Overcoming Load Discontinuity in Step-by-Step Solution of Shock Response
Publication: Journal of Engineering Mechanics
Volume 135, Issue 7
Abstract
A scheme is proposed to overcome the discontinuity at the end of an impulse. This scheme is very simple in the step-by-step solution of shock response. The only change is the loading input at the time instant of load discontinuity in performing the step-by-step integration. The average value of the two discontinuity values at the integration point of load discontinuity is used to replace the use of one of them for loading input. The motivation of this change originates from the concept of no loading input error associated with the integration point of load discontinuity. The feasibility of this scheme is analytically explored. Analytical results reveal that this change in loading input will lead to no extra impulse and thus no extra displacement. Consequently, an accurate shock response can be computationally efficiently obtained. Two numerical examples are also used to confirm the analytical results. The scheme proposed will not increase any computational effort or complicate the dynamic analysis codes.
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Acknowledgments
The writer gratefully acknowledges financial support for this study provided by the National Science Council, Taiwan, R.O.C., under Grant No. NSCTNSC-96-2221-E-027-030.
References
Chang, S. Y. (2001a). “Analytical study of the superiority of the momentum equations of motion for impulsive loads.” Comput. Struct., 79(15), 1377–1394.
Chang, S. Y. (2001b). “Application of the momentum equations of motion to pseudodynamic testing.” Philos. Trans. R. Soc. London, Ser. A, 359(1786), 1801–1827.
Chang, S. Y. (2003). “Accuracy of time history analysis of impulses.” J. Struct. Eng., 129(3), 357–372.
Chang, S. Y. (2006). “Accurate representation of external force in time history analysis.” J. Eng. Mech., 131(12), 1257–1269.
Chang, S. Y. (2007a). “Approach for overcoming numerical inaccuracy caused by load discontinuity.” J. Eng. Mech., 133(5), 555–565.
Chang, S. Y. (2007b). “Improved explicit method for structural dynamics.” J. Eng. Mech., 133(7), 748–760.
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.
Newmark, N. M. (1959). “A method of computation for structural dynamics.” J. Engrg. Mech. Div., 85, 67–94.
Tamma, K. K., Zhou, X., and Sha, D. (2001). “A theory of development and design of generalized integration operators for computational structural dynamics.” Int. J. Numer. Methods Eng., 50, 1619–1664.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 135 • Issue 7 • July 2009
Pages: 733 - 737
Copyright
© 2009 ASCE.
History
Received: Feb 28, 2007
Accepted: Oct 6, 2008
Published online: Jun 15, 2009
Published in print: Jul 2009
Notes
Note. Associate Editor: Arif Masud
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