Comparison of capability of time integration methods in capturing dynamic loading

• Published in: Earthquake Engineering and Engineering Vibration 2010-09, Vol.9 (3), p.409-423
• Main Authors: Chang, Shuenn-Yih, Hsu, Chi-Wei, Chen, Ting-Wei
• Format: Article
• Language: English
• Subjects: Civil Engineering; Computational efficiency; Control; Displacement; Dynamical Systems; Dynamics; Earth and Environmental Science; Earth Sciences; Geotechnical Engineering & Applied Earth Sciences; Linear equations; Loads (forces); Mathematical analysis; Numerical analysis; Quadratures; Time integration; Vibration; 位移增量; 公式推导; 数值积分法; 积分方法; 空空导弹
• ISSN: 1671-3664; 1993-503X
• DOI: 10.1007/s11803-010-0025-1

Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.