. 1st Conference on Matrix Methods in Structural Mechanics, Wright-Patterson, AFB, Ohio, 1965
20. de Veubeke Fraeijs B. A conforming finite element for plate bending Int. J. Solids Struct. 4 1968 95-108
21. Hall C.A. Bicubic interpolation over triangles J. Math. Mech. 19 1969 1-11
22. S. Hao, W.K. Liu, Revisit of moving particle finite element method, in: Fifth World Congress on Computational Mechanics, Vienna, Austria, 7-12 July 2002
23. H. Hencky, Der Spannungszustand in rechtechigen platten, Ph.D. thesis, Darmstadt, Published by R. Oldenbourg, Munich and Berlin, Germany, 1913
24. Hughes T.J.R. The Finite Element Method 1987 Prentice Hall Inc Englewood Cliffs, NJ
25. Irons B.M. A conforming quartic triangular element for plate bending Int. J. Numer. Methods Engrg. 1 1969 29-45
26. Li S. Liu W.K. Meshfree and particle methods and their applications Appl. Mech. Rev. 55 2002 1-34
27. n hierarchy, Comput. Meth. Appl. Mech. Engrg., in press
28. S. Li, D.C. Simkins Jr., H. Lu, Compatible reproducing kernel quadrilateral elements and applications, in press
29. Liu W.K. Chen Y. Uras R.A. Chang T.C. Generalized multiple scale reproducing kernel particle methods Comput. Methods Appl. Mech. Engrg. 139 1996 91-157
30. Liu W.K. Jun S. Zhang Y.F. Reproducing kernel particle methods Int. J. Numer. Methods Fluids 20 1995 1081-1106
31. Liu W.K. Uras R.A. Chen Y. Enrichment of the finite element method with the reproducing kernel particle method J. Appl. Mech., ASME 64 1997 861-870
32. Liu W.K. Guo Y. Tang S. Belytschko T. A multiple-quadrature eight-node hexahedral finite element for large deformation elastoplastic analysis Comput. Methods Appl. Mech. Engrg. 154 1998 69-132
33. Liu W.K. Zhang Y. Ramirez M.R. Multiple scale finite element methods Int. J. Numer. Methods Engrg. 32 1991 969-990
34. W.K. Liu, W. Han, H. Lu, S. Li, J. Cao, Reproducing kernel element, Part I. Theoretical formulation, Comput. Methods Appl. Mech. Engrg., in press
35. H. Lu, W.K. Liu, J.S. Chen, J. Cao, Consistent reproducing kernel element smoothing in progressive adaptive finite element method, Int. J. Numer. Methods Engrg., in press
36. H. Lu, H.S. Cheng, J. Cao, W.K. Liu, Adaptive enrichment meshfree simulation and experiment on buckling and post-buckling analysis in sheet metal forming, Comput. Methods Appl. Mech. Engrg., in press
37. n(n≥1) triangular hierarchy, Comput. Methods Appl. Mech. Engrg., in press
38. Szilard R. Theory and Analysis of Plates 1974 Prentice-Hall Englewood Cliffs, NJ
39. R.L. Taylor, S. Govinfjee, Solution of clamped rectangular plate problems, Technical Report, UCB/SEMM-2002/09, University of California, Berkeley
40. Timoshenko S.P. Woinowsky-Krieger S. Theory of Plates and Shells second ed. 1959 McGraw-Hill New York