Implementation of an Advanced Macroelement Beam Model under Moving Load (Case Study: Iranian Railroad Projects)

This study aims to present a new three-dimensional moving macroelement for the numerical analysis of beam on the elastic foundation under moving loads as a railroad track vibration. Our research is based on a case study conducted in Iranian Railroad Projects. Due to involving a large number of elements, vibration analysis of beams as railroad tracks with standard three-dimensional elements is time-consuming. Two approaches are used and combined in this research to improve analysis of realistic models. The former is to use a macroelement with a number of degrees of freedom that can be used in lieu of standard three-dimensional elements. The latter is to use moving elements to ensure that the loads do not approach the boundaries of the model, thus leading to boundary errors. Accordingly, the moving element was formulated at different velocities to allow correct evaluation of the trains’ acceleration and deceleration effect. The analysis is based on a linear model. Examples with different number of elements and boundary conditions were included to evaluate the effects of the track parameters. One important aspect of the formulation is the asymmetric nature of stiffness and damping matrices due to the effects of velocity and the moving load. In the moving element method, with a sufficient number of elements, no end condition effect exists. However, because acceleration may be a more critical parameter than displacement, the number of elements must be determined for acceleration, as well. Our important achievements include formulating the interaction of lateral and torsional degrees of freedom, the possibility of calculating probable warping in the beam due to cross-sectional slenderness both directly and based on introducing a dependent degree of freedom, and also determining the model length based on vibrational acceleration at the end of the model. Besides, reduction of analysis time is a prominent feature of the present model.