Insight into an implicit time integration scheme for structural dynamics

In Refs. [1] and [2], an effective implicit time integration scheme was proposed for the finite element solution of nonlinear problems in structural dynamics. Various important attributes were demonstrated. In particular, it was shown that the scheme remains stable, without the use of adjustable parameters, when the commonly used trapezoidal rule results in unstable solutions. In this paper we focus on additional important attributes of the scheme, and specifically on showing that the procedure can also be effective in linear analyses. We give, in comparison to other methods, the spectral radius, period elongation, and amplitude decay of the scheme and study the solution of a simple ‘model problem’ with a very flexible and stiff response.

► Novel insight into a new time integration scheme, the Bathe method, is given.
► The spectral radius, period elongation, and amplitude decay are presented.
► The performance of the method is compared with that of other existing techniques in the solution of a model problem.