0
Technical Brief

Weak Instability of Chen–Ricles Explicit Method for Structural Dynamics

[+] Author and Article Information
Shuenn-Yih Chang

Professor
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Chang, S. Y. , 2002, “Explicit Pseudodynamic Algorithm With Unconditional Stability,” ASCE J. Eng. Mech., 128(9), pp. 935–947. [CrossRef]
Chen, C. , and Ricles, J. M. , 2008, “Development of Direct Integration Algorithms for Structural Dynamics Using Discrete Control Theory,” ASCE J. Eng. Mech., 134(8), pp. 676–683. [CrossRef]
Chang, S. Y. , 2009, “An Explicit Method With Improved Stability Property,” Int. J. Numer. Method Eng., 77(8), pp. 1100–1120. [CrossRef]
Chang, S. Y. , 2010, “A New Family of Explicit Method for Linear Structural Dynamics,” Comput. Struct., 88(11–12), pp. 755–772. [CrossRef]
Gui, Y. , Wang, J. T. , Jin, F. , Chen, C. , and Zhou, M. X. , 2014, “Development of a Family of Explicit Algorithms for Structural Dynamics With Unconditional Stability,” Nonlinear Dyn., 77(4), pp. 1157–1170. [CrossRef]
Chen, C. , Ricles, J. M. , Marullo, T. , and Mercan, O. , 2009, “Real-Time Hybrid Testing Using the Unconditionally Stable Explicit CR Integration Algorithm,” Earthquake Eng. Struct. Dyn., 38(1), pp. 23–44. [CrossRef]
Chen, C. , Ricles, J. M. , Karavasilis, T. L. , Chae, Y. , and Sause, R. , 2012, “Evaluation of a Real-Time Hybrid Simulation System for Performance Evaluation of Structures With Rate Dependent Devices Subjected to Seismic Loading,” Eng. Struct., 35, pp. 71–82. [CrossRef]
Chang, S. Y. , 2015, “Comparisons of Structure-Dependent Explicit Methods for Time Integration,” Int. J. Struct. Stab. Dyn., 15(3), p. 1450055. [CrossRef]
Goudreau, G. L. , and Taylor, R. L. , 1973, “Evaluation of Numerical Integration Methods in Elasto-Dynamics,” Comput. Methods Appl. Mech. Eng., 2(1), pp. 69–97. [CrossRef]
Newmark, N. M. , 1959, “A Method of Computation for Structural Dynamics,” ASCE J. Eng. Mech. Div., 85(3), pp. 67–94. http://cedb.asce.org/CEDBsearch/record.jsp?dockey=0011858
Chang, S. Y. , 2006, “Accurate Representation of External Force in Time History Analysis,” ASCE J. Eng. Mech., 132(1), pp. 34–45. [CrossRef]
Chang, S. Y. , 2016, “A Loading Correction Scheme for a Structure-Dependent Integration Method,” ASME J. Comput. Nonlinear Dyn., 12(1), p. 011005. [CrossRef]
Chang, S. Y. , 2018, “Elimination of Overshoot in Forced Vibration Response for Chang Explicit Family Methods,” J. Eng. Mech., 144(2), p. 04017177. [CrossRef]
Chang, S. Y. , 2018, “An Amplitude Growth Property and Its Remedy for Structure-Dependent Integration Methods,” Comput. Methods Appl. Mech. Eng., 330, pp. 498–521. [CrossRef]
Chang, S. Y. , and Wu, T. H. , 2017, “Assessments of Structure-Dependent Integration Methods With Explicit Displacement and Velocity Difference Equations,” J. Mech., epub.

Figures

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

Tables

Errata

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In