Investigations of nonlinear performances of implicit pseudodynamic algorithms

Abstract

Although it has been shown that the implementation of the HHT α method can result in improved error propagation properties in pseudodynamic testing if the equation of motion is used instead of the difference equation to evaluate the next step acceleration, this paper proves that this method might lead to instability when used to solve a nonlinear system. Its unconditional stability is verified only for linear elastic systems, while for nonlinear systems, instability occurs as the step degree of convergence is less than 1. It is worth noting that the step degree of convergence can frequently be less than 1 in pseudodynamic testing, since a convergent solution is achieved only when the step degree of convergence is close to 1 regardless of whether its value is greater or less than 1. Therefore, the application of this scheme to pseudodynamic testing should be prohibited, since the possibility of instability might incorrectly destroy a specimen. Consequently, the implementation of the HHT α method by using the difference equation to determine the next step acceleration is recommended for use in pseudodynamic testing.