Comparisons of model-based explicit integration algorithms in real-time substructure testing

In real-time substructure testing, a key issue is the numerical simulation of the numerical substructure, which can be done by applying appropriate integration algorithms to solve the step-by-step structural equations of motion. Three well-developed model-based explicit integration algorithms, that is, Chang, CR and RST methods, are discussed and compared in terms of the numerical properties in linear and non-linear systems. Stability analysis indicates that the three methods are unconditionally stable for linear and instantaneous stiffness softening systems while they are only conditionally stable for instantaneous stiffness hardening systems. The three methods show exactly the same characteristics for zero-damping systems as no numerical damping is produced and the period error (PE) increases with the increase of Ω. However, the three methods introduce numerical damping into the simulation for damped systems, and the numerical damping caused by the CR method is the smallest at a certain value of Ω. Meanwhile, the RST method has a smaller PE than the other two methods for damped systems. Two examples indicate that the RST method and Chang method have a better accuracy than the CR method in solving dynamic problems of both linear and non-liner systems. Since the velocity of the Chang method is in an implicit form, the RST is more advantageous in real-time substructure testing. © 2020, Engineering Mechanics Press. All right reserved.