Full operator algorithm for hybrid simulation

Abstract

One of the weaknesses of the operator splitting method (OSM) is that its corrector step employs the approximation that incremental forces are linearly related to the tested structure's initial stiffness matrix. This paper presents a new predictor–corrector technique in which the assumptions about the tested structure's response are shifted to the predictor step, which results in an enhancement in overall simulation accuracy, especially for nonlinear structures. Unlike OSM, which splits the displacement and velocity operators into explicit and implicit terms, the new method uses predicted accelerations to compute fully explicit displacement and velocity values in the predictor step. Another advantage of the proposed technique, termed the full operator method (FOM) is that its formulation makes it suitable for both quasi-static and real-time hybrid simulation. The effectiveness of FOM is first evaluated by investigating error propagation in an undamped single degree-of-freedom model. It is shown that the corrector step in FOM is able to significantly suppress aberrant simulation results caused by incorrect estimation of the structure's stiffness matrix. The performance of FOM is demonstrated by exercising two additional models, which exhibit significant inelastic behavior under the prescribed excitation. The simulation results show that the proposed FOM algorithm is capable of producing accurate solutions and that the corrector step is influential in effectively reducing simulation errors. It is also shown that FOM suppresses actuator displacement control errors because of its reliance on measured quantities in the corrector step. Copyright © 2009 John Wiley & Sons, Ltd.