Improved implementation of concentrated plasticity models in real-time hybrid simulation

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Real-time hybrid simulation (RTHS) is a cost-effective experimental testing technique for evaluating the dynamic response of structural systems. In RTHS, a portion of the structure is modeled numerically (i.e., numerical substructure), while the remaining part is tested physically (i.e., experimental substructure). These substructures are coupled in real time. A significant challenge in RTHS is accurately computing the dynamic response of the numerical substructure in real time during testing. Constrained by this challenge, numerical substructures in RTHS are often oversimplified (e.g., spring-mass-dashpot models), failing to capture more complex dynamic behaviors and limiting the applicability of RTHS. However, with the increasing use of innovative structural systems, new materials, and advanced design guidelines to ensure resilient and sustainable civil infrastructure against natural hazards, the demand for real-time executable higher-fidelity numerical substructures in RTHS is growing. Consequently, concentrated plasticity model (CPM) has gained attention as the numerical substructure in RTHS for its good balance between numerical accuracy and computational efficiency, as well as its popularity in structural engineering applications. Currently, static condensation is utilized to prevent an increase in computational degrees of freedom (DOFs) induced by the hinges in CPM, aiming to save computational cost. However, this method proves counterproductive for nonlinear analyses. While reducing the number of computational DOFs, it complicates the stiffness representation, thereby necessitating more demanding arithmetic operations for stiffness updating. In this study, multi-point constraints are applied to enhance the computational efficiency, specifically for nonlinear analyses involving stiffness updating, and the versatility of CPM. Moreover, direct stiffness updating method and sparse matrix-vector multiplication are introduced for further enhancement in computation. An open-source MATLAB/Simulink-based computational tool, namely the Hybrid2D, is developed to promote the use of the improved CPMs in RTHS as numerical substructures. Numerical simulations are first conducted to verify the accuracy and the computational efficiency of the improved CPMs in Hybrid2D. Subsequently, two RTHS examples are experimentally conducted to demonstrate the effectiveness of the Hybrid2D in enabling RTHS with a higher-fidelity numerical substructure for more complex structural systems.