Unconditionally Stable Central Difference Dissipative Algorithm for Multi-Directional Real-Time Hybrid Simulations of Large Nonlinear Structural Systems

ABSTRACT

The central difference is a popular algorithm used to integrate the equations of motion, yet suffers from two drawbacks: (1) it is only conditionally stable and requires a small-time step to maintain numerical stability; (2) it is non-dissipative, and high-frequency spurious oscillations may appear and compromise the accuracy of the solution. These drawbacks are detrimental to applying the algorithm to the real-time hybrid simulation of large, complex nonlinear structural systems. In this paper, the conventional central difference algorithm is modified to overcome these drawbacks, and the modified algorithm is applied to the real-time hybrid simulation of complex structural systems.

KEYWORDS:

• 3D real-time hybrid simulation
• nonlinear multi-directional response
• unconditionally stability
• explicit formulation
• controllable numerical damping
• model-based explicit integration algorithm
• discrete control theory

Acknowledgments

This research was performed at the NHERI Lehigh Experimental Facility, whose operation is supported by a grant from the National Science Foundation (NSF) under Cooperative Agreement No. CMMI-2037771. This material is based upon the research supported by the NSF under Grant No. 1463497. The support by NSF is gratefully acknowledged. Any opinions, findings, conclusions, or recommendations expressed herein are the authors and do not necessarily reflect the views or policies of the NSF. Many thanks to the staff of the NHERI Lehigh Experimental Facility for their continued support of this project.

Disclosure Statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

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Funding

The work was supported by the National Science Foundation.