An unconditionally stable implicit time integration algorithm: Modified quartic B-spline method. (June 2015)

• Record Type: Journal Article
• Authors: Shojaee, Saeed; Rostami, Sobhan; Abbasi, Asghar
• Is Part Of: Computers & structures. Volume 153(2015)
• Page Start: 98
• Page End: 111
• Publication Date: 2015-06
• Subjects: Quartic B-spline -- Time integration -- Implicit -- Second order acceleration -- Unconditional stability; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2015.02.030
• Languages: English
• ISSNs: 0045-7949

Abstract

Highlights: 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. Abstract: 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.