An explicit time integration method for structural dynamics using cubic BB-spline polynomial functions

This paper presents a scheme where the cubic BB-spline method is developed for Multi-Degrees-Of-Freedom (MDOF) systems. In the proposed approach, a straightforward formulation in a fluent manner was derived from the approximation of the response of the system with a BB-spline basis. In this way, there is no need to use a special pre-starting procedure to commence solving the problem. A simple step-by-step algorithm is implemented and presented to calculate the dynamic response of MDOF systems. Stability and accuracy analyses have been done in this paper. The results of the accuracy investigation were compared with some other state of the art methods. Actually, this method lies in cases of conditionally stable methods. The validity and effectiveness of the proposed method is demonstrated with two examples.