## 1 Introduction  
A common method of changing the direction of a railway vehicle or diverting rail traffics from one route to another includes the use of railway turnouts, or so called'switches and crossings', as illustrated in Figure 1. The design of a railway turnout entails multidisciplinary engineering to overcome the burdens of the complex geometry of a turnout, which imposes restrictions such as lower operational speeds and high-quality maintenance to prevent derailments. The average cost of turnouts is estimated at 26,000 Euros per km by Banverket in Sweden [1]. The cost occupies 24% of maintenance and 23% of renewal budgets in the UK [2]. Furthermore, approximately 12,000 turnout related derailments have been reported in the EU, the annual cost of which is an estimated 200 million Euros [3]. Consequently, they are considered to be a top concern for smooth traffic management by infrastructure managers in Europe [4]. Accordingly, many studies have been devoted to improving the design and performance of the railway turnout system. Several types of research have offered effective configurations (such as gauge widening [5] and movable crossings [6]) to mitigate dynamic wheel-rail forces and to improve ride comfort. In reality, fundamental problems, such as fatigue and plastic damage caused by impact forces and stiffness variations along a turnout, still attract the attention of many researchers [7; 8; 9; 10; 11; 12]. Specifically, the number of studies has increased, in the last two decades, along with development of the computational power that facilitates the use of a numerical process. The reason behind opting for a numerical process is that analytical solutions are rare, and experimental setups to analyze the behavior of a turnout are expensive and time consuming. Furthermore, numerical tools provide a flexible environment for changing the parameters or generating various scenarios. The diverse applications of numerical methods include risk analysis [13], maintenance [14], failure detection [15], etc. ; however, the general propensity here involves investigating the dynamic behavior of wheel-rail contact forces over a turnout globally or locally [5; 9; 10; 11; 12]. The main motivation was that the prediction of track force spectra can be used for service life predictions of the safety-critical components [16; 17; 18; 19; 20]. Global or whole turnout analyses were conducted to evaluate the general behavior of a turnout under static or dynamic conditions [9; 11; 12], to optimize the design of a turnout [5; 21], or to tune the vertical track stiffness [22]. This type of analysis holds the advantage that the components of the track-vehicle couple are relatively simple/simply modeled and therefore, computationally less expensive. A common numerical tool for whole turnout analyses is multi-body simulation (MBS)  
Figure 1: The Finite Element Method (FEM) model. (**a**) The layout of a standard turnout; (**b**) the schematic vehicle-track couple; and (**c**) the crossing nose and wheel trajectory. where the bodies are simulated by multi degrees of freedom, and the contact theories are used to estimate contact forces. In general, Hertzian, Non-Hertzian, or Multi-Hertzian contact theories have been adopted to calculate normal contact forces and [PERSON]'s theories or [PERSON]'s method have been used for tangential forces [23; 24]. The disadvantage of the MBS is the limitation of the accuracy of estimated contact forces. For instance, it was found that the multi body simulation, having a resolution range over 500 Hz, consumed a significant amount of time and resources [25] whereas rail irregularities range up to 2000 Hz [26]. As a consequence, particular studies [14; 27; 28; 29] use quite detailed FEM (Finite Element Method) models to increase accuracy in the estimation of the contact forces. These FEM models require more computational power than MBS models, but their accuracy is higher and allows stress-strain level investigations on the contact patch.