A new time integration scheme is presented for solving the differential equation of motion with nonlinear stiffness. In this new implicit method, it is assumed that the acceleration varies quadratically within each time step. By increasing the order of acceleration, more terms of the Taylor series are used, which are expected to have responses with better accuracy than the classical methods. By considering this assumption and employing two parameters δ and α, a new family of unconditionally stable schemes is obtained. The order of accuracy, numerical dissipation, and numerical dispersion are used to measure the accuracy of the proposed method. Second order accuracy is achieved for all values of δ and α. The proposed method presents less dissipation at the lower modes in comparison with Newmark's average acceleration, Wilson-θ, and generalized-α methods. Moreover, this second order accurate method can control numerical damping in the higher modes. The numerical dispersion of the proposed method is compared with three unconditionally stable methods, namely, Newmark's average acceleration, Wilson-θ, and generalized-α methods. Furthermore, the overshooting effect of the proposed method is compared with these methods. By evaluating the computational time for analysis with similar time step duration, the proposed method is shown to be faster in comparison with the other methods.
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March 2013
Research-Article
A New Unconditionally Stable Time Integration Method for Analysis of Nonlinear Structural Dynamics
Ali Akbar Gholampour,
Ali Akbar Gholampour
1
Graduate Student
e-mail: aagholampour@ut.ac.ir
e-mail: aagholampour@ut.ac.ir
1Corresponding author.
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Mehdi Ghassemieh,
Mehdi Ghassemieh
Associate Professor
e-mail: mghassem@ut. ac.ir
e-mail: mghassem@ut. ac.ir
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Mahdi Karimi-Rad
Mahdi Karimi-Rad
Graduate Student
e-mail: hk_civil@yahoo.com
Tehran, 14174
e-mail: hk_civil@yahoo.com
School of Civil Engineering
,University of Tehran
,Tehran, 14174
Iran
Search for other works by this author on:
Ali Akbar Gholampour
Graduate Student
e-mail: aagholampour@ut.ac.ir
e-mail: aagholampour@ut.ac.ir
Mehdi Ghassemieh
Associate Professor
e-mail: mghassem@ut. ac.ir
e-mail: mghassem@ut. ac.ir
Mahdi Karimi-Rad
Graduate Student
e-mail: hk_civil@yahoo.com
Tehran, 14174
e-mail: hk_civil@yahoo.com
School of Civil Engineering
,University of Tehran
,Tehran, 14174
Iran
1Corresponding author.
Manuscript received November 28, 2011; final manuscript received September 12, 2012; accepted manuscript posted September 25, 2012; published online January 30, 2013. Assoc. Editor: Marc Geers.
J. Appl. Mech. Mar 2013, 80(2): 021024 (12 pages)
Published Online: January 30, 2013
Article history
Received:
November 28, 2011
Revision Received:
September 12, 2012
Accepted:
September 25, 2012
Citation
Akbar Gholampour, A., Ghassemieh, M., and Karimi-Rad, M. (January 30, 2013). "A New Unconditionally Stable Time Integration Method for Analysis of Nonlinear Structural Dynamics." ASME. J. Appl. Mech. March 2013; 80(2): 021024. https://doi.org/10.1115/1.4007682
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