Improved Explicit Method for Structural Dynamics

An explicit method, which simultaneously has the most promising advantages of the explicit and implicit methods, is presented. It is shown that numerical properties of the proposed explicit method are exactly the same as those of the constant average acceleration method for linear elastic systems. However, for nonlinear systems, it has unconditional stability for an instantaneous stiffness softening system and conditional stability for an instantaneous stiffness hardening system. This conditional stability property is much better than that of the Newmark explicit method. Hence, the proposed explicit method is possible to have the most important property of unconditional stability for an implicit method. On the other hand, this method can be implemented as simply as an explicit method, and hence, possesses the most important property of explicit implementation for an explicit method. Apparently, the integration of these two most important properties of explicit and implicit methods will allow the proposed explicit method to be competitive with other integration methods for structural dynamics.