Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-05T23:26:51.892Z Has data issue: false hasContentIssue false
  • English
  • Français

Discretization of Dynamic Loading in Time History Analysis

Published online by Cambridge University Press:  14 November 2013

S.-Y. Chang
S.-Y. Chang*
Affiliation:
Department of Civil Engineering, National Taipei University of Technology, Taipei, Taiwan 10608, R.O.C.
*
[email protected]
Get access

Abstract

Although the numerical properties of a step-by-step integration method can be evaluated based on the currently available techniques, there is still lack of a technique for evaluating its capability to capture dynamic loading. In this work, the amplitude error caused by the step discretization error is identified and the correlation between the relative amplitude error and relative step discretization error is analytically established. As a result, it is thoroughly confirmed that the asymptotic constant of the discretization error amplification factor for the displacement response to a cosine loading can be considered as an indicator of the capability to capture dynamic loading for a general step-by-step integration method.

Keywords

Equations of motionDynamic loadsDynamic analysisSolutionsAccuracy
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 1 , February 2014 , pp. 57 - 65
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Newmark, N. M., “A Method of Computation for Structural Dynamics,” Journal of Engineering Mechanics Division, ASCE, 85, pp. 67–94 (1959).CrossRefGoogle Scholar
2.Hilber, H. M., Hughes, T. J. R. and Taylor, R. L., “Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics,” Earthquake Engineering and Structural Dynamics, 5, pp. 283–292 (1977).Google Scholar
3.Chang, S. Y., “Improved Explicit Method for Structural Dynamics,” Journal of Engineering Mechanics, ASCE, 133, pp. 748–760 (2007).Google Scholar
4.Chang, S. Y., “An Explicit Method with Improved Stability Property,” International Journal for Numerical Method in Engineering, 77, pp. 1100–1120 (2009).CrossRefGoogle Scholar
5.Chang, S. Y., “A New Family of Explicit Method for Structural Dynamics,” Computers & Structures, 88, pp. 755–772 (2010).Google Scholar
6.Belytschko, T. and Hughes, T. J. R., Computational Methods for Transient Analysis, Elsevier Science Publishers B.V., North-Holland (1983).Google Scholar
7.Chang, S. Y., “Accuracy of Time History Analysis of Impulses,” Journal of Structural Engineering, ASCE, 129, pp. 357–372 (2003).Google Scholar
8.Chopra, A. N., Dynamics of Structures, Prentice Hall, Inc., International Editions (1997).Google Scholar
9.Bathe, K. J., Finite Element Procedures, Prentice Hall, Inc., International Editions (1996).Google Scholar
10.Strang, G., Linear Algebra and its Applications, Harcourt Brace Jovanovich, San Diego (1986).Google Scholar