Application of 2D-infinite beam elements in dynamic analysis of train-track interaction

Abstract

Railway structure is a structure with an infinite length for which its modeling is usually carried out by accepting some assumptions for boundary conditions. In practice, there are various methods of modeling by forming equations of motions and dynamic analysis. One of these methods is modeling the railway track by finite element method. Generally in such modeling, a limited length of a track is modeled and executed by implementing some boundary conditions. Assortment of boundary conditions has an effect on dynamic responses. To reduce such effects, usually the length of the track is chosen to such a measure to minimize the dynamic responses of the end points of the track elements to zero. Doing so would cause an increase in the length of the track and hence add to an equation's degrees of freedom, volume of output and prolongation of analysis time. For this reason, a combination of finite elements and infinite beam elements (two end elements) has been proposed for railway track modeling. Also, matrices of mass, damping and stiffness of one infinite element which has been laid on a visco-elastic bed, have been calculated by implementing selected shape functions. Therefore, by applying two infinite beam elements on either side of the model, a railway track is formed like a beam on an elastic bed which creates the possibility of eliminating the boundary condition effects.

Investigation on dynamic behavior of railway track in transition zone

“…The model length can exceed or, as in previous studies [9], the infinite boundary elements can be used to reduce the effects of the boundary conditions both in the ballasted and slab track models. The infinite boundary elements have been applied in this study.…”

Effects of vibration in desert area caused by moving trains

“…Fig. 5 Step load of train Then, finite and infinite elements were used in the modeling of track and its bed (infinite elements in boundary) [20]; see Fig. 6.…”

Evaluation of railway trackbed moduli using the rail falling weight test method and its backcalculation model

“…C r n is calculated from the Rayleigh method 18 as a function of K r n and M r n . Using the mapping method of Zakeri and Xia, 19 K r n and M r n are given as follows…”

“…in which is the mapping variable; J b j j ¼ 2a=ð1 À Þ 2 ; and the displacement is forced to be zero at distance ''a'' and farther. Zakeri and Xia 19 show that ''a'' equals to 10 sleeper spacing (6 m) and N…”

“…Cn r is calculated from the Rayleigh method 18 as a function of Kn r and Mn r. Using the mapping method of Zakeri and Xia, 19 Kn r and Mn r are given as follows where m r is the mass of rail per unit length, E is Young’s modulus of the rail, and I is the moment of inertia. [R1] and [R2] are described as follows 19 in which ξ is the mapping variable; |Jb|=2a/(1-ξfalse)2; and the displacement is forced to be zero at distance “a” and...…”