Time discretized operators. Part 1: Towards the theoretical design of a new generation of a generalized family of unconditionally stable implicit and explicit representations of arbitrary order for computational dynamics

Computer Methods in Applied Mechanics and Engineering

Volumn 192, Issue 3-4, 2003, Pages 257-290

  Tamma, K K ^a   Sha, D ^a   Zhou, X ^a  

^a University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL METHODS; NUMERICAL METHODS;

TIME DISCRETIZED OPERATORS;

MATHEMATICAL OPERATORS;

ALGORITHM; COMPUTATIONAL MODEL; DYNAMICS;

EID: 0037449579     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0045-7825(02)00515-7     Document Type: Article

References (43)

1. G. Dahlquist, A special stability problem for linear multistep methods, BIT 3 (1963) 27.
2. K.K. Tamma, X. Zhou, D. Sha, The time dimension: a theory of development/ evolution classification characterization and design of computational algorithms for transient/dynamic applications, Archives in Computational Mechanics 7 (2) (2000) 67-290.
3. K.K. Tamma, X. Zhou, D. Sha, A theory of development and design of generalized integration operators for computational structural dynamics, International Journal for Numerical Methods in Engineering 50 (2001) 1619-1664.
4. X. Zhou, K.K. Tamma, A uni.ed theory underlying computational algorithms for linear .rst-order systems, International Journal for Numerical Methods in Engineering, to appear.
5. X. Zhou, K.K. Tamma, Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics, International Journal for Numerical Methods in Engineering, to appear.
6. K.K. Tamma, X. Zhou, R. Valasutean, Computational algorithms for transient analysis:is: The burden of weight and consequences towards formalizing discrete numerically assigned DNA algorithmic markers: Wp-family,, Computer Methods in Applied Mechanics and Engineering 149 (1997) 153.
7. J.C. Simo, K.K. Wong, Unconditional stable algorithm for rigid body dynamics that exactly preserve energy and momentum, International Journal for Numerical Methods in Engineering 31 (1991) 19.
8. J.C. Simo, N. Tarnow, K.K. Wang, Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics, Computer Methods in Applied Mechanics and Engineering 100 (1992) 63.
9. J.C. Houbolt, A recurrence matrix solution for the dynamic response of elastic aircraft, Journal of Aerosol Science 17 (1950) 540.
10. E.L. Wilson, A Computer Program for Dynamic Stress Analysis of Underground Structures, SESM Univ. California, Berkeley, 1968.
11. K.C. Park, An improved sti.y stable method for direct integration of nonlinear structural dynamic equations, Transactions of the American Society of Mechanical Engineers 1 (1975) 464.
12. H.M. Hilber, T.J.R. Hughes, R.L. Taylor, Improved numerical dissipation for time integration algorithms in structural dynamics, Earthquake Engineering and Structural Dynamics 5 (1977) 283.
13. W.L. Wood, M. Bossak, O.C. Zienkiewicz, An alpha modification of Newmark's method, International Journal for Numerical Methods in Engineering 15 (1980) 1562.
14. O.C. Zienkiewicz, W.L. Wood, N.W. Hine, R.L. Taylor, A unified set of single-step algorithms, Part 1: General formulations and applications, International Journal for Numerical Methods in Engineering 20 (1984) 1529.
15. J. Chung, G. Hulbert, A time integration method for structural dynamics with improved numerical dissipation: The generalized a-method, Journal of Applied Mechanics 30 (371) (1993).
16. G.L. Goudreau, R.L. Taylor, Evaluation of numerical methods in elastodynamics, Journal of Computer Methods in Applied Mechanics and Engineering 2 (1973) 69.
17. J.H. Argyris, P.C. Dunne, T. Angelopoulos, Nonlinear oscillations using the finite element technique, Computer Methods in Applied Mechanics and Engineering 2 (1973) 203.
18. R.D. Krieg, S.W. Key, Transient shell responses by numerical time integration, International Journal for Numerical Methods in Engineering 17 (1973) 273-286.
19. C. Ho., P.J. Pahl, Development of an implicit method with numerical dissipation from a generalized single step algorithm for structural dynamics, Computer Methods in Applied Mechanics and Engineering 67 (1988) 367.
20. X. Zhou, K.K. Tamma, R. Kanapady, D. Sha. The time dimension: new and recent advances and a uni.ed framework towards design of time discretized operators for structural dynamics, in: European Congress on Computational Methods in Applied Science and Engineering (ECCOMAS) 2000, Barcelona, Spain, 11-14 September 2000.
