An Unconditionally Stable Explicit Method for Structural Dynamics

An explicit integration method with unconditional stability was proposed and presented in this paper. Numerical characteristics of this explicit method for linear elastic sys-tems are almost the same as those of the constant average acceleration method while for a nonlinear system it is more efficient in computing than for the constant average acceleration method. This explicit method integrates the most promising advantages possessed by the explicit and implicit methods. No limitation on the time step in satisfying the stability limit, which is the most important property for an implicit method, is theoretically proved for this explicit method. Furthermore, the avoidance of solving any implicit system or using any iterative procedure, which usually brings considerable simplification in practical applications for explicit methods, leads to the very low cost of one explicit step. Thus, the computational effort can be significantly reduced when compared to implicit methods in each time step. Consequently, this explicit method can be used to solve dynamic problems efficiently due to the unconditional stability and the very low cost of explicit steps. Rough guidelines with regards to the selection of a time step in achieving accurate solutions for the constant average acceleration method are also appropriate for the proposed explicit method.