Stable particle methods based on Lagrangian kernels

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 12-14, 2004, Pages 1035-1063

  Rabczuk, T ^a   Belytschko, T ^a   Xiao, S P ^a  

^a Northwestern University   (United States)

Author keywords

EFG; Meshfree methods; Particle methods; SPH

Indexed keywords

BOUNDARY CONDITIONS; DEFORMATION; FUNCTIONS; GALERKIN METHODS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; PROBLEM SOLVING;

LAGRANGIAN KERNELS; LINEAR TRANSFORMATION;

LAGRANGE MULTIPLIERS;

MATHEMATICAL METHOD;

EID: 1842471032     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2003.12.005     Document Type: Article

References (47)

1. Beissel S. Belytschko T. Nodal integration on the element-free Galerkin method Comput. Methods Appl. Mech. Engrg. 139 1996 49-74
2. Belytschko T. Krongauz Y. Dolbow J. Gerlach C. On the completeness of meshfree particle methods Int. J. Numer. Methods Engrg. 43 1998 785-819
3. Belytschko T. Fleming M. Organ D. Krongauz Y. Liu W.K. Smoothing and accelerated computations in the element free Galerkin method J. Comput. Appl. Math. 74 1996 111-126
4. Belytschko T. Krongauz Y. Organ D. Krysl P. Meshless methods: An overview and recent developments Comput. Methods Appl. Mech. Engrg. 139 1996 S.3-S.47
5. Belytschko T. Lu Y.Y. Gu L. Element-free Galerkin methods Int. J. Numer. Methods Engrg. 37 1994 229-256
6. Belytschko T. Guo Y. Liu W.K. Xiao S.P. A unified stability analysis of meshless particle methods Int. J. Numer. Methods Engrg. 48 2000 1359-1400
7. Belytschko T. Xiao S.P. Stability analysis of particle methods with corrected derivatives Comput. Math. Appl. 43 2000 329-350
8. Belytschko T. Crack propagation by element free Galerkin methods Engrg. Fract. Mech. 51/2 1995 295-315
9. Belytschko T. Lu Y.Y. Element-free Galerkin methods for static and dynamic fracture Int. J. Solids Strucut. 32 1995 2547-2570
10. Belytschko T. Liu W.K. Moran B. Nonlinear Finite Elements for Continua and Structures 2000 John Wiley and Sons, Ltd New York
11. Belytschko T. Chiang H.Y. Plaskacz E. High resolution two-dimensional shear band computations imperfections and mesh dependency Comput. Methods Appl. Mech. Engrg. 119 1994 1-15
12. Black T. Belytschko T. Convergence of corrected derivative methods for second-order linear partial differential equations Int. J. Numer. Methods Engrg. 44 2 1999 177-203
13. Bonet J. Lok T.-S.L. Variational and momentum preservation aspects of Smooth Particle Hydrodynamics formulations Comput. Methods Appl. Mech. Engrg. 180 1999 97-155
14. 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
15. Dilts G.A. Moving least squares particle hydrodynamics II: Conservation and boundaries Int. J. Numer. Methods Engrg. 2000 1503-1524
16. Dilts G.A. Moving-least-squares-particle hydrodynamics I: Consistency and stability Int. J. Numer. Methods Engrg. 44 1999 S.1115-S.1155
17. G.A. Dilts, Some recent developments for moving-least-squares particle methods, First M.I.T. Conference on Computational Fluid and Soil Mechanics, June 12-14, 2001, Preprint, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
18. Dyka C.T. Ingel R.P. An approach for tensile instability in smoothed particle hydrodynamics Comput. Struct. 57 1995 573-580
19. Dyka C.T. Ingel R.P. Addressing Tension Instability in SPH Method 1994 Naval Research Laboratory Washington
20. Gingold R.A. Monaghan J.J. Smoothed particle hydrodynamics: theory and applications to non-spherical stars Mon. Not. R. Astr. Soc. 181 1977 375-389
