A new model-dependent time integration scheme with effective numerical damping for dynamic analysis

Abstract

This paper presents a new semi-explicit dissipative model-dependent time integration algorithm for solving structural dynamics problems. Motivated by the superior properties of the composite time-stepping scheme, the proposed method is designed, so that it fully inherits the numerical characteristics of its parent algorithm, namely the Bathe method. The algorithm design procedure is carried out by assuming unknown integration parameters for the proposed method. Afterwards, by time discretization of an SDOF model equation, the unknown parameters can be obtained explicitly by solving nonlinear system of equations. Some numerical examples are analyzed by the presented technique and comparisons are also made with two other dissipative model-dependent time integration algorithms as well as the Bathe method. Results demonstrate that the suggested technique can effectively damp out the spurious oscillations of the high-frequency modes, while the other schemes exhibit significant overshoot in the calculated responses. Furthermore, it is also observed that numerical results of the presented method totally coincide with the parent algorithm. While the Bathe method subdivides each time increment into two sub-steps, the proposed algorithm is single-step, non-iterative and does not involve any time-step subdividing.