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

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.

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Fig. 1

Kinetic energy history of kinetic relaxation

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Fig. 2

Amplification factor of CKDR

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Fig. 3

Amplification factors of CKDR with various integrators

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Fig. 4

Simple pendulum model

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Fig. 5

Convergence of the pendulum with h = 0.45

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Fig. 6

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

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Fig. 7

Amplification ratios of the simple pendulum model

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Fig. 8

Static shape of the cable model

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Fig. 9

Deflection of node 10 with h = 0.45

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Fig. 10

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

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Fig. 11

Amplification ratio of the cable model at node 10



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