A non-oscillatory time integration method for numerical simulation of stress wave propagations

•A new time integration scheme is proposed to solve stress wave propagation problems.•Stability, accuracy, and dispersion of the proposed method are analyzed.•The response for the 1D and 2D wave problems are provided using the proposed method.•The proposed method yields non-oscillatory results for wave propagation problems. When the compressive loads are dominant in a composite structure, a tensile stress may be induced owing to the propagation of a stress wave and the interaction between an incident wave and a reflection wave, thus leading to the occurrence of cracks. Therefore, stress wave have a significant effect on the life of composite structures. In this study, a four sub-step explicit time integration scheme is proposed for solving stress wave propagation problems. This method builds on the fourth-order central difference method and a high-order derivative term to minimize the numerical oscillation. The proposed scheme possesses a first-order accuracy in the case of undamped and damped systems. Stability, accuracy, and dispersion of the proposed explicit direct time integration scheme are analyzed. Furthermore, the performance of this scheme is illustrated by the solution of a stress wave propagation and wave reflection in a one-dimensional impact problem and two-dimensional scalar wave propagation.