A‐stable two‐step time integration methods with controllable numerical dissipation for structural dynamics

Abstract

SummaryA comprehensive study of A‐stable linear two‐step time integration methods for structural dynamics analysis is presented in this paper. An optimal A‐stable linear two‐step (OALTS) time integration method is revealed with desirable performance on low‐frequency accuracy and high‐frequency numerical dissipation properties. The OALTS time integration method is implemented in a direct integration manner for the second‐order equations of structural dynamics; is implicit, A‐stable, and second‐order accurate in displacement, velocity, and acceleration, simultaneously; is easily started; and is numerical dissipation controllable. The OALTS time integration method shows desirable performance on spectral radius distribution, dissipation and dispersion errors, and overshooting behavior, where the results of some typical algorithms in the literature are also compared. Benchmark examples with/without physical damping are performed to validate the accuracy, stability, and efficiency of the OALTS time integration method.