Approach for Overcoming Numerical Inaccuracy Caused by Load Discontinuity
Publication: Journal of Engineering Mechanics
Volume 133, Issue 5
Abstract
It was found that the discontinuity at the end of an impulse will lead to numerical inaccuracy as this discontinuity will result in an extra impulse and thus an extra displacement in the time history analysis. In addition, this extra impulse is proportional to the discontinuity value at the end of the impulse and the size of integration time step. To overcome this difficulty, an effective approach is proposed to reduce the extra impulse and hence the extra displacement. In fact, the novel approach proposed in this paper is to perform a single small time step immediately upon the termination of applied impulse, whereas other time steps can be conducted by using the step size determined from accuracy consideration in period. The feasibility of this approach is analytically explored. Further, analytical results are confirmed by numerical examples. Numerical studies also show that this approach can be applied to other step-by-step integration methods. It seems that to slightly complicate the programming of dynamic analysis codes is the only disadvantage of this approach.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The writer gratefully acknowledges the financial support for this study provided by the National Science Council, Taiwan, R.O.C., under Grant No. UNSPECIFIEDNSC-93-2211-E-027-012.
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 Publishers B.V., Amsterdam, The Netherlands.
Bochev, P. B., Gunzburger, M. D., and Shadid, J. N. (2003). “On inf-sup stabilized finite element methods for transit problems.” Comput. Methods Appl. Mech. Eng., 193(15–16), 1471–1489.
Bradford, S. F., and Katopodes, N. D. (2000). “The anti-dissipative, non-monotone behavior of Petrov-Galerkin upwinding.” Int. J. Numer. Methods Fluids, 33(4), 583–608.
Chang, S. Y. (1994). “Improved dynamic structural analysis for linear and nonlinear systems.” Ph.D. thesis, Univ. of Illinois, Urbana-Champaign, Ill.
Chang, S. Y. (1996). “A series of energy conserving algorithms for structural dynamics.” J. Chin. Inst. Eng., 19(2), 219–230.
Chang, S. Y. (1997). “Improved numerical dissipation for explicit methods in pseudodynamic tests.” Earthquake Eng. Struct. Dyn., 26, 917–929.
Chang, S. Y. (2002). “Explicit pseudodynamic algorithm with unconditional stability.” J. Eng. Mech., 128(9), 935–947.
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., 132(1), 34–45.
Chopra, A. N. (1997). Dynamics of structures, International Ed., Prentice-Hall, Englewood Cliffs, N.J.
Clough, R. W., and Penzien, J. (1993). Dynamics of structures, International Ed., McGraw-Hill, New York.
Harari, I. (2003). “Stability of semidiscrete formulations for parabolic problems at small time steps.” Comput. Methods Appl. Mech. Eng., 193(15–16), 1491–1516.
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. (1987). The finite element method, Prentice-Hall, Englewood Cliffs, N.J.
Newmark, N. M. (1959). “A method of computation for structural dynamics.” J. Engrg. Mech. Div., 85, 67–94.
Park, K. C. (1975). “An improved stiffly stable method for direct integration of nonlinear structural dynamic equations.” J. Appl. Mech., 42, 464–470.
Strang, G. (1986). Linear algebra and its applications, Harcourt Brace Jovanovich, San Diego.
Wilson, E. L. (1968). “A computer program for the dynamic stress analysis of underground structures.” SESM Rep. No. 68-1, Division Structural Engineering and Structural Mechanics, Univ. of California, Berkeley, Calif.
Wilson, E. L., Farhoomand, I., and Bathe, K. J. (1973). “Nonlinear dynamic analysis of complex structures.” Earthquake Eng. Struct. Dyn., 1, 241–252.
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.
Zienkiewicz, O. C. (1977). The finite element method, 3rd Ed., McGraw-Hill, London.
Information & Authors
Information
Published In
Copyright
© 2007 ASCE.
History
Received: Sep 20, 2005
Accepted: Oct 3, 2006
Published online: May 1, 2007
Published in print: May 2007
Notes
Note. Associate Editor: Arif Masud
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.