An explicit time integration method for structural dynamics using septuple B-spline functions

Abstract

SUMMARYIn this paper, an explicit time integration method with three parameters is proposed for structural dynamics using periodic septuple B‐spline interpolation polynomial functions. In this way, by use of septuple B‐splines, the authors have proceeded to solve the DE of motion governing a single DOF system, and later, the presented method has been generalized for a multiple DOF system. In the proposed method, a direct recursive formula for response of the system was formulated on the basis of septuple B‐spline interpolation approximation. In terms of the specific requirements of this proposed method, two initialization approaches are given for initial calculation. One is called direct initialization, and the other is indirect initialization. The stability analysis of the proposed method illustrates that, by use of adjustable parameters, a high‐frequency response can be damped out without inducing excessive algorithmic damping in important low frequency modes. The computational accuracy and efficiency of the proposed method is demonstrated with three numerical examples, and the results from the proposed method are compared with those from some of the existent numerical methods, such as the Newmark and Wilson‐ θ methods. The compared results show that the proposed method has high accuracy with low time consumption. Copyright © 2013 John Wiley & Sons, Ltd.

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