New Unconditionally Stable Explicit Integration Algorithm for Real-Time Hybrid Testing

In the numerical simulation of a real-time hybrid testing, integration algorithms are one of the most-effective methods to obtain solutions to discrete equations of motion at selected time steps. A variety of integration algorithms have been well established using different methods. In order to apply traditional integration algorithms to real-time hybrid testing, different assumptions are introduced in corresponding integration algorithms to make the expressions for both displacement and velocity explicit in form. In this paper, a pole-mapping rule from a discrete domain is used to develop a new explicit integration algorithm. Based on control theory, properties of all algorithms are investigated by a discrete transfer function approach. The stability analysis results show that both the Newmark method with constant average acceleration and the Chen and Ricles (CR) algorithm are unconditionally stable. Meanwhile, by assigning proper stable poles to the discrete transfer function, the newly developed algorithm can still be unconditionally stable. Accuracy analysis is carried out for the proposed algorithm and compared with other two unconditionally stable algorithms. It is shown that the proposed algorithm has a better accuracy than either the Newmark method or the CR algorithm, and provides more benefit in computational efficiency. (C) 2017 American Society of Civil Engineers.