An unconditionally stable implicit time integration algorithm: Modified quartic B-spline method

•Proposing an implicit unconditionally stable time integration method.•Using quartic B-spline basis function.•Good accuracy compared to the methods in the literature.•The scheme can achieve lower numerical amplitude dissipation and period dispersion. In Ref. [1] an effective conditionally stable exp...

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Published in:Computers & structures Vol. 153; pp. 98 - 111
Main Authors: Shojaee, Saeed, Rostami, Sobhan, Abbasi, Asghar
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.06.2015
Subjects:
Algorithms
Dynamics
Implicit
Mathematical analysis
Mathematical models
Quartic B-spline
Second order acceleration
Stability
Stabilization
Time integration
Unconditional stability
Unconditional stability
Quartic B-spline
Implicit
Second order acceleration
Time integration
ISSN:0045-7949, 1879-2243
Online Access:Get full text
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Summary:•Proposing an implicit unconditionally stable time integration method.•Using quartic B-spline basis function.•Good accuracy compared to the methods in the literature.•The scheme can achieve lower numerical amplitude dissipation and period dispersion. In Ref. [1] an effective conditionally stable explicit time integration scheme using quartic B-spline function was proposed for solving the problems in structural dynamics. The current paper presents a scheme where this method is developed to an implicit unconditionally stable time integration method. Using quartic B-spline basis function, this method gained second order of acceleration at each time-step. In this research, in order to applying the stabilization process, first, a series of implicit standard formulas were derived from previous formulation. Then after inserting two controlling parameters γ and β in the standard formulas, unconditional stability is guaranteed.
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ISSN:0045-7949
1879-2243
DOI:10.1016/j.compstruc.2015.02.030