The Bathe time integration method revisited for prescribing desired numerical dissipation

Abstract

Abstract In this paper we further consider the Bathe method for the direct time integration in structural dynamics and wave propagations. The method uses two sub-steps per time step and is an unconditionally stable scheme frequently used without adjusting any parameter. In the first sub-step the trapezoidal rule is used and in the second sub-step the 3-point Euler backward method is employed. In this contribution we derive the method using, instead of the Euler scheme, the 3-point trapezoidal rule for the complete step with two Newmark parameters. The parameters can then be used to smoothly prescribe desired numerical dissipation, from zero to very significant dissipation. To highlight the performance of the method, the stability, accuracy and overshooting are studied and some illustrative problems are solved. The results are compared with those of some other methods that also use parameters to introduce numerical dissipation. We conclude that the use of the parameters in the Bathe method can be valuable but probably will require some numerical experimentation.