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Extensions of nonlinear error
propagation analysis
for explicit pseudodynamic testing
Shuenn-Yih Chang
Department of Civil Engineering,Taipei University of Technology, NTUT
Box 2653, Chinese Taipei 106-08
Abstract: Two important extensions of a technique to perform a
nonlinear error propagation analysis for an explicit pseudodynamic
algorithm (Chang, 2003) are presented. One extends the stability study
from a given time step to a complete step-by-step integration procedure.
It is analytically proven that ensuring stability conditions in each
time step leads to a stable computation of the entire step-by-step
integration procedure. The other extension shows that the nonlinear
error propagation results, which are derived for a nonlinear single
degree of freedom (SDOF) system, can be applied to a nonlinear multiple
degree of freedom (MDOF) system. This application is dependent upon the
determination of the natural frequencies of the system in each time
step, since all the numerical properties and error propagation
properties in the time step are closely related to these frequencies.
The results are derived from the step degree of nonlinearity. An
instantaneous degree of nonlinearity is introduced to replace the step
degree of nonlinearity and is shown to be easier to use in practice. The
extensions can be also applied to the results derived from a SDOF system
based on the instantaneous degree of nonlinearity, and hence a time step
might be appropriately chosen to perform a pseudodynamic test prior to
testing.
Keywords: nonlinear error propagation; explicit pseudodynamic
algorithm; stability condition; step-by-step integration procedure; step
degree of nonlinearity
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