Investigations of nonlinear performances of implicit pseudodynamic
algorithms
Shuenn-Yih Chang ()1 , Yu-Chun Huang (Sԣx)2 and
Yu-Chi Sung (ԣ)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− 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− 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− method
