Explicit Pseudodynamic Algorithm with Unconditional Stability
Publication: Journal of Engineering Mechanics
Volume 128, Issue 9
Abstract
An unconditionally stable explicit pseudodynamic algorithm is proposed herein. This pseudodynamic algorithm can be implemented as simply as the very commonly used explicit pseudodynamic algorithms, such as the central difference method and the Newmark explicit method as reported in 1959. Thus, it can be used to perform pseudodynamic tests without using any iterative scheme or extra hardware that is generally needed by the currently available implicit pseudodynamic algorithms. This integration method is second-order accurate and the most promising property of this explicit pseudodynamic algorithm is its unconditional stability. In addition, it possesses much better error propagation properties when compared to the Newmark explicit method and the central difference method.
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References
Bathe, K. J., and Wilson, E. L.(1973). “Stability and accuracy analysis of direct integration methods.” Earthquake Eng. Struct. Dyn., 1, 283–291.
Belytschko, T., and Hughes, T. J. R. (1983). Computational methods for transient analysis, Elsevier Science, North-Holland, Amsterdam.
Chang, S. Y. (1996). “The smoothing effect in structural dynamics and pseudodynamic tests.” Rep. No. NCREE-96-008, National Center for Research on Earthquake Engineering, National Taiwan Univ., Taipei, Taiwan, Republic of China.
Chang, S. Y.(1997). “Improved numerical dissipation for explicit methods in pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 26, 917–929.
Chang, S. Y. (1999). “An unconditionally stable explicit algorithm in time history analysis.” Rep. No. NCREE-99-001, National Center for Research on Earthquake Engineering, National Taiwan Univ., Taipei, Taiwan, Republic of China.
Chang, S. Y.(2000). “The γ-function pseudodynamic algorithm.” J. Earthquake Eng., 4(3), 303–320.
Chang, S. Y.(2001). “Application of the momentum equations of motion to pseudodynamic testing.” Philos. Trans. R. Soc. London, Ser. A, 359(1786), 1801–1827.
Chang, S. Y., and Mahin, S. A. (1992). “Two new implicit algorithms of pseudodynamic test methods.” MEng thesis, Univ. of California, Berkeley, Calif.
Chang, S. Y., Tsai, K. C., and Chen, K. C.(1998). “Improved time integration for pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 27, 711–730.
Clough, R. W., and Penzien, J. (1993). Dynamics of structures, McGraw-Hill, International Editions, New York.
Goudreau, G. L., and Taylor, R. L.(1972). “Evaluation of numerical integration methods in elasto-dynamics.” Comput. Methods Appl. Mech. Eng., 2, 69–97.
Hilber, H. M., and Hughes, T. J. R.(1978). “Collocation, dissipation, and ‘overshoot’ for time integration schemes in structural dynamics.” Earthquake Eng. Struct. Dyn., 6, 99–118.
Hilber, H. M., Hughes, T. J. R., and Taylor, R. L.(1977). “Improved numerical dissipation for time integration algorithms in structural dynamics.” Earthquake Eng. Struct. Dyn., 5, 283–292.
Houbolt, J. C.(1950). “A recurrence matrix solution for the dynamic response of elastic aircraft.” J. Aeronaut. Sci., 17, 540–550.
Hughes, T. J. R., Pister, K. S., and Taylor, R. L.(1979). “Implicit-explicit finite elements in nonlinear transient analysis.” Comput. Methods Appl. Mech. Eng., 17(18), 159–182.
Nakashima, M., Kaminosomo, T., and Ishida, M.(1990). “Integration techniques for substructure pseudodynamic test.” Proc., 4th U.S. National Conf. on Earthquake Engineering, 2, 515–524.
Newmark, N. M.(1959). “A method of computation for structural dynamics.” J. Eng. Mech. Div., Am. Soc. Civ. Eng., 67–94.
Park, K. C.(1975). “An improved stiffly stable method for direct inte-gration of nonlinear structural dynamic equations.” J. Appl. Mech., 42, 464–470.
Shing, P. B., and Mahin, S. A.(1987a). “Cumulative experimental errors in pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 15, 409–424.
Shing, P. B., and Mahin, S. A.(1987b). “Elimination of spurious higher-mode response in pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 15, 425–445.
Shing, P. B., and Mahin, S. A.(1990). “Experimental error effects in pseudodynamic testing.” J. Eng. Mech., 116(4), 805–821.
Shing, P. B., Vannan, M. T., and Carter, E.(1991). “Implicit time integration for pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 20, 551–576.
Strang, G. (1986). Linear algebra and its applications, Harcourt Brace Jovanovich, San Diego.
Thewalt, C. R., and Mahin, S. A.(1995). “An unconditionally stable hybrid pseudodynamic algorithm.” Earthquake Eng. Struct. Dyn., 24, 723–731.
Wood, W. L., Bossak, M., and Zienkiewicz, O. C.(1981). “An alpha modification of Newmark’s method.” Int. J. Numer. Methods Eng., 15, 1562–1566.
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Copyright © 2002 American Society of Civil Engineers.
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Received: Apr 25, 2001
Published online: Aug 15, 2002
Published in print: Sep 2002
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