A STAGGERED TIME-INTEGRATION METHOD ON THE INTEGRAL FORM OF MOTION EQUATION FOR REAL-TIME HYBRID SIMULTAION
Journal
World Conference on Earthquake Engineering proceedings
Journal Volume
2021
ISSN
30065933
Date Issued
2021-01-01
Author(s)
Wang K.J.
Abstract
In hybrid simulation the complete structural model is divided into two categories: the numerical substructure (NS) and the physical substructure (PS). The NS consists of structural elements that can be numerically simulated correctly. The PS consists of structural elements whose mechanical behaviors can only be accurately captured via real experiments. In each integration time step of the dynamic time-history analysis, the nodal displacements are firstly calculated and then the corresponding resisting forces of all the structural elements are obtained, either by numerical simulation (for NS) or by direct measurement from the experiment (for PS). Once all the element forces are obtained they are used to solve for the velocity and the acceleration responses to complete the analysis of the current integration time step. These operations are executed sequentially within an integration time step, and the process is repeated until the end of the analysis. In real-time hybrid simulation, the target displacement should be imposed on the specimens with correct velocity. This means theoretically all the time should be consumed by the actuation system. However, the sequential nature of the execution of the procedures mentioned above inevitably conflicts with this testing requirement. For structural systems with only a limited number of degree-of-freedoms (DOFs), or for those systems whose dynamic responses essentially remain elastic, it might still be acceptable since the computation time might be very limited. However, for more generic testing scenarios this undoubtedly becomes one of the biggest challenges in real-time hybrid simulation. This study proposed a new time-stepping integration method to address the aforementioned issues. Succinctly put, in the proposed integration method, two ordinary integration schemes were performed respectively on the odd-number and the even-number time steps staggeringly, on the integral form of the motion equation (the momentum equation). The staggered integration method allows the actuation system to continuously imposing the target displacements on the specimens without the need to pause at the end of an integration time step to wait for the computation of the displacement command corresponding to the next integration time step. In addition, as the proposed staggered integration method works on the momentum equation which is obtained by integrating the motion equation with respect to time, the staggered responses resulting from the two independently running ordinary integration schemes can be effectively diminished because the two schemes uses the common momentum of the system in their respective computation processes. The derivation of the proposed integration method was given. The stability criterion and accuracy characteristics were studied. The effects of the proposed integration method were investigated by applying the method on numerical examples of single DOF systems.
Subjects
hybrid simulation
integration method
momentum equation
real-time
staggered
Publisher
International Association for Earthquake Engineering
Type
conference paper