21. Girkmann K. Flaechentragwerke, 6 1974 Springer Verlag, Wiley New York
22. Grady D.E. Benson D.A. Fragmentation of metal rings by electromagnetic loading Exp. Mech. 12 187 1983 393-400
23. Hao S. Liu W.K. Chang C.T. Computer implementation of damage models by finite element and meshfree methods Comput. Methods Appl. Mech. Engrg. 187 2000 401-440
24. Johnson G.R. Beissel S.R. Normalized smoothing functions for SPH impact computations Int. J. Numer. Methods Engrg. 39 1996 S.2725-S.2741
25. Kachanov L.M. Time of the rupture process under creep conditions Izv. Akad. Nauk SSR Otd. Tech. 8 1958 26-31
26. Kachanov L.M. Foundations of the Theory of Plasticity 1971 North Holland London
27. Krongauz Y. Belytschko T. Consistent pseudo derivatives in meshless methods Comput. Methods Appl. Mech. Engrg. 146 1997 371-386
28. L.D. Libersky, A.G. Petschek, Smooth particle hydrodynamics with strength of materials, Advances in the Free Lagrange Method, Lecture Notes in Physics, 395, 1990
29. Liu W.K. Jun S. Adee J. Belytschko T. Reproducing kernel particle method for structural dynamics Int. J. Numer. Methods Engrg. 38 1995 1665-1679
30. Liu W.K. Jun S. Zhang Y.F. Reproducing kernel particle methods Int. J. Numer. Methods Fluid 20 1995 1081-1106
31. Lu Y.Y. Belytschko T. Gu L. A new implementation of the element free Galerkin method Comput. Methods Appl. Mech. Engrg. 113 1994 397-414
32. Lucy L.B. A numerical approach to the testing of fission hypothesis Astronom. J. 82 1977 1013-1024
33. Monaghan J.J. Kernel estimates as a basis for general particle methods in hydrodynamics J. Comput. Phys. 46 1982 S.429-S.453
34. Monoghan J.J. An introduction to sph Comput. Phys., Commun. 48 1988 89-96
35. Mott N.F. Fragmentation of shell cases Proc. Roy. Soc. London 300 1947 300-308
36. Nayroles B. Touzot G. Villon P. Generalizing the finite element method: diffuse approximation and diffuse elements Comput. Mech. 10 1992 307-318
37. Needleman A. Dynamic shear band development in plane strain J. Appl. Mech. 56/1 March 1989
38. P.E. Petersson, Crack growth development of fracture zone in plain concrete and similar materials, Report No. TVBM-1006, Division of Building Materials, 1981, University of Lund, Sweden 1981
39. T. Rabczuk, Numerische Untersuchungen zum Fragmentierungsverhalten von Beton mit Hilfe der SPH-Methode, Dissertation, Inst. Massivbau, Universitaet Karlsruhe, 2002
40. Rabczuk T. Eibl J. Simulation of high velocity concrete fragmentation using SPH/MLSPH Int. J. Numer. Methods Engrg. 56 2003 1421-1444
41. Randles P.W. Libersky L.D. Recent improvements in SPH modeling of hypervelocity impact Int. J. Impact Engrg. 20 1997 525-532
42. Randles P.W. Libersky L.D. Normalized SPH with stress points Int. J. Numer. Methods Engrg. 48 2000 1445-1462
43. Schmidt-Hurtienne: Ein dreiaxiales Schaedigungsmodell zur Beschreibung des Dehnrateneffektes von Beton, Dissertation, Institut fuer Massivbau und Baustofftechnologie, Universitaet Karlsruhe, 2000
44. Simo J.C. Hughes T.J.R. On the variational foundations of assumed strain methods J. Appl. Mech. 53 1986 1685-1695
45. J.W. Swegle, S.W. Attaway, M.W. Heinstein, F.J. Mello, Hicks D.L., An Analysis of Smoothed Particle Hydrodynamics, Sandia Report SAND93-2513,1994,SNL,Albuquerque, NM 87185
46. Swegle J.W. Hicks D.A. Smooth particle hydrodynamics stability analysis J. Comput. Phys. 116 1995 123-134
47. S.P. Xiao, T. Belytschko, Material stability analysis of particle methods, Adv. Comput. Math., accepted for publication