Weak Instability of Chen–Ricles Explicit Method for Structural Dynamics

Although the Chen–Ricles (CR) explicit method (CRM) (proposed by Chen and Ricles) has been claimed to have desired numerical properties, such as unconditional stability, explicit formulation, and second-order accuracy, it also shows some unusual properties, such as a less accuracy of solving highly nonlinear systems, a high-frequency overshoot in steady-state responses, and a weak instability. A correction scheme by adjusting the displacement difference equation with a loading term can be employed to extinguish the high-frequency overshoot in steady-state responses. However, there is still no way to get rid of the weak instability and to improve the less accuracy of solving highly nonlinear systems. It is recognized that a weak instability might result in inaccurate solutions or numerical explosions. Hence, the practical applications of CRM are strictly limited.