A family of second-order fully explicit time integration schemes

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 intern...

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Bibliographic Details
Published in:Computational & applied mathematics 2018-07, Vol.37 (3), p.3431-3454
Main Authors: Rezaiee-Pajand, Mohammad, Karimi-Rad, Mahdi
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Damping
Mass matrix
Mathematical analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematics
Mathematics and Statistics
Matrix methods
Numerical dissipation
Time integration
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Summary: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.
ISSN:0101-8205
2238-3603
1807-0302
DOI:10.1007/s40314-017-0520-3