Real-time substructure is a novel hybrid method for the dynamic testing of structures. During an experiment, the structure of interest is divided into two entities. The crucial parts for the project undertaken are physically replicated and loaded dynamically through powerful actuators while the rest is numerically modelled and solved via real-time software.
The dynamics of both substructures must be accurately reproduced, as well as their mutual interaction. The applications are multiple but that of earthquake engineering is primarily considered in this research.
Beyond the accurate modelling of both substructures, three main issues are crucial to the validity of a real-time hybrid simulation. Firstly, the loading equipment must be capable of imposing large loads and accurate displacements on the laboratory specimen.The behaviour of this loading system must be consistent and predictable over a wide range of frequencies and velocities. Secondly, the computational solver employed to emulate the numerical model dynamics requires stability, computational efficiency and accuracy.
It must be able to deal with non-linear multi-degree of freedom systems. Thirdly, the interaction between the two substructures must be reliably emulated by a set of communication devices. The reciprocal boundary conditions must be imposed on the interface of each substructure. This notably implies quasi-instantaneous measurement and application of physical forces and displacements. The two substructures have to be solved simultaneously and in real-time.
The three areas mentioned above have been investigated in this research. Initially, the laboratory installations of the hardware and software were focussed on. The servo-controlled hydraulic actuation system was optimised and a development rig was designed and constructed. It was found that hardware settings could greatly improve the general actuator performance, even though some particular situations could compromise it. This work was then complemented by an extensive study of the necessary actuation compensation.
Numerous algorithms – either previously published or developed in the course of this research – were implemented and formally compared through a set of real-time experiments. Particularly, some challenging multi-axis experiments with a high level of actuator coupling were conducted. Direct extrapolation coupled with adaptive delay estimation was found to be the most effective approach to ensure synchronisation of the substructures. Attention was then given to the integration algorithms used to solve the numerical substructure problem and output the actuator demand on a real-time basis. Both explicit and implicit schemes were considered, even though an explicit formulation is required for this hybrid application.
Computationally simple schemes are more suitable and several were shown to satisfy the necessary accuracy and stability requirements. Successful realtime hybrid tests were carried out with fifty degrees of freedom in the numerical substructure, including non-linear force/displacement relationships and using integration time-steps proving unconditional stability of the algorithms used.
Finally, a realistic earthquake engineering application of the real-time substructure method was conducted. A steel column was tested physically as part of 20-storey building structure subject to the 1940 El Centro earthquake. To further display the usefulness of the method, an energy dissipative device was also integrated in the numerical model and its effect on the building response was shown.
Source: University of Oxford
Author: Paul A. Bonnet