# Dynamic Load Modelling within Combined Transport Trains during Transportation on a Railway Ferry
## 4 Results  
To check the adequacy of the mathematical model (1), we carried out a computer simulation of the dynