Enhanced, Unconditionally Stable, Explicit Pseudodynamic Algorithm
Publication: Journal of Engineering Mechanics
Volume 133, Issue 5
Abstract
In performing a pseudodynamic test, an explicit method is generally preferred over an implicit method since it involves no iteration procedure or extra hardware that is often needed for an implicit method. However, its integration time step is usually limited by stability. Hence, it is very promising for the pseudodynamic testing if an explicit method can have unconditional stability, which might eliminate the limitation on time step for the testing of a multiple degree of freedom system or a substructure system. Although an explicit pseudodynamic algorithm with unconditional stability has been successfully implemented and its superior characteristics have been identified, an enhanced unconditionally stable explicit pseudodynamic algorithm is further proposed. In this study, it is verified that both explicit pseudodynamic algorithms possess the same numerical characteristics in the step-by-step integration. However, the newly developed explicit pseudodynamic algorithm shows better error propagation properties when compared to that developed previously.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writer is grateful to acknowledge that this study was financially supported by the National Science Council, Taiwan, R.O.C., under Grant No. NSC-91-2218-E-027-010. All the experimental works were performed at the National Center for Research on Earthquake Engineering (NCREE), and the writer is very grateful to acknowledge technical support from the NCREE’s staff, especially K. J. Wang, C. H. Chou, and C. P. Cheng.
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, New York.
Chang, S. Y. (1997). “Improved numerical dissipation for explicit methods in pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 26, 917–929.
Chang, S. Y. (2000). “The –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. (2002). “Explicit pseudodynamic algorithm with unconditional stability.” J. Eng. Mech., 128(9), 935–947.
Chang, S. Y., and Liao, W. I. (2005). “An unconditionally stable explicit method for structural dynamics.” J. Earthquake Eng., 9(3), 349–370.
Chang, S. Y., and Mahin, S. A. (1993). “Two new implicit algorithms of pseudodynamic test methods.” J. Chinese Institute of Engineers, 16(5), 651–664.
Chang, S. Y., Tsai, K. C., and Chen, K. C. (1998). “Improved time integration for pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 27, 711–730.
Goudreau, G. L., and Taylor, R. L. (1972). “Evaluation of numerical integration methods in elastodynamics.” 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.
Meirovitch, L. (1986). Elements of vibration analysis, McGraw-Hill, New York.
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. Engrg. Mech. Div., 85(EM3), 67–94.
Peek, R., and Yi, W. H. (1990a). “Error analysis for pseudodynamic test method. I: Analysis.” J. Eng. Mech., 116(7), 1618–1637.
Peek, R., and Yi, W. H. (1990b). “Error analysis for pseudodynamic test method. II: Application.” J. Eng. Mech., 116(7), 1638–1658.
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. (2006). Linear algebra and its applications, 4th Ed., Thomson, Brooks/Cole, Belmont, Calif.
Thewalt, C. R., and Mahin, S. A. (1995). “An unconditionally stable hybrid pseudodynamic algorithm.” Earthquake Eng. Struct. Dyn., 24, 723–731.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 5 • May 2007
Pages: 541 - 554
Copyright
© 2007 ASCE.
History
Received: Apr 26, 2005
Accepted: Sep 13, 2006
Published online: May 1, 2007
Published in print: May 2007
Notes
Note. Associate Editor: Henri P. Gavin
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.