A Rosenbrock‐W method for real‐time dynamic substructuring and pseudo‐dynamic testing

Abstract

SUMMARYA variant of the Rosenbrock-W integration method is proposed for real-time dynamic substructuring and pseudo-dynamic testing. In this variant, an approximation of the Jacobian matrix that accounts for the properties of both the physical and numerical substructures is used throughout the analysis process. Only an initial estimate of the stiffness and damping properties of the physical components is required. It is demonstrated that the method is unconditionally stable provided that specific conditions are fulfilled and that the order accuracy can be maintained in the nonlinear regime without involving any matrix inversion while testing. The method also features controllable numerical energy dissipation characteristics and explicit expression of the target displacement and velocity vectors. The stability and accuracy of the proposed integration scheme are examined in the paper. The method has also been verified through hybrid testing performed of SDOF and MDOF structures with linear and highly nonlinear physical substructures. The results are compared with those obtained from the operator splitting method. An approach based on the modal decomposition principle is presented to predict the potential effect of experimental errors on the overall response during testing.

Effective strategies for real time hybrid simulation of near seismic collapse response of moment resisting frames

“…The RTDS tests were conducted using a variant of the Rosenbrock-W integration method [7]. In this variant, an approximation of the Jacobian matrix that accounts for the properties of both the physical and numerical substructures is used throughout the analysis process.…”

An overview of seismic hybrid testing of engineering structures

“…A number of authors have developed implicit algorithms specifically for RTHT, namely; [52], [66], [67], [68] and [69].…”

Iterative implicit integration procedure for hybrid simulation of large nonlinear structures

“…These combined methods are non-iterative and simple to apply since they use the initial stiffness matrix to predict the behavior of nonlinear substructures in a correction step. Similarly, implicit integration algorithms have been reformulated to a non-iterative form by making use of the initial stiffness matrix [11][12][13][14]. The initial stiffness approximation may be reasonable for mildly nonlinear behavior, and when the experimental tangent stiffness matrix is difficult to estimate.…”

“…These methods, along with those that use a fixed number of small substeps in each integration step [20], require intense communication between the experiments and the numerical integrator, making them impractical for geographically distributed simulations. Alternatively, the interface forces between the experimental and numerical substructures have been treated as constant external forces [14,21,22].In an effort to extend the capabilities of hybrid simulation to complex structural systems with nonlinear behavior distributed throughout the experimental and numerical structural models, a fully implicit integration procedure is presented that is compatible with experimental substructures. The objective is not to present a new integration algorithm, but rather to present a methodology that enables local and geographically distributed hybrid simulations of complex structural systems using existing advanced integration algorithms as they would be used in pure numerical simulations.…”

“…These methods, along with those that use a fixed number of small substeps in each integration step [20], require intense communication between the experiments and the numerical integrator, making them impractical for geographically distributed simulations. Alternatively, the interface forces between the experimental and numerical substructures have been treated as constant external forces [14,21,22].…”