Extrapolated Galerkin time finite elements

Computational Mechanics

Volumn 17, Issue 6, 1996, Pages 398-405

  Fung, T C ^a   Fan, S C ^a   Sheng, G ^a  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; DYNAMICS; EQUATIONS OF MOTION; INTEGRATION; MATRIX ALGEBRA; STATE SPACE METHODS;

EXTRAPOLATION TECHNIQUE; GALERKIN METHOD; NUMERICAL AMPLIFICATION MATRIX; NUMERICAL DISPERSION; NUMERICAL DISSIPATION; TIME INTEGRATION METHOD; WEIGHTING FACTORS;

FINITE ELEMENT METHOD;

EID: 0030126671     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00363983     Document Type: Article

References (24)

1. Argyris, J. H.; Dunne, T.; Angelopoulos, 1973: Non-linear oscillations using the finite element technique. Comp. Methods Appl. Mech. Eng. 2: 203-250
2. Austin, M. 1993: High-order integration of smooth dynamical system: theory and numerical experiments. Int. J. Numer. Method. Eng. 36: 2107-2122
3. Bathe, K. J.; Wilson, E. L. 1976: Numerical Methods in Finite Element Analysis. Prentice-Hall, Englewood Cliffs
4. Bathe, K. J.; 1982: Finite Element Procedures in Engineering Analysis. Prentice-Hall, Englewood Cliffs
5. Bismarck-Nasr, M. N.; Oliveria, A. M. 1991: On enhancement of accuracy in direct integration dynamic response problems. Earthquake Eng. Struct. Dyn. 20: 699-703
6. Blum, H.; Lin, Q. 1987: Asymptotic error expansion and Richardson extrapolation for linear finite elements. Numer. Math. 49: 11-37
7. Davis, P. J.; Rabinowitz, P.; 1984: Methods of Numerical Integration. Academic Press
8. Fatunla, S. O. 1988: Numerical Methods for initial value problems in ordinary differential equations. Academic Press
9. Hilber, H. M.; Hughes, T. J. R; Taylor, R. L. 1977: Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Eng. Struct. Dyn. 5: 283-292
10. 1 method and comparison with other dissipative algorithms in structural dynamics. Comput. Methods Appl. Mech. Eng. 67: 87-110
11. Hoff, C.; Pahl, P. J. 1988: Development of an implicit method with numerical dissipation from a generalized single-step algorithm for structural dynamics. Comput. Meth. Appl. Mech. Eng. 67: 367-385
12. Houbolt, J. C. 1950: A recurrence matrix solution for the dynamic response of elastic aircraft. J. Aeronaut. Sci. 17: 540-550
13. Hughes, T. J. R. 1987: The Finite Element Method: linear static and dynamic finite element analysis. Prentice-Hall, Englewood Cliffs
14. Hulbert, G. M.; Hughes, T. J. R. 1987: An error analysis of truncated starting conditions in step-by-step time integration: consequences for structural dynamics. Earthquake Eng. Struct. Dyn. 15: 901-910
15. Katona, M. G.; Zienkiewicz, O. C. 1985: A unified set of single-step algorithms, part 3: the beta-m method, a generalization of the Newmark scheme. Int. J. Numer. Methods Eng. 21: 1345-1359
16. Kujawaski, J.; Gallagher, R. H. 1989: A generalised least-squares family of algorithms for transient dynamic analysis. Earthquake Eng. Struct. Dyn. 18: 539-550
17. Marchuk, G. I.; Shaiduvov, V. V. 1983: Difference Methods and Their Extrapolations. Springer-Verlag
18. Newmark, N. M. 1959: A method of computation for structural dynamics. J. Eng. Mech. Div. ASCE 85, EM 3, 67-94
19. Paz, M. 1991: Structural Dynamics Theory and Computation. Van Nostrand Reinhold.
20. Rao, S. S. 1986: Mechanical Vibrations. Addison-Wesley, Reading.
21. Tamma, K. K.; Namburu, R. R. 1990: A robust self-starting explicit computational methodology for structural dynamic applications: architecture and representations. Int. J. Numer. Methods Eng. 29: 1441-1454
22. Wilson, E. L.; Farhoomand, I.; Bathe, K. J. 1973: Non-linear dynamic analysis of complex structures. Earthq. Engng. Struct. Dyn. 1: 241-252
23. Wood, W. L.; Bossak, M.; Zienkiewicz, O. C. 1981: An Alpha modification of Newmark's method. Int. J. Numer. Methods Eng. 15: 1562-1566
24. Zienkiewicz, O. C.; Taylor, R. L. 1991: The Finite Element Method. McGraw-Hill. Vol. II