A comprehensive unified set of single-step algorithms with controllable dissipation for dynamics part II. Algorithms and analysis

Computer Methods in Applied Mechanics and Engineering

Volumn 145, Issue 1-2, 1997, Pages 99-107

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

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; FINITE ELEMENT METHOD;

PARAMETRIZED TEMPORAL FINITE ELEMENTS; SINGLE STEP ALGORITHMS;

DYNAMICS;

EID: 0031166434     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(96)01190-5     Document Type: Article

References (24)

1. J.C. Houbolt, A recurrence matrix solution for the dynamic response of elastic aircraft, J. Aeronaut. Sci. 17 (1950) 540-550.
2. N.M. Newmark, A method of computation for structural dynamics, J. Engrg. Mech. Div. ASCE 85 (1959) EM3, 67-94.
3. J.H. Argyris, H. Dunne and T. Angelopoulos, Non-linear oscillations using the finite element technique, Comput. Methods Appl. Mech. Engrg. 2 (1973) 203-250.
4. E.L. Wilson, I. Farhoomand and K.J. Bathe, Non-linear dynamic analysis of complex structures, Earthq. Engrg. Struct. Dyn. 1 (1973) 241-252.
5. H.M. Hilber, T.J.R. Hughes and R.L. Taylor. Improved numerical dissipation for time integration algorithms in structural dynamics. Earthquake Engrg. Struct. Dyn. 5 (1977) 283-292.
6. W.L. Wood, M. Bossak and O.C. Zienkiewicz, An Alpha modification of Newmark's method, Int. J. Numer. Methods Engrg. 15 (1981) 1562-1566.
7. M.G. Katona and O.C. Zienkiewicz, A unified set of single-step algorithms, part 3: the beta-m method, a generalization of the Newmark scheme, Int. J. Numer. Methods Engrg. 21 (1985) 1345-1359.
8. 1 method and comparison with other dissipative algorithms in structural dynamics, Comput. Methods Appl. Mech. Engrg. 67 (1988) 87-110.
9. C. Hoff and P.J. Pahl, Development of an implicit method with numerical dissipation from a generalized single-step algorithm for structural dynamics, Comput. Methods Appl. Mech. Engrg. 67 (1988) 367-385.
10. J. Kujawaski and R.H. Gallagher, A generalised least-squares family of algorithms for transient dynamic analysis, Earthquake Engrg. Struct. Dyn. 18 (1989) 539-550.
11. K.K. Tamma and R.R. Namburu, A robust self-starting explicit computational methodology for structural dynamic applications: architecture and representations, Int. J. Numer. Methods Engrg. 29 (1990) 1441-1454.
12. T.J.R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1987).
13. E. Hairer, S.P. Norsett and G. Wanner, Solving Ordinary Differential Equations I (Springer, Berlin, 1987).
14. B. Owren and H.H. Simonson, Alternative integration methods for problems in structural dynamics, Comput. Methods Appl. Mech. Engrg. 122 (1995) 1-10.
15. J. Argyris and H.P. Mlejnek, Dynamics of Structures (North-Holland, 1991).
16. T.J.R. Hughes and G.M. Hulbert, Space-time finite element methods for elastodynamics: formulations and error estimates, Comput. Methods Appl. Mech. Engrg. 66 (1988) 339-363.
17. G.M. Hulbert, Time finite element methods for structural dynamics, Int. J. Numer. Methods Engrg. 33 (1990) 307-331.
18. G.M. Hulbert, A unified set of single-step asymptotic annihilation algorithms for structural dynamics, Comput. Methods Appl. Mech. Engrg. 113 (1994) 1-9.
19. D. Aharoni and P. Bar-Yoseph, Mixed finite element formulations in the time domain for solution of dynamic problems, Comput. Mech. 9 (1992) 359-374.
20. M. Borri and C. Bottasso, A general framework for interpreting time finite element formulations, Comput. Mech. 13 (1993) 33-142.
21. J.A. Stricklin and W.E. Haisler, Formulation and solution procedures for nonlinear structural analysis, Comput. Struct. 7 (1977) 125-136.
22. K.J. Bathe, Finite Element Procedures in Engineering Analysis (Prentice-Hall, Englewood Cliffs, NJ, 1982).
23. W. Ginsburg and L.C. Gellert, Numerical solution of static and dynamic nonlinear multi-degree of freedom systems, Comput. Methods Appl. Mech. Engrg. 23 (1980) 111-125.
24. M. Paz, Structural Dynamics Theory and Computation (Van Nostrand, Reinhold, 1991).