Real-Time Hybrid Simulation of a Reinforced Concrete Structure Using Flexibility-Based Fiber Elements and Advanced Integration Algorithms

Abstract eng:
An accurate and efficient state determination of the analytical substructure plays an important role in real-time hybrid simulation (RTHS) of a structure subjected to seismic excitations. This becomes even more important for RTHS of reinforced concrete (RC) structures because the hysteretic behavior of RC members is complex and generally involve pinching, softening, and strength degradation in their force-deformation response. Such complex hysteretic behavior is better modeled using the force-based fiber element formulation compared with the stiffness-based approach. The main advantage of the force-based formulation, which stems from the enforcement of equilibrium along the element in a strict sense, is that the material nonlinearity can be modeled using a single element per structural member. This results in a significant reduction of the number of a model’s degrees of freedom. However, the implementation of a force-based fiber element formulation in a standard stiffness-based finite element program requires an iterative state determination procedure to satisfy compatibility within a specified tolerance. This iterative procedure is not feasible for RTHS because convergence cannot be guaranteed in real time. This issue is addressed by implementing a force-based fiber element formulation with a fixed number of iterations for application to RTHS using an explicit direct integration algorithm. When the maximum number of iterations is reached, element end forces are corrected to re-establish compatibility and the unbalanced section forces are carried over to and corrected in the next integration time step. Using this implementation scheme and the modified KR-α (MKR-α) method, a recently developed family of unconditionally stable explicit parametrically dissipative direct integration algorithms, RTHS of a two-story RC special moment resisting frame (SMRF) building with a nonlinear viscous damper are performed under the maximum considered earthquake hazard level. The RC SMRF is modeled analytically using the force-based fiber element and the nonlinear viscous damper is modeled physically in the laboratory. The efficacy of the proposed iterative scheme is assessed based on RTHS results which show that an accurate solution can be obtained even when no iteration is performed at the element level.

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