A novel sub-step explicit time integration method based on cubic B-spline interpolation for linear and nonlinear dynamics.

A novel sub-step explicit time integration method is proposed. In the procedure, uniform cubic B-spline function interpolation is employed to achieve high-order accuracy. The proposed method has multiple free parameters which can be used to control algorithm properties. The proposed method shows at least second-order accuracy for linear systems with and without damping, and especially, when proper algorithmic parameters are selected, it can achieve third-order accuracy for no damping case. Numerical example analysis confirms higher accuracy than other classical explicit methods. For both linear and nonlinear dynamic problems, the proposed method shows desirable accuracy and efficiency.