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 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 γγ and ββ in the standard formulas, unconditional stability is guaranteed.