Nonlinear Error Propagation Analysis for Explicit Pseudodynamic Algorithm

A technique to evaluate the error propagation of the pseudodynamic testing of a nonlinear system is proposed. This technique mainly relies upon the introduction of the degree of nonlinearity to describe the variation of stiffness for each time step. The commonly used Newmark explicit method is chosen for this study and it is analytically proved that the upper stability limit is enlarged for the case of stiffness softening and is reduced for the case of stiffness hardening. These theoretical results are thoroughly confirmed with numerical examples. It is also theoretically and numerically verified that for each time step stiffness softening encounters less error propagation while stiffness hardening experiences more severe error propagation than for the stiffness invariant case. This is because stiffness softening results in the decrease of the natural frequency and the value of the degree of softening nonlinearity while stiffness hardening leads to the increase of the natural frequency and the value of the degree of hardening nonlinearity.