Nonlinear Performance of Explicit Pseudodynamic Algorithms

A previously published explicit method has been proved to have the same numerical properties as those of constant average acceleration method for linear elastic systems. Although its application to the pseudodynamic testing of nonlinear systems with high frequency modes has been conducted and thus unconditional stability for nonlinear systems was indicated, there is still lack of an analytical proof. In order to explore the nonlinear performance of this explicit pseudodynamic algorithm, a new parameter of instantaneous degree of nonlinearity is introduced to monitor the stiffness change between the stiffness at the end of a time step and the initial stiffness. This parameter enables basic analysis and error propagation analysis for a nonlinear system. In addition, it can also be applied to construct the rough guidelines to select an appropriate time step to conduct a pseudodynamic test although it is almost impossible to achieve this goal using the currently available techniques for a nonlinear system. Analytical results reveal that this algorithm can have unconditional stability for instantaneous stiffness softening and linear elastic systems while it has conditional stability for instantaneous stiffness hardening systems. The proposed rough guidelines for selecting a time step to yield a reliable pseudodynamic test are confirmed with numerical examples.