Explicit reproducing kernel particle methods for large deformation problems

International Journal for Numerical Methods in Engineering

Volumn 41, Issue 1, 1998, Pages 137-166

  Jun, Sukky ^a,b   Liu, Wing Kam ^a,c   Belytschko, Ted ^a,c  

^a Northwestern University   (United States)

^b INST OF PHYS AND CHEMICAL RESEARCH   (Japan)

^c Department of Mechanical Engineering ^*  (United States)

Author keywords

Large deformation; Meshless methods; Non linear elasticity; Reference configuration; Reproducing kernel particle methods; Underwater bubble dynamics

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; DEFORMATION; ELASTICITY; FINITE ELEMENT METHOD; INTEGRATION; LAGRANGE MULTIPLIERS;

REFERENCE CONFIGURATION; REPRODUCING KERNEL PARTICLE METHOD (RKPM); UNDERWATER BUBBLE DYNAMICS;

STRUCTURAL ANALYSIS;

EID: 0031678553     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0207(19980115)41:1<137::AID-NME280>3.0.CO;2-A     Document Type: Article

References (82)

1. T. Belytschko and J. M. Kennedy, Computer methods for subassembly simulation, Nucl. Engng. Des., 49, 17-38 (1978).
2. T. Belytschko, D. P. Flanagan and J. M. Kennedy, Finite element methods with user-controlled meshes for fluid-structure interaction' Comput. Methods Appl. Mech. Engng., 33, 669-688 (1982).
3. D. J. Benson, 'An efficient, accurate, simple ALE method for nonlinear finite element problems', Comput. Methods in Appl. Mech. Engng., 72, 305-350 (1989).
4. D. J. Benson, 'Computational methods in Lagrangian and Eulerian hydrocodes', Comput. Methods Appl. Mech. Engng., 99, 235-394 (1992).
5. T. J. R. Hughes, W. K. Liu and T. K. Zimmerman, 'Lagrangian-Eulerian finite element formulations for incompressible viscous flows', Comput. Methods Appl. Mech. Engng., 29, 329-349 (1981).
6. W. K. Liu, 'Finite element procedures for fluid-structure interactions and applications to liquid storage tanks,' Nucl. Engng. Des., 65, 221-238 (1981).
7. W. K. Liu, T. Belytschko and H. Chang, 'An arbitrary Lagrangian Eulerian finite element method for path-dependent materials', Comput. Methods Appl. Mech. and Engng., 58, 227-246 (1986).
8. W. K. Liu, T. Belytschko and H. Chang, 'An arbitrary Lagrangian and Eulerian Petrov-Galerkin finite elements for nonlinear continua', Comput. Methods Appl. Mech. Engng., 68, 259-310 (1988).
9. W. K. Liu, Y. F. Zhang, T. Belytschko and J. S. Chen, 'Adaptive ALE finite elements with particular reference to external work rate on factional interface, Comput. Methods Appl. Mech. Engng., 93, 189-216 (1991).
10. W. K. Liu and D. C. Ma, 'Computer implementation aspects for fluid structure interaction problems', Comput. Methods Appl. Mech. Engng., 31, 129-148 (1982).
11. S. K. Aliabadi and T. E. Tezduyar, 'Space-time finite element computations of compressible flows involving moving boundaries and interfaces', Comput. Methods Appl. Mech. Engng., 107, 209-224 (1993)
12. T. E. Tezduyar, M. Behr and J. Liou, 'A new strategy for finite element computations involving moving boundaries and interfaces-the deforming-spatial-domain/space-time procedure: I. The concept and the preliminary numerical tests, Comput. Methods Appl. Mech. Engng., 94, 339-351 (1992).
13. G. Wren, S. Ray, S. Aliabadi and T. Tezduyar, 'Space-time finite element computation of compressible flow between moving components', AHPCRC Preprint 94-005, University of Minnesota.
14. L. Lucy, 'A numerical approach to testing the fission hypothesis,' A. J., 82, 1013-1024 (1977).
15. R. A. Gingold and J. J. Monaghan, 'Smoothed particle hydrodynamics: theory and application to non-spherical stars, Mon. Not. Roy. Astron. Soc., 181, 375-389 (1977).
