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Investigations of nonlinear performances of implicit pseudodynamic algorithms

Shuenn-Yih Chang (張順益)1 , Yu-Chun Huang (黃裕鈞)2 and Yu-Chi Sung (宋裕祺)1

  1. Department of Civil Engineering, Taipei University of Technology, Chinese Taipei
  2. Department of Construction Management, Hwa Hsia Institute of Technology, Chinese Taipei

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.

Keywords: nonlinear analysis; nonlinearity; convergence; instability; pseudodynamic test; HHT−α method

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Copyright 2009 IEM. Journal of Earthquake Engineering and Engineering Vibration. All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as described below, without written permission from the Publisher. Copying of articles is not permitted except for personal and internal use, to the extent permitted by national copyright law, or under the terms of a license issued by the National Reproduction Rights Organization of China.