0
Research Papers

Dynamic Relaxation Using Continuous Kinetic Damping—Part I: Basic Algorithm

[+] Author and Article Information
Samuel Jung

Mechanical Engineering,
Pusan National University,
Busan 609-735, South Korea
e-mail: jung40L@hanmail.net

Tae-Yun Kim

Mechanical Engineering,
Pusan National University,
Busan 609-735, South Korea
e-mail: tykid76@gmail.com

Wan-Suk Yoo

Professor
Fellow ASME
Mechanical Engineering,
Pusan National University,
Busan 609-735, South Korea
e-mail: wsyoo@pusan.ac.kr

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 7, 2017; final manuscript received March 21, 2018; published online July 6, 2018. Assoc. Editor: Zdravko Terze.

J. Comput. Nonlinear Dynam 13(8), 081006 (Jul 06, 2018) (7 pages) Paper No: CND-17-1300; doi: 10.1115/1.4039838 History: Received July 07, 2017; Revised March 21, 2018

Dynamic relaxation (DR) is the most widely used approach for static equilibrium analyses. Specifically, DR compels dynamic systems to converge to a static equilibrium through the addition of fictitious damping. DR methods are classified by the method in which fictitious damping is applied. Conventional DR methods use a fictitious mass matrix to increase the fictitious damping while maintaining numerical stability. There are many calculation methods for the fictitious mass matrix; however, it is difficult to select the appropriate method. In addition, these methods require a stiffness matrix of a model, which makes it difficult to apply nonlinear models. To resolve these problems, a new DR method that uses continuous kinetic damping (CKDR) is proposed in this study. The proposed method does not require the fictitious mass matrix and any tuning coefficients, and it possesses a second-order convergence rate. The aforementioned advantages are unique and significant when compared to those of conventional methods. The stability and convergence rate were analyzed by using an eigenvalue analysis and demonstrated by simulating nonlinear models of a pendulum and cable. Simple but representative models were used to clearly demonstrate the features of the proposed DR method and to enable the reproducibility of the verification results.

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

References

Garcia, J. R. , 2011, “ Numerical Study of Dynamic Relaxation Methods and Contribution to the Modelling of Inflatable Lifejackets,” Ph.D. dissertation, Université de Bretagne Sud, Lorient, France.
Rezaiee-Pajand, M. , and Taghavian-Hakkak, M. , 2006, “ Nonlinear Analysis of Truss Structures Using Dynamic Relaxation,” Int. J. Eng., 19(1), pp. 11–22.
Rezaiee-Pajand, M. , and Rezaee, H. , 2012, “ Fictitious Time Step for the Kinetic Dynamic Relaxation Method,” Mech. Adv. Mater. Struct., 21(8), pp. 631–644. [CrossRef]
Day, A. S. , 1965, “ An Introduction to Dynamic Relaxation(Dynamic Relaxation Method for Structural Analysis, Using Computer to Calculate Internal Forces Following Development From Initially Unloaded State),” Eng., 219(5688), pp. 218–221.
Cundall, P. A. , 1976, “ Explicit Finite Difference Methods in Geomechanics,” International Conference on Numerical Methods in Geomechanics, pp. 132–150.
Namadchi, A. H. , and Alamatian, J. , 2016, “ Explicit Dynamic Analysis Using Dynamic Relaxation Method,” Comput. Struct., 175, pp. 91–99. [CrossRef]
Altair®, 2011, “ RADIOSS User's Guide: Example 16—Dummy Positioning,” Altair, Troy, MI.
Chung, J. , and Hulbert, G. M. , 1993, “ A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method,” ASME J. Appl. Mech., 60(2), pp. 371–375. [CrossRef]
Petyt, M. , 2010, Introduction to Finite Element Vibration Analysis, 2nd ed., Cambridge University Press, Cambridge, UK.
Hilber, H. M. , Hughes, T. J. R. , and Taylor, R. L. , 1977, “ Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics,” Earthquake Eng. Struct. Dyn., 5(3), pp. 283–292. [CrossRef]
Hulbert, G. M. , and Chung, J. , 1994, “ The Unimportance of the Spurious Root of Time Integration Algorithms for Structural Dynamics,” Commun. Numer. Methods Eng., 10(8), pp. 591–597. [CrossRef]
Cellier, F. E. , and Kofman, E. , 2006, Continuous System Simulation, Springer Science & Business Media, Berlin.
FunctionBay, 2014, “ Theoretical Manual: RecuryDyn/Solver,” FunctionBay, Gyeonggi-do, South Korea.

Figures

Grahic Jump Location
Fig. 1

Kinetic energy history of kinetic relaxation

Grahic Jump Location
Fig. 2

Amplification factor of CKDR

Grahic Jump Location
Fig. 3

Amplification factors of CKDR with various integrators

Grahic Jump Location
Fig. 4

Simple pendulum model

Grahic Jump Location
Fig. 5

Convergence of the pendulum with h = 0.45

Grahic Jump Location
Fig. 6

Number of time steps of KDR and CKDR for the pendulum model

Grahic Jump Location
Fig. 7

Amplification ratios of the simple pendulum model

Grahic Jump Location
Fig. 8

Static shape of the cable model

Grahic Jump Location
Fig. 9

Deflection of node 10 with h = 0.45

Grahic Jump Location
Fig. 10

Number of time steps of KDR and CKDR for the pendulum model

Grahic Jump Location
Fig. 11

Amplification ratio of the cable model at node 10

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