16. J. J. Monaghan, 'Why particle methods work', SIAM J. Sci. Statist. Comput., 3, 422-433.
17. J. J. Monaghan, An introduction to SPH', Comp. Phys. Comm., 48, 89-96 (1988).
18. S. W. Attaway, M. W. Heinstein and J. W. Swegle, 'Coupling of smooth particle hydrodynamics with the finite element method,' Nucl. Engng. Des., 150, 199-205 (1994).
19. G. R. Johnson, E. H. Peterson and R. A. Stryrk, Incorporation of a SPH option into the EPIC code for a wide range of high velocity impact computations, preprint, (1993).
20. G. R. Johnson, R. A. Stryrk and S. R. Beissel, 'SPH for high velocity impact computations,' Comput. Methods Appl. Mech. Engng., to appear.
21. L. D. Libersky and A. G. Petschek, 'Smooth particle hydrodynamics with strength of materials', in Advances in the Free-Lagrange Method, Lecture Notes in Physics, Vol. 395, 1990, pp. 248-257 (1990).
22. L. D. Libersky, A. G. Petschek, T. C. Carney, J. R. Hipp and F. A. Allahdadi, High strain Lagrangian hydrodynamics: A three-dimensional SPH code for dynamic material response', Journal of Computational Physics, 109, 67-75 (1993).
23. A. G. Petschek and L. D. Libersky, 'Cylindrical smoothed particle hydrodynamics,' J. Comput. Phys., 19, 76-83 (1993).
24. P. W. Randles and L. D. Libersky, 'Smoothed Particle Hydrodynamics: Some Recent Improvements and Applications', Comput. Methods Appl. Mech. Engng., to appear.
25. R. F. Stellingwerf and C. A. Wingate, 'Impact modeling with smoothed particle hydrodynamics', Int. J. Impact Engng., 14, 707-718 (1993).
26. D. Sulsky and J. U. Brackbill, 'A numerical method for suspension flow', J. Comput. Phys., 96, 339-368 (1991).
27. D. Sulsky, Z. Chen and H. L. Schreyer, 'A particle method for history-dependent materials', Comput. Methods Appl. Mech. Engng., 118, 179-196 (1994).
28. D. Sulsky, S.-J. Zhou and H. L. Schreyer, 'Application of a particle-in-cell method to solid mechanics', Comput. Phys. Commun., 87, 236-252 (1995).
29. D. Sulsky and H. L. Schreyer, 'Axisymmetric form of the material point method with application to upsetting and Taylor impact problems', Comput. Methods Appl. Mech. Engng., to appear.
30. T. Belytschko, Y. Y. Lu and L. Gu, 'Element free Galerkin methods', Int. J. Numer. Meth. Engng., 37, 229-256 (1994).
31. Y. Y. Lu, T. Belytschko and L. Gu, 'A new implementation of the element free Galerkin methods', Comput. Methods Appl. Mech. Engng., 113, 397-414 (1994).
32. T. Belytschko, L. Gu and Y. Y. Lu, 'Fracture and crack growth by element free Galerkin methods', Modeling Simul. Mater. Sci. Engng., 115, 277-286 (1994).
33. T. Belytschko, Y. Y. Lu and L. Gu, 'Crack propagation by element free Galerkin methods', Engng Fracture Mech., to appear.
34. T. Belytschko, Y. Y. Lu, L. Gu and M. Tabbara, 'Element free Galerkin methods for static and dynamic fracture', Int. J. Solids Struct., 32, 2547-2570 (1995).
35. T. Belytschko and M. Tabbara, 'Dynamic fracture using element free Galerkin methods, Int. J. Numer. Meth. Engng., to appear.
36. Y. Y. Lu, T. Belytschko and M. Tabbara, 'Element free Galerkin methods for wave propagation and dynamic fracture', Comput, Methods Appl. Mech. Engng., submitted.
37. F. H. Harlow and J. E. Welch, 'Numerical study of large-amplitude free-surface motion', Phys. Fluids, 9, 842-851 (1966).
38. C. A. Duarte, 'A review of some meshless methods to solve partial differential equations', TICAM Report 95-06, (1995).
39. C. A. Duarte and J. T. Oden, 'Hp clouds - a meshless method to solve boundary-value problems', TICAM Report 95-05, (1995).
