Alpha-Modification of Cubic B-Spline Direct Time Integration Method

Abstract

Recently, a conditionally stable explicit time integration scheme using the cubic B-spline function was proposed for solving the structural dynamic problems. This paper presents a new unconditionally stable version of the previous algorithm, based on the uniform cubic B-spline piecewise polynomial approximations and collocation method. First, the method is implemented to solve the differential equation of motion for the single-degree-of-freedom (SDOF) systems. Then, it is generalized for the multi-degree-of-freedom (MDOF) systems. In this paper, a simple step-by-step algorithm is presented for the proposed method, with the stability and accuracy analyses carried out. The unconditional stability of the method is achieved through use of an adjustable collocation parameter [Formula: see text]. The computational accuracy and efficiency of the proposed method are demonstrated in three numerical examples.