Force-Based Frame Element Implementation for Real-Time Hybrid Simulation Using Explicit Direct Integration Algorithms

Existing state determination procedures for force-based finite elements use either an iterative scheme at the element level or a noniterative scheme at the element level that relies on an iterative solution algorithm for the global equilibrium equations. The former cannot ensure convergence in real-time computations, whereas the latter requires an implicit direct integration algorithm; therefore, these procedures are not applicable to real-time hybrid simulation (RTHS) utilizing an explicit direct integration algorithm. A new procedure is developed based on a fixed number of iterations and an unconditionally stable explicit model-based integration algorithm. If the maximum number of iterations is reached, element resisting forces are corrected to re-establish compatibility, and unbalanced section forces are carried over to and corrected in the next time step. This procedure is used in the numerical simulation and RTHS of an earthquake-excited two-story reinforced concrete building. Results show that an accurate solution can be obtained even without performing any iteration. The influence of the model-based parameters of the integration algorithm on the stability and accuracy of the RTHS is also studied.