Computational and Applied Mathematics

, Volume 37, Issue 3, pp 3431–3454 | Cite as

A family of second-order fully explicit time integration schemes

  • Mohammad Rezaiee-PajandEmail author
  • Mahdi Karimi-Rad


A new family of fully explicit time integration methods is proposed, which has second-order accuracy for structures with and without damping. Using a diagonal mass matrix, the suggested scheme remains fully explicit not only for structures with a non-diagonal damping matrix, but also when the internal force vector is a nonlinear function of velocity. The present algorithm has an acceptable domain of stability, and it is self-starting. This technique introduces effectively numerical dissipation to suppress the high-frequency spurious modes, while at the same time the lower modes are not affected too much. In addition, numerical dispersion error of the scheme is considerably smaller than that of the central difference method. Solving several linear and nonlinear problems highlights the superior performance of the authors’ approach. Findings demonstrate that solution time for the suggested scheme is much less than that of the central difference technique. The related algorithm can be easily implemented into programs, which already contain the central difference method.


Explicit time integration Second-order accuracy Numerical dissipation Nonlinear structural dynamics Numerical dispersion 


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Department of Civil EngineeringFerdowsi University of MashhadMashhadIran

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