A parabolic acceleration time integration method for structural dynamics using quartic B-spline functions

In this paper, an explicit time integration method is proposed for structural dynamics using periodic quartic B-spline interpolation polynomial functions. In this way, at first, by use of quartic B-splines, the authors have proceeded to solve the differential equation of motion governing SDOF systems and later the proposed method has been generalized for MDOF systems. In the proposed approach, a straightforward formulation was derived in a fluent manner from the approximation of response of the system with B-spline basis. Because of using a quartic function, the system acceleration is approximated with a parabolic function. For the aforesaid method, a simple step-by-step algorithm was implemented and presented to calculate dynamic response of MDOF systems. The proposed method has appropriate convergence, accuracy and low time consumption. Accuracy and stability analyses have been done perfectly in this paper. The proposed method benefits from an extraordinary accuracy compared to the existing methods such as central difference, Runge–Kutta and even Duhamel integration method. The validity and effectiveness of the proposed method is demonstrated with four examples and the results of this method are compared with those from some of the existent numerical methods. The high accuracy and less time consumption are only two advantages of this method.