# Model Updating of a Freight Wagon Based on Dynamic Tests under Different Loading Scenarios
## 4 Numerical Modelling  
### Description  
A three-dimensional finite element model of the _Sgnss_ was developed in ANSYS [55] software, as presented in Figure 10. The FE model allows for the reproduction of the dynamic behaviour of the vehicle in the vertical (Z) direction. Some strategic degrees-of-freedom in the lateral (Y) and longitudinal (X) directions of the wagon platform were restrained to prevent movements in these two directions as well as yaw rotations.  
The vehicle's main platform was modelled with beam finite elements (BEAM 188), taking into consideration their corresponding geometrical properties validated on field observations. The plates attached to the platform extremities were modelled through shell elements (SHELL 181) considering their real thickness. The bogie frames and axles were modelled using flexible beam elements based on their corresponding geometrical properties, and the axle boxes and spring holders were modelled using rigid beam elements, as shown in Figure 10. The suspensions were modelled as spring-dashpot assemblies using COMBIN14 elements in the vertical direction. The wheel-rail contact was modelled by a spring-dashpot assembly (COMBIN14), whose stiffness is estimated by the Hertz contact theory [56]. The vehicle tare mass was incorporated into the model by an equivalent density  
Figure 10: FE numerical model of the _Sgnss_ vehicle including a detail of the bogie.  
of the steel girders and plates to consider the extra mass associated with bolted/welded connections, strengthening plates, etc. Additionally, concentrated mass elements (MASS 21) were added to account for the mass of some non-structural elements, namely the stanchions for the roundwood accommodation (including or not including the timber, accordingly to the adopted loading scheme), suspensions and other bogie components, braking system, reservoirs, piping, on-board control equipment, wheelset and edges back stop and front stop. The positioning of the concentrated masses is presented in Figure 10, where a detail of one bogie is also shown.  
The loaded numerical model considered the towel load configuration (load values and layout), similar to the one used during the dynamic test of the _Sgnss_ wagon (Section 3). In the unloaded numerical model, no overload due to the eucalyptus roundwood was considered, but it included the masses of the stanchion structures. In the loaded model, the mass of the stanchions indirectly considers the effect of the masses distributed along its height, namely those related to the laterally supported towel overload. Thus, besides the towel load translational mass, the stanchions masses also include the rotary mass inertias dependent of the distance between the base of the stanchion and the towel mass levels.  
Table 2 summarizes the geometric and mechanical parameters of the numerical model of the Sgnss wagon, including its designation, the adopted value and respective unit, as well as some references. Additionally, Table 2 lists the lower and upper limits of the parameters that were used in the model calibration phase (Section 5). The limits adopted for the steel deformability modulus indirectly consider the existing uncertainties on the dimensions of the steel sections (and corresponding geometrical properties) and on the type of connections between steel bars (assumed as rigid, but in some cases might have a semi-rigid behaviour). The vertical stiffness of each set of suspension springs, represented by the parameters \(K_{1}\) to \(K_{4}\), was considered independent since there was no guarantee that all the sets of coil springs had the same conservation state.