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An Amplification Factor to Enhance Stability for Structure-Dependent Integration Method

Published online by Cambridge University Press:  16 October 2012

S.-Y. Chang
S.-Y. Chang*
Affiliation:
Department of Civil Engineering, National Taipei University of Technology, Taipei, Taiwan 10608, R.O.C.
*
* Corresponding author ([email protected])
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Abstract

Chang explicit method (2007) has been shown to be unconditionally stable for a linear elastic system and any instantaneous stiffness softening system while it is only conditionally stable for any instantaneous stiffness hardening system. Its coefficients of the difference equation for displacement increment are functions of initial tangent stiffness. Since Chang explicit method is unconditionally stable for a linear elastic system and any instantaneous stiffness softening system, its stability range can be enlarged if the initial tangent stiffness is enlarged by an amplification factor and then this amplified initial tangent stiffness is used to determine the coefficients. The detailed implementation of this scheme for Chang explicit method is presented and the feasibility of this scheme is verified.

Keywords

Dynamic analysisTime integrationStabilityAccuracyStructure-dependent method
Type
Articles
Information
Journal of Mechanics , Volume 28 , Issue 4 , December 2012 , pp. 665 - 676
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2012

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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.Shing, P. B. and Mahin, S. A., “Elimination of Spurious Higher-Mode Response in Pseudo-Dynamic Tests,” Earthquake Engineering and Structural Dynamics, 15, pp. 425–445.CrossRefGoogle Scholar
3.Chang, S. Y. “Improved Numerical Dissipation for Explicit Methods in Pseudodynamic Tests,” Earthquake Engineering and Structural Dynamics, 26, pp. 917–929 (1997).3.0.CO;2-9>CrossRefGoogle Scholar
4.Chang, S. Y., “The γ-Function Pseudodynamic Algorithm,” Journal of Earthquake Engineering, 4, pp. 303–320 (2000).CrossRefGoogle Scholar
5.Houbolt, J. C., “A Recurrence Matrix Solution for the Dynamic Response of Elastic Aircraft,” Journal of the Aeronautical Sciences, 17, pp. 540–550 (1950).Google Scholar
6.Wilson, E. L., Farhoomand, I. and Bathe, K. J., “Nonlinear Dynamic Analysis of Complex Structures,” Earthquake Engineering and Structural Dynamics, 1, pp. 241–252 (1973).Google Scholar
7.Park, K. C., “An Improved Stiffly Stable Method for Direct Integration of Nonlinear Structural Dynamic Equations,” Journal of Applied Mechanics, 42, pp. 464–470 (1975).Google Scholar
8.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).CrossRefGoogle Scholar
9.Wood, W. L.Bossak, M. and Zienkiewicz, O. C., “An Alpha Modification of Newmark's Method,” International Journal for Numerical Methods in Engineering, 15, pp. 1562–1566 (1981).CrossRefGoogle Scholar
10.Chung, J. and Hulbert, G. M., “A Time Integration Algorithm for Structural Dynamics with Improved Numerical Dissipation: The Generalized-α Method,” Journal of Applied Mechanics, 60, pp. 371–375 (1993).CrossRefGoogle Scholar
11.Chang, S. Y., “A Series of Energy Conserving Algorithms for Structural Dynamics,” Journal of the Chinese Institute of Engineers, 19, pp. 219–230 (1996).Google Scholar
12.Chang, S. Y., “Improved Explicit Method for Structural Dynamics,” Journal of Engineering Mechanics, ASCE, 133, pp. 748–760 (2007).CrossRefGoogle Scholar
13.Belytschko, T. and Hughes, T. J. R., Computational Methods for Transient Analysis, Elsevier Science Publishers B. V., North-Holland (1983).Google Scholar
14.Hughes, T. J. R., The Finite Element Method, Prentice- Hall, Inc., Englewood Cliffs, N. J., U.S.A. (1987).Google Scholar
15.Zienkiewicz, O. C., The Finite Element Method, McGraw-Hill Book Co (UK) Ltd. Third Edition (1977).Google Scholar
16.Goudreau, G. L. and Taylor, R. L., “Evaluation of Numerical Integration Methods in Elasto- Dynamics,” Computer Methods in Applied Mechanics and Engineering, 2, pp. 69–97 (1972).CrossRefGoogle Scholar
17.Hilber, H. M. and Hughes, T. J. R., “Collocation, Dissipation, and ‘Overshoot’ for Time Integration Schemes in Structural Dynamics,” Earthquake Engineering and Structural Dynamics, 6, pp. 99–118 (1978).Google Scholar
18.Clough, R. W. and Penzien, J., Dynamics of structures, McGraw-Hill, Inc., International Editions (1993).Google Scholar
19.Bathe, K. J., “Finite Element Procedure in Engineering Analysis,” Prentice-Hall, Inc., Englewood Cliffs, N.J., U.S.A. (1996).Google Scholar
20.Chang, S. Y., “Accuracy of Time History Analysis of Impulses,” Journal of Structural Engineering, ASCE, 129, pp. 357–372 (2003).CrossRefGoogle Scholar
21.Chang, S. Y., “Accurate Representation of External Force in Time History Analysis,” Journal of Engineering Mechanics, ASCE, 132, pp. 34–45 (2006).CrossRefGoogle Scholar
22.Chang, S. Y., Hsu, C. W. and Chen, T. W., “Comparison of Capability of Time Integration Methods in Capturing Dynamic Loading,” Earthquake Engineering and Engineering Vibration, 9, pp. 409–423 (2010).Google Scholar
23.Krieg, R. D., “Unconditional Stability in Numerical Time Integration Methods,” Journal of Applied Mechanics, 40, pp. 417–421 (1973).CrossRefGoogle Scholar