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Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

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Volume 7, Issue 3


A Weighted Residual Parabolic Acceleration Time Integration Method for Problems in Structural Dynamics

S.H. Razavi
A. Abolmaali
M. Ghassemieh
  • Department of Civil Engineering, Faculty of Engineering, University of Tehran, Tehran, Iran.
  • Other articles by this author:
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In the proposed method, the variation of displacement in each time step is assumed to be a fourth order polynomial in time and its five unknown coefficients are calculated based on: two initial conditions from the previous time step; satisfying the equation of motion at both ends of the time step; and the zero weighted residual within the time step. This method is non-dissipative and its dispersion is considerably less than in other popular methods. The stability of the method shows that the critical time step is more than twice of that for the linear acceleration method and its convergence is of fourth order.

Keywords: structural dynamics; time integration; numerical stability; numerical accuracy; convergence; dissipation; dispersion; implicit method; explicit method

About the article

Received: 2007-04-26

Revised: 2007-08-29

Accepted: 2007-09-21

Published in Print:

Citation Information: Computational Methods in Applied Mathematics Comput. Methods Appl. Math., Volume 7, Issue 3, Pages 227–238, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: https://doi.org/10.2478/cmam-2007-0014.

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© Institute of Mathematics, NAS of Belarus. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. BY-NC-ND 4.0

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