Assessment of explicit and semi‐explicit classes of model‐based algorithms for direct integration in structural dynamics

Abstract

Summary The ‘model‐based’ algorithms available in the literature are primarily developed for the direct integration of the equations of motion for hybrid simulation in earthquake engineering, an experimental method where the system response is simulated by dividing it into a physical and an analytical domain. The term ‘model‐based’ indicates that the algorithmic parameters are functions of the complete model of the system to enable unconditional stability to be achieved within the framework of an explicit formulation. These two features make the model‐based algorithms also potential candidates for computations in structural dynamics. Based on the algorithmic difference equations, these algorithms can be classified as either explicit or semi‐explicit, where the former refers to the algorithms with explicit difference equations for both displacement and velocity, while the latter for displacement only. The algorithms pertaining to each class are reviewed, and a new family of second‐order unconditionally stable parametrically dissipative semi‐explicit algorithms is presented. Numerical characteristics of these two classes of algorithms are assessed under linear and nonlinear structural behavior. Representative numerical examples are presented to complement the analytical findings. The analysis and numerical examples demonstrate the advantages and limitations of these two classes of model‐based algorithms for applications in structural dynamics. Copyright © 2015 John Wiley & Sons, Ltd.

Response to Maxam and Tamma's discussion (EQE‐18‐0306) to Kolay and Ricles's paper, “Development of a family of unconditionally stable explicit direct integration algorithms with controllable numerical energy dissipation”

“…2 In subsequent studies, the authors have demonstrated the efficacy of the KRmethod in conducting large-scale real-time hybrid simulation of structures with nonlinear seismic response modification devices 3 and in simulating collapse response of reinforced concrete (RC) frame structures. The proposed family of algorithms, referred to as the KR-method, features an explicit formulation, unconditional stability, and controllable numerical energy dissipation.…”

“…2 In subsequent studies, the authors have demonstrated the efficacy of the KRmethod in conducting large-scale real-time hybrid simulation of structures with nonlinear seismic response modification devices 3 and in simulating collapse response of reinforced concrete (RC) frame structures. 4 The authors have also assessed the numerical characteristics of similar model-based algorithms 2 and developed a modified formulation to improve the overshoot and nonlinear stability characteristics of the KR-method. 5 The authors would like to thank Dean J. Maxam and Prof. Kumar K. Tamma (hereafter the Discussers) for their interest in the KR-method.…”

Experimental study of seismic response reduction effects of particle damper using substructure shake table testing method

“…To fill the gap, Chen and Ricles developed an explicit unconditionally stable CR algorithm primarily for applications in RTHS. Kolay and Ricles theoretically analyzed the reason why the CR algorithm possesses the two great features: explicit formulation and unconditional stability. According to Kolay and Ricles, the CR algorithm is a particular case of model‐based integration algorithms, which indicates that model‐based algorithmic parameters should be predefined prior to the integration process.…”

“…Kolay and Ricles theoretically analyzed the reason why the CR algorithm possesses the two great features: explicit formulation and unconditional stability. According to Kolay and Ricles, the CR algorithm is a particular case of model‐based integration algorithms, which indicates that model‐based algorithmic parameters should be predefined prior to the integration process. The CR algorithm has been successfully applied in a number of RTHS …”

Theory and Implementation of a Two-Step Unconditionally Stable Explicit Integration Algorithm for Vibration Analysis of Structures

“…The commonly referenced explicit algorithm is Central Difference Method (CDM) (ref), CDM is easy to use, but it is only conditionally stable. Many new explicit methods which are unconditionally stable [17][18][19] have been developed. Though these methods are unconditionally stable, they require multiple steps which are not as efficient as the CDM.…”