Nonlinear error propagation analysis of implicit pseudodynamic algorithm

Abstract

An implementation of the HHT‐α method for pseudodynamic testing has been proposed by Chang and Mahin (1993). This implicit algorithm has been shown to be unconditionally stable and to possess less error propagation than any other implicit pseudodynamic algorithm. However, these conclusions are true only for linear elastic systems but might not be applicable to nonlinear systems. A technique is proposed to analyze the nonlinear error propagation of the implicit pseudodynamic algorithm, where only the member of the constant average acceleration method is investigated for simplicity. It is analytically and numerically verified that the constant average acceleration method might lead to numerical instability in the pseudodynamic testing of a nonlinear system although it is unconditionally stable for a linear elastic system. Furthermore, analytical results of the nonlinear error propagation analysis and numerical experiments conclude that the error propagation of the improved implementation is much better than that of the direct implementation. This is consistent with results from use on linear elastic systems.