Generalized Implicit Multi Time Step Integration for Nonlinear Dynamic Analysis

Abstract

This paper deals with a generalized multi time step integration used for structural dynamic analysis. The proposed method presents three kinds of implicit schemes in which the accelerations and the velocities of the previous steps are utilized to integrate the equations of motion. This procedure employs three groups of weighted factors calculated by minimizing the numerical errors of displacement and velocity in Taylor series expansion. Moreover, a comprehensive study on mathematical stability of the proposed technique which is performed based on the amplification matrices proves that the new method is more stable than existing schemes such as IHOA. For numerical verification, wide range of dynamic systems including linear and nonlinear, single and multi degrees of freedom, damped and undamped, forced and free vibrations from finite element and finite difference methods are analyzed. These numerical studies demonstrate that efficiency and accuracy of the proposed method are higher than other techniques.