Error Propagation in Implicit Pseudodynamic Testing of Nonlinear Systems

Error propagation analysis of an implicit pseudodynamic algorithm has been developed for linear elastic systems. However, these error propagation results might not be applicable to nonlinear systems. Since the pseudodynamic testing method aims at investigating the nonlinear behavior of a seismically loaded structure it is important to perform the error propagation analysis of the implicit pseudodynamic algorithm for nonlinear systems. A technique to conduct the nonlinear error propagation analysis of an implicit pseudodynamic algorithm is constructed and is illustrated by analyzing the constant average acceleration method. Theoretical results reveal that the numerical and error propagation properties for nonlinear systems are generally inherited from those of linear elastic systems although some properties are affected by the step degree of nonlinearity. It is verified that the most important property of unconditional stability is preserved for nonlinear systems for a complete pseudodynamic test procedure even if the convergence error is present. It is concluded that error propagation for the improved implementation is superior to that of the direct implementation and is consistent with that developed for linear elastic systems.