An explicit method with improved stability property

Abstract

AbstractA new explicit method is presented. This method has an enhanced stability property when compared with the previously published explicit method (J. Eng. Mech. 2007; 133(7):748–760), which is unconditionally stable for linear elastic and any instantaneous stiffness softening systems based on linearized analysis whereas it is only conditionally stable for any instantaneous stiffness hardening system. In contrast to the previously published explicit method, the most important improvement of the new explicit method is that it can have unconditional stability for general instantaneous stiffness hardening systems in addition to linear elastic and instantaneous stiffness softening systems. Since these stability results are obtained from a linearized stability analysis they are applicable to the non‐linear systems that satisfied the simplifications used for the analysis. This explicit method is also shown to be second‐order accurate. It is computationally efficient in the solution of a general structural dynamic problem, where the total response is dominated by low‐frequency modes, when compared with explicit methods, such as the Newmark explicit method and the family of explicit methods developed by Tamma et al. (Comput. Methods Appl. Mech. Eng. 2003; 192:257–290), and implicit methods, such as the constant average acceleration method. Some numerical examples are used to confirm the enhanced stability property and the efficiency in computing. Copyright © 2008 John Wiley & Sons, Ltd.