A time stepping method in analysis of nonlinear structural dynamics

Abstract

In this paper a new method is proposed for the direct time integration method for structural dynamics problems. The proposed method assumes second order variations of the acceleration at each time step. Therefore more terms in the Taylor series expansion were used compared to other methods. Because of the increase in order of variations of acceleration, this method has higher accuracy than classical methods. The displacement function is a polynomial with five constants and they are calculated using: two equations for initial conditions (from the end of previous time step), two equations for satisfying the equilibrium at both ends of the time step, and one equation for the weighted residual integration. Proposed method has higher stability and order of accuracy than the other methods.