time integration method

The selection of a suitable numerical method to evaluate the dynamic behavior of structures, especially in nonlinear cases, is an important task in practice. Accordingly, the purpose of this study is to demonstrate the numerical features of a new single-step type of the Modified Energy Method (MEM) to compute the dynamic response of structural systems. A comprehensive formulation of this energy-based time integration scheme to incorporate the general nonlinear behavior in MDOF systems is presented for the first time ever in this paper. After discussing the stability and accuracy of the proposed time-stepping integration procedure, five applicable numerical examples in structural dynamics and earthquake engineering practices involving the various hysteretic behaviors and the effects of consistent mass and non-classical damping matrices are examined by the presented technique. In each case, the relevant comparisons are given in accordance to other available methods (e.g., Newmark and Runge-Kutta). Overall, the results indicate that the MEM yields a better accuracy than the 2nd Runge-Kutta approach. Furthermore, the distinguishing feature of the proposed method is to provide information about choosing the optimal size of the time intervals, especially in the nonlinear analyzes, which is not achievable in other applicable approaches.