21. N.M. Newmark, A method of computation for structural dynamics, Journal American Society of Civil Engineers 1 (1959) 67.
22. T. Belytschko, T.J.R. Hughes, Computational Methods in Transient Analysis, North Holland, 1983.
23. C.C. Fu, A method for the numerical integration of equations of motion arising from a finite element analysis, Journal of Applied Mechanics 39 (1970) 559.
24. G.D. Hahn, A modi.ed Euler method for dynamic analysis, International Journal for Numerical Methods in Engineering 32 (1991) 943.
25. O.C. Zienkiewicz, R.L. Taylor, in: The Finite Element Method, vol. 1, McGraw-Hill, New York, 1994.
26. W.L. Wood, Practical Time Stepping Schemes, Clarendon Press, Oxford, 1990.
27. K.K. Tamma, R.R. Namburu, A new .nite element based Lax-Wendro./ Taylor-Galerkin methodology for computational dynamics, Computer Methods in Applied Mechanics and Engineering 71 (1988) 137.
28. K.K. Tamma, R.R. Namburu, Explicit second-order accurate Taylor-Galerkin based finite element formulation for linear/nonlinear transient heat transfer, Numerical Heat Transfer 13 (1988) 409.
29. M. Li, K.K. Tamma, R.R. Namburu, Evaluation and applicability of explicit self-starting formulations for nonlinear structural dynamics, AIAA SDM Conference, San Diego, CA, April, 1991.
30. I. Miranda, R.M. Hulbert, T.J.R. Hughes, An improved implicit-explicit time integration method for structural dynamics, Earthquake Engineering and Structural Dynamics 18 (1989) 643.
31. G.M. Hulbert, J. Chung, Explicit time integration algorithms for structural dynamics with optimal numerical dissipation, Computer Methods in Applied Mechanics and Engineering 137 (1996) 175.
32. D.M. Trujillo, An unconditionally stable explicit algorithm for structural dynamics, International Journal for Numerical Methods in Engineering 11 (1977) 1579.
33. T.C. Fung, Third-order time-step integration methods with controllable numerical dissipation, Communications in Numerical Methods in Engineering 13 (1997) 307.
34. J. Kujawski, R.H. Gallagher, A family of higher-order explicit algorithms for the transient dynamic analysis, Transactions of the Society for Computer Simulation 1 (1984) 155.
35. C. Ho., R.L. Taylor, Higher derivative explicit one step methods for non-linear dynamic problems. Part I: Design and theory, International Journal for Numerical Methods in Engineering 29 (1990) 275.
36. C. Ho., R.L. Taylor, Higher derivative explicit one step methods for non-linear dynamic problems. Part II: Practical calculations and comparisons with other higher methods, International Journal for Numerical Methods in Engineering 29 (1990) 291.
37. K.K. Tamma, D. Sha, X. Zhou. Energy-conserving/L-stablenth-order integration operators E/LNInO for computational dynamics, in: Proceedings of the World Congress in Computational Mechanics, IV, Buenos Aires, Argentina, June-July 1998.
38. X. Chen, K.K. Tamma, D. Sha, On coupled vibrations of thin-walled beam structures employing the virtual-pulse time integral methodology, in: Proceedings of the 1992 International Conference on Agricultural Engineering, Beijing, China, October 1992.
39. X. Chen, K.K. Tamma, D. Sha, Applicability/evaluation of the virtual-pulse time integral methodology for linear transient structural problems, in: Proceedings of the Second US Congress on Computational Mechanics, Washington DC, August 1993.
40. X. Chen, K.K. Tamma, D. Sha, Virtual-pulse time integral methodology: a new approach for computational dynamics. Part 2: Theory for nonlinear structural dynamics, Finite Elements in Analysis and Design 20 (1995) 195.
41. D. Sha, X. Chen, K.K. Tamma, A new virtual-pulse time integral methodology: a new approach for computational dynamics, Finite Elements in Analysis and Design, also see Erratum (l996) Parts 1 and 2 20 and 22 (1995) 179.
42. K.K. Tamma, X. Chen, D. Sha, An overview of recent advances and evaluation of the virtual-pulse (VIP) time integral methodology for general structural dynamics problems: computational issues and implementation aspects, International Journal for Numerical Methods in Engineering 39 (1996) 1955.
43. X. Zhou, D. Sha, K.K. Tamma, A novel nonlinearly explicit second-order accurate L-stable methodology for .nite deformation hypoelastic/ hypoelasto-plastic structural dynamics problems with total/updated lagrangian formulations. International Journal for Numerical Methods in Engineering, submitted for publication.