A Family of Cubic B-Spline Direct Integration Algorithms with Controllable Numerical Dissipation and Dispersion for Structural Dynamics

In recent years, a conditionally stable explicit time integration scheme using cubic B-spline function has been proposed for solving the problems in structural dynamics. The current paper presents a scheme where this method is developed to an efficient implicit unconditionally stable time integration method. In this research, in order to apply the stabilization process, first, a series of implicit standard formulas were derived from previous explicit formulation. Then after inserting two controlling parameters γ and β in the standard formulas, unconditional stability is guaranteed. The values of these two parameters have been determined to not only maintain the stability but also ensure the desired accuracy. Finally, for the new method, a simple step-by-step algorithm is presented. Stability and accuracy analysis of the proposed algorithm has been completely investigated. The efficiency and computational cost of the proposed method are demonstrated through two numerical simulations. Compared with those from some of the existing numerical methods in the literature, such as the Bathe method, the proposed method has higher computation efficiency with less time consumption.