Error Propagation in Implicit Pseudodynamic Testing of Nonlinear Systems
Publication: Journal of Engineering Mechanics
Volume 131, Issue 12
Abstract
Error propagation analysis of an implicit pseudodynamic algorithm has been developed for linear elastic systems. However, these error propagation results might not be applicable to nonlinear systems. Since the pseudodynamic testing method aims at investigating the nonlinear behavior of a seismically loaded structure it is important to perform the error propagation analysis of the implicit pseudodynamic algorithm for nonlinear systems. A technique to conduct the nonlinear error propagation analysis of an implicit pseudodynamic algorithm is constructed and is illustrated by analyzing the constant average acceleration method. Theoretical results reveal that the numerical and error propagation properties for nonlinear systems are generally inherited from those of linear elastic systems although some properties are affected by the step degree of nonlinearity. It is verified that the most important property of unconditional stability is preserved for nonlinear systems for a complete pseudodynamic test procedure even if the convergence error is present. It is concluded that error propagation for the improved implementation is superior to that of the direct implementation and is consistent with that developed for linear elastic systems.
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Acknowledgment
The writer is grateful for the financial supported by the National Science Council, Taiwan, R.O.C., under Grant No. NSCTNSC-91-2218-E-027-010.
References
Belytschko, T., and Hughes, T. J. R. (1983). Computational methods for transient analysis, Elsevier Science Publishers B.V., North-Holland, Amsterdam, The Netherland.
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. (2003). “Nonlinear error propagation analysis for explicit pseudodynamic algorithm.” J. Eng. Mech., 129(8), 841–850.
Chang, S. Y., and Mahin, S. A. (1993). “Two new implicit algorithms of pseudodynamic test methods.” J. Chin. Inst. Eng., 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.
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.
Nakashima, M., Kaminosomo, T., and Ishida, M. (1990). “Integration techniques for substructure pseudodynamic Test.” Proc. 4th U.S. National Conf. on Earthquake Engineering, Vol. 2, 515–524.
Newmark, N. M. (1959). “A method of computation for structural dynamics.” J. Eng. Mech. Div., 85, 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. (1987). “Cumulative experimental errors in pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 15, 409–424.
Shing, P. B., and Mahin, S. A. (1990). “Experimental error effects in pseudodynamic testing.” J. Eng. Mech., 116(4), 805–821.
Shing, P. B., and Manivannan, T. (1990). “On the accuracy of an implicit algorithm for pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 19, 631–651.
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.
Takanashi, K., Udagawa, K., Seki, M., Okada, T., and Tanaka, H. (1975). “Nonlinear earthquake response analysis of structures by a computer-actuator on-line system.” Bulletin of Earthquake Resistant Structure Research Center, No. 8, Institute of Industrial Science, Univ. of Tokyo, Tokyo.
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 131 • Issue 12 • December 2005
Pages: 1257 - 1269
Copyright
© 2005 ASCE.
History
Received: Aug 9, 2004
Accepted: Feb 15, 2005
Published online: Dec 1, 2005
Published in print: Dec 2005
Notes
Note. Associate Editor: Eric N. Landis
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