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Development of Non-Dissipative Direct Time Integration Method for Structural Dynamics Application

Sun-Beom Kwon1, Jae-Myung Lee1,*
1 Department of Naval Architecture and Ocean Engineering, Pusan National University, Jangjeon-Dong, Geumjeong-Gu, Busan 609-735, Korea.
* Corresponding Author: Jae-Myung Lee. Email: .

Computer Modeling in Engineering & Sciences 2019, 118(1), 41-89. https://doi.org/10.31614/cmes.2019.03879

Abstract

A direct time integration scheme based on Gauss-Legendre quadrature is proposed to solve problems in linear structural dynamics. The proposed method is a one-parameter non-dissipative scheme. Improved stability, accuracy, and dispersion characteristics are achieved using appropriate values of the parameter. The proposed scheme has second-order accuracy with and without physical damping. Moreover, its stability, accuracy, and dispersion are analyzed. In addition, its performance is demonstrated by the two-dimensional scalar wave problem, the single-degree-of-freedom problem, two degrees-of-freedom spring system, and beam with boundary constraints. The wave propagation problem is solved in the high frequency wave regime to demonstrate the advantage of the proposed scheme. When the proposed scheme is applied to solve the wave problem, more accurate solutions than those of other methods are obtained by using the appropriate value of the parameter. For the single-degree-of-freedom system, two degrees-of-freedom system, and the time responses of beam, the proposed scheme can be used effectively owing to its high accuracy and lower computational cost.

Keywords

Structural dynamics, finite elements, direct time integration, Gauss-Legendre quadrature, non-dissipative scheme.

Cite This Article

Kwon, S., Lee, J. (2019). Development of Non-Dissipative Direct Time Integration Method for Structural Dynamics Application. CMES-Computer Modeling in Engineering & Sciences, 118(1), 41–89.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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