Stability of an explicit multi-time step integration algorithm for linear structural dynamics equations

Computational Mechanics

Volumn 18, Issue 3, 1996, Pages 236-244

  Smolinski, P ^a   Sleith, S ^a   Belytschko, T ^b  

^a University of Pittsburgh   (United States)

^b Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; INTEGRATION; STABILITY;

AMPLIFICATION MATRICES; EXPLICIT MULTISTEP INTEGRATION METHOD;

ALGORITHMS;

EID: 0030192828     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00369941     Document Type: Article

References (17)

1. Belytschko, T.; Gilbertsen, N. D. 1992: Implementation of Mixed Time Integration Techniques on a Vectorized Computer with Shared Memory. Int. J. Numer. Meth. Engrg. 35: 1803-1828
2. Belytschko, T.; Hughes, T. J. R. 1983: Computational Methods for Transient Analysis. North Holland, Amsterdam
3. Belytschko, T.; Lu, Y. Y. 1992: Stability analysis of elemental explicit-implicit partitions by Fourier methods, Comp. Meth. Appl. Mech. Engrg. 95: 87-96
4. Belytschko, T.; Mullen, R. 1977: Explicit integration of structural problems, In: Finite Elements in Nonlinear Mechanics, P. Bergen, et al. Eds Vol. 2, pp. 697-720
5. Belytschko, T.; Mullen, R. 1978: Stability of explicit-implicit mesh partitions in time integration, Int. J. Num. Meth. Engrg., 12: -1575-1586
6. Belytschko, T.; Smolinski, P.; Liu, W. K. 1985: Stability of multi-time partitioned integrators for first-order systems, Comp. Meth. Appl. Mech. Engrg. 49(3): 281-297
7. Belytschko, T.; Yen, H.-J.; Mullen, R. 1979: Mixed methods for time integration, Comp. Meth. Appl. Mech. Engrg. 17/18: 259-275
8. Donea, J.; Laval, H. 1988: Nodal partition of explicit finite element methods for unsteady diffusion problems, Comp. Meth. Appl. Mech. Engrg. 68: 189-204
9. Flanagan, D.; Belytschko, T. 1981: Simultaneous relaxation in structural dynamics, ASCE J. Engrg. Mech. Div. 107: 1039-1055
10. Hughes, T. J. R.; Liu, W. K. 1978: Implicit-explicit finite elements in transient analysis: stability theory, J. Appl. Mech. 45: 371-374
11. Irons, B. M. 1970: Applications of a theorem on eigenvalues to finite element problems (CR/132/70), University of Wales, Department of Civil Engineering, Swansea
12. Mizukami, A. 1986: Variable explicit finite element methods for unsteady heat conduction, Comp. Meth. Appl. Mech. Engrg. 59. 101-109
13. Neal, M. O.; Belytschko, T. 1989: Explicit-explicit subcycling with non-integer time step ratios for structural dynamics systems, Comp. Struct. 31 (6): 871-880
14. Park, K. C. 1980: Partitioned transient analysis procedure for coupled field problems: stability analysis, J. Appl. Mech. 47: 370-376
15. Smolinski, P. 1991: Stability of variable explicit time integration for unsteady diffusion problems, Comp. Meth. Appl. Mech. Engrg. 93: 247-252
16. Smolinski, P. 1992: Stability analysis of a multi-time step explicit integration method, Comp. Meth. Appl. Mech. Engrg. 95: 291-300
17. Smolinski, P.; Belytschko, T.; Neal, M. O. 1988: Multi-time step integration using nodal partitioning, Int. J. Numer. Meth. Engrg. 26: 349-359