Technical Brief

Weak Instability of Chen–Ricles Explicit Method for Structural Dynamics

[+] Author and Article Information
Shuenn-Yih Chang

Department of Civil Engineering,
National Taipei University of Technology,
NTUT Box 2653,
No. 1, Section 3, Jungshiau East Road,
Taipei 106-08, Taiwan
e-mail: changsy@ntut.edu.tw

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 23, 2017; final manuscript received February 7, 2018; published online March 21, 2018. Assoc. Editor: Jozsef Kovecses.

J. Comput. Nonlinear Dynam 13(5), 054501 (Mar 21, 2018) (6 pages) Paper No: CND-17-1178; doi: 10.1115/1.4039379 History: Received April 23, 2017; Revised February 07, 2018

Although the Chen–Ricles (CR) explicit method (CRM) (proposed by Chen and Ricles) has been claimed to have desired numerical properties, such as unconditional stability, explicit formulation, and second-order accuracy, it also shows some unusual properties, such as a less accuracy of solving highly nonlinear systems, a high-frequency overshoot in steady-state responses, and a weak instability. A correction scheme by adjusting the displacement difference equation with a loading term can be employed to extinguish the high-frequency overshoot in steady-state responses. However, there is still no way to get rid of the weak instability and to improve the less accuracy of solving highly nonlinear systems. It is recognized that a weak instability might result in inaccurate solutions or numerical explosions. Hence, the practical applications of CRM are strictly limited.

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Grahic Jump Location
Fig. 1

Free vibration responses to a nonlinear system

Grahic Jump Location
Fig. 2

Displacement responses of SDOF systems under sine loading for CEM and CRM

Grahic Jump Location
Fig. 3

Displacement responses of SDOF systems under sine loading for modified CEM and CRM

Grahic Jump Location
Fig. 4

Free vibration responses to 2DOF system

Grahic Jump Location
Fig. 5

Comparisons of overshoot responses due to nonzero initial displacement or velocity



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