40. C. A. Duarte and J. T. Oden, 'An hp adaptive method using clouds', Comput. Methods Appl. Mech. Engng., to appear.
41. C. A. Duarte and J. T. Oden, 'Hp clouds - an hp meshless method', Numer. Methods Partial Differential Equations, to appear.
42. I. Babuska and J. M. Melenk, The partition of unity finite element method, Univ. of Maryland Technical Note BN-1185, (1995).
43. J. M. Melenk and I. Babuska, The partition of unity finite element methods,' basic theory and applications', Comput. Methods Appl. Mech. Engng., to appear.
44. G. Yagawa, 'Some remarks on free mesh method: a kind of meshless finite element method', Presented in Int. Conf. on Computational Engineering Science, Hawaii, USA, August, (1995).
45. G. Yagawa and T. Yamada, 'Free mesh method: a new finite element method, Comput. Mech., to appear.
46. E. Oñate, S. Idelson, T. Fischer and O. C. Zienkiewicz, 'A finite point method for analysis of fluid flow problems', presented at the 9th Int. Conf. on Finite Elements in Fluids, Venezia, Italy, 15-21 October 1995.
47. E. Oñate, S. Idelson, O. C. Zienkiewicz, R. L. Taylor and C. Sacco, 'A stabilized finite point method for analysis of fluid mechanics problems', Comput. Methods Appl. Mech. Engng., to appear.
48. W. K. Liu, J. Adee and S. Jun, 'Reproducing kernel particle methods for elastic and plastic problems', B. J. Benson and R. A. Asaro, (eds), in Advanced Computational Methods for Material Modeling, Vol. AMD 180 and PVP 268, ASME, New York, 1993, pp. 175-190.
49. W. K. Liu, S. Jun, S. Li, , J. Adee and T. Belytschko, 'Reproducing kernel particle methods for structural dynamics', Int. J. Numer. Meth. Engng., 38, 1655-1679 (1995).
50. W. K. Liu, S. Jun and Y. Zhang, 'Reproducing kernel particle methods', Int. J. Numer. Meth. Fluids, 20, 1081-1106 (1995).
51. W. K. Liu, S. Jun, D. T. Sihling, Y. Chen and W. Hao, 'Multiresolution reproducing kernel particle method for computational fluid dynamics', Int. J. Numer. Meth. Fluids, 24, 1391-1415 (1997).
52. W. K. Liu and Y. Chen, 'Wavelet and multiple scale reproducing kernel methods', Int. J. Numer. Meth. Fluids, 21, 901-931 (1995).
53. J. S. Chen, C. Pan, C. T. Wu and W. K. Liu, 'Reproducing kernel particle methods for large deformation analysis of nonlinear structures', Comput. Methods Appl. Mech. Engng., 139, 195-228 (1996).
54. R. A. Uras, C. T. Chang, Y. Chen and W. K. Liu, 'Multiresolution reproducing kernel particle methods in acoustics', J. Comput. Acoust., 5(1), 71-94 (1997).
55. H. M. Shodja, T. Mura and W. K. Liu, 'Multiresolution analysis of a micromechanical model', Computat. Methods Micromechan., Ed. S. Ghosh and M. Ostoja-Starzewski, ASME, AMD 212/MD 62, 33-54 (1995).
56. W. K. Liu, Y. Chen and R. A. Uras, 'Enrichment of the finite element method with reproducing kernel particle method', in J. F. Cory, Jr. and J. L. Gordon, (eds), Current Topics in Computational Mechanics, Vol. , 305, ASME, New York, 1995, pp. 253-258.
57. G. M. Hulbert, 'Application of reproducing kernel particle method in electromagnetics', Comput. Meth. Appl. Mech. Engng., 139, 229-236 (1996).
58. W. K. Liu, S. Li and T. Belytschko, 'Moving least square reproducing kernel method. Part 1: Methodology and convergence', Comput. Meth. Appl. Mech. Engng., 143, 113-154 (1997).
59. S. Li and W. K. Liu, 'Moving least square reproducing kernel method (II) Fourier analysis', Comput. Methods Appl. Mech. Engng., 139, 159-194 (1996).
60. W. K. Liu, Y. Zhang and M. R. Ramirez, 'Multiple scale finite element methods', Int. J. Numer. Meth. Engng., 32, 969-990 (1991).
