General Framework for Multi‐Degree‐of‐Freedom Stiffness Matrix Updating for Iterative Solution Algorithms in Hybrid Simulation

ABSTRACT Iterative solvers are advantageous for handling nonlinear structural analysis problems. The iterative solvers often require updating the stiffness matrix, which limits their application in static and pseudo‐dynamic hybrid simulations because: (1) updating the stiffness matrix of a system involving a physical specimen is challenging; (2) measurement noise degrades the quality of the estimated stiffness matrix, potentially leading to numerical instabilities; and (3) as a general drawback, iterative solvers often produce uneven displacement increments between iterations, with progressively smaller increments toward the end of a step, which can cause force relaxation in hybrid simulations. To address these limitations, this study proposes a comprehensive framework for multi‐degree‐of‐freedom (MDOF) stiffness matrix updating in slow‐rate hybrid simulation for static testing (e.g., pushover or collapse analyses) and for pseudo‐dynamic testing. The framework integrates a load‐reversal identification procedure, a displacement‐scaling scheme, an approximated stiffness‐based force compensation algorithm, and several safeguard parameters, thereby enhancing the stability, accuracy, and robustness of iterative solution algorithms in hybrid simulation. The framework is designed to be compatible with a wide range of stiffness‐updating methods. Serving as middleware in hybrid simulation, HISA can be easily implemented. The effectiveness of the proposed method is validated through extensive numerical hybrid simulations of MDOF substructures. Investigation into the effects of measurement noise levels demonstrates that the framework's performance remains robust under varying levels of the noise, further confirmed that the framework effectively manages moderate‐to‐high levels of material nonlinearity in the presence of measurement noise, thereby extending the applicability of iterative solvers in hybrid simulation.