| Investigations of nonlinear performances of implicit pseudodynamic algorithms |
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| 作者姓名： | 張順益 黃裕鈞 宋裕祺 |
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| 作者单位： | [1]Department of Civil Engineering, Taipei University of Technology, Chinese Taipei [2]Department of Construction Management, Hwa Hsia Institute of Technology, Chinese Taipei |
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| 基金项目： | Supported by： Science Council of Chinese Taipei Under Grant No. NSC-94-2211-E-027-011 |
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| 摘 要： | Although it has been shown that the implementation of the HHT-α method can result in improved error propagation properties in pseudodynamic testing if the equation of motion is used instead of the difference equation to evaluate the next step acceleration, this paper proves that this method might lead to instability when used to solve a nonlinear system. Its unconditional stability is verified only for linear elastic systems, while for nonlinear systems, instability occurs as the step degree of convergence is less than 1. It is worth noting that the step degree of convergence can frequently be less than 1 in pseudodynamic testing, since a convergent solution is achieved only when the step degree of convergence is close to 1 regardless of whether its value is greater or less than 1. Therefore, the application of this scheme to pseudodynamic testing should be prohibited, since the possibility of instability might incorrectly destroy a specimen. Consequently, the implementation of the HHT-α method by using the difference equation to determine the next step acceleration is recommended for use in pseudodynamic testing.
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| 关 键 词： | HHT-α method |
| 文章编号： | 1671-3664（2006）02-0257-10 |
| 收稿时间： | 2006-06-21 |
| 修稿时间： | 2006-08-20 |
Investigations of nonlinear performances of implicit pseudodynamic algorithms |
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| Shuenn-Yih Chang,Yu-Chun Huang,Yu-Chi Sung.Investigations of nonlinear performances of implicit pseudodynamic algorithms[J].Earthquake Engineering and Engineering Vibration,2006,5(2):257-266. |
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| Authors: | Shuenn-Yih Chang Yu-Chun Huang Yu-Chi Sung |
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| Institution: | 1. Department of Civil Engineering, Taipei University of Technology, Chinese Taipei
2. Department of Construction Management, Hwa Hsia Institute of Technology, Chinese Taipei |
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| Abstract: | Although it has been shown that the implementation of the HHT α method can result in improved error propagation properties in pseudodynamic testing if the equation of motion is used instead
of the difference equation to evaluate the next step acceleration, this paper proves that this method might lead to instability
when used to solve a nonlinear system. Its unconditional stability is verified only for linear elastic systems, while for
nonlinear systems, instability occurs as the step degree of convergence is less than 1. It is worth noting that the step degree
of convergence can frequently be less than 1 in pseudodynamic testing, since a convergent solution is achieved only when the
step degree of convergence is close to 1 regardless of whether its value is greater or less than 1. Therefore, the application
of this scheme to pseudodynamic testing should be prohibited, since the possibility of instability might incorrectly destroy
a specimen. Consequently, the implementation of the HHT α method by using the difference equation to determine the next step acceleration is recommended for use in pseudodynamic testing.
Supported by: Science Council of Chinese Taipei Under Grant No. NSC-94-2211-E-027-011 |
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| Keywords: | nonlinear analysis nonlinearity convergence instability pseudodynamic test |
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