A weighted composite implicit direct time integration method in structural dynamics and wave propagation

This paper introduces a novel two-step composite implicit direct time integration method for linear and non-linear problems in the fields of structural dynamics and wave propagation. This method employs a hybrid approach, utilizing both the Newmark method and backward differential formulas (BDFs). The first sub-step of this method involves the application of a weighted combination of the Newmark and three-point backward methods, while the second sub-step employs the four-point backward method. The method introduced herein exhibits both unconditional stability and commendable accuracy. The efficiency of the new method was evaluated through numerical simulations. These results were then compared to those obtained using the single-step Newmark scheme and Wen and Bathe family’s composite methods. To assess the performance of the developed method, both linear and non-linear problems were examined, including challenging examples from the fields of structural dynamics and wave propagation.