A Modified Multi Time Step Integration for Dynamic Analysis

This paper deals with new implicit multi time step integration for numerical dynamic analysis in constant time step. The proposed method tries to improve the main difficulties of the multi time stepintegrations i.e. high calculations and also high required memory. For this purpose, several previousvelocity and acceleration vectors are used to integrate the displacement and velocity of the current time step, respectively. It could be shown that only one set of weighted factors appears in the proposed technique so that the computational efforts and the required memory reduce compared with the similarmulti time step integrations which use several groups of weighted factors for controlling the stability and the accuracy. Therefore, simplicity, lower computational tasks and lower required memory are the main advantages of the new integration which made this method suitable for nonlinear dynamicanalysis of large systems. Here, the Taylor series expansion and the Routh-Hurwitz criterion are utilized to calculate the weighted factors and determine the stability domain of the proposed integration, respectively. For numerical verification, some dynamic systems i.e. the nonlinearvibration, the portal frame and the elastic pendulum are analyzed to clarify the ability and the efficiency of the new method. Results show that by a similar time step, the proposed time integration is more accurate and more rapid compared with the common approaches such as the Wilson-θ, the Newmark-β and some other multi time step schemes

Keywords:

Dynamic Analysis , Implicit Multi Time Step , Higher Order Integration