Abstract
A family of new explicit time-integration method is proposed herein, which inherits the numerical characteristics of any existing implicit Runge–Kutta algorithms for a linear conservative system. Based on an exact derivation of the increment of mechanical energy, the method proposed is demonstrated to be unconditionally stable. Also, the stability condition of the proposed method is derived when applied to solving a nonlinear system. The characteristics of the proposed method are investigated by observing the mechanical-energy time history of a nonlinear conservative system. The numerical results can be explained by the stability condition derived in the nonlinear regime. Finally, the computational accuracy and efficiency between the Newmark time integration method and the proposed explicit method are compared in solving the dynamic response of a couple of linear oscillators.
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