Further insights into an implicit time integration scheme for structural dynamics

The objective in this paper is to present some new insights into an implicit direct time integration scheme, the Bathe method, for the solution of the finite element equations of structural dynamics. The insights pertain to the use of the parameters in the method, and in particular the value of the time step splitting ratio. We show that with appropriate values of this ratio large amplitude decays can be obtained as may be desirable in some solutions. We give the theoretical analysis of the method for the parameters used, including for very large time steps, and illustrate numerically the new insights gained.