61. W. K. Liu and U. Haeussermann, 'Multiple temporal and spatial scale methods', in P. Smolinski, W. K. Liu, G, Hulbert and K. Tamma (eds), New Methods in Transient Analysis, Vol. PVP 246/AMD 143, ASME New York, 1992, pp. 51-64.
62. W. K. Liu and C. Oberste-Brandenburg, 'Reproducing kernel and wavelet particle methods', in J. P. Cusumand, C. Pierre and S. T. Wu, (eds), Aerospace Structures: Nonlinear Dynamics and System Response, Vol. AD 33, ASME, New York, pp. 39-56.
63. W. K. Liu, Y. Chen, C. T. Chang and T. Belytschko, 'Advances in multiple scale kernel particle methods', Comput. Mech., 18-2, 73-111 (1996).
64. W. K. Liu, Y. Chen, S. Jun, J. S. Chen, T. Belytschko, C. Pan, R. A. Uras, and C. T. Chang, 'Overview and applications of the reproducing kernel particle methods, Arch. Comput. Methods Engng., 3, 1-80 (1996).
65. W. K. Liu, Y. Chen, R. A. Uras and C. T. Chang, 'Generalized multiple scale reproducing kernel particle method', Comput. Methods Appl. Mech. Engng., 139, 91-158 (1996).
66. W. K. Liu, W. Hao, Y. Chen, S. Jun and J. Gosz, 'Multiresolution reproducing kernel particle methods, in W. Dahmen, A. Kurdila and P. Oswala (eds), Multiresolution Analysis and Wavelets for Numerical Solution of Partial Differential Equations Academic Press, New York, to appear.
67. W. K. Liu, 'An introduction to wavelet reproducing kernel particle methods', USACM Bull., 8, 3-16 (1995).
68. Y. Krongauz and T. Belytschko, 'Enforcement of essential boundary conditions in meshless approximation using finite elements', Comput. Methods Appl. Mech. Eng., to appear.
69. I. Fried and A. R. Johnson, 'A note on elastic energy density function for largely deformed compressible ruber solids', Comput. Methods Appl. Mech. Engng., 69, 53-64 (1988).
70. W. J. Chung, J. W. Cho and T. Belytschko, 'A study on dynamic effects of dynamic explicit FEM in sheet metal forming analysis, Presented in NUMISHEET '96, Dearborn, MI, September 1996.
71. Lord, Rayleigh, 'On the pressure developed in a liquid during the collapse of a spherical cavity', Phil. Mag., 34, 94-98 (1917).
72. L. Trilling, 'The collapse and rebound of a gas bubble', J. Appl. Phys., 23, 14-17 (1952).
73. J. B. Keller and I.I. Kolodner, 'Damping of underwater explosion bubble oscillations', J. Appl. Phys., 27, 1152-1161 (1956).
74. J. G. Kirkwood and H. Bethe, OSRD Report No. 588, 1942.
75. H. G. Flynn, 'Physics of acoustic cavitation in liquids', in W. P. Mason, (ed.), Physical Acoustics Vol. 1, Part B, Academic Press, New York, 1964, pp. 58-172.
76. D. L. Frost, J. H. S. Lee and P. Thibault, 'Numerical computation of underwater explosions due to fuel-coolant interactions', Nucl. Engng. Des., 146, 167-179 (1994).
77. C. Y. Wang, 'ICECO-CEL: a coupled Eulerian-Lagrangian code for analyzing primary system response in fast reactors', ANL Report No. 81-9, 1981.
78. T. Belytschko, 'Fluid-structure interaction', Comput. Struct., 12, 459-469 (1980).
79. A. Benuzzi, 'Comparison of different LMFBR primary containment codes applied to a benchmark problem', Nucl. Engng. Des., 100, 239-249 (1987).
80. R. E. Tipton, D. J. Steinberg and Y. Tomita, 'Bubble expansion and collapse near a rigid wall, JSME Int. J., 35, 67-75 (1992).
81. C. D. Milligan and J. H. Duncan, 'A numerical method for prediction of bubble-structure interaction', Proc. 63rd Shock and Vibration Symposium, Las Cruces, NM, 1992.
82. J. E. Chisum and Y. S. Shin, 'Multimaterial Eulerian and coupled Lagrangian-Eulerian finite element analysis of underwater shock problems', NPS Report ME-95-001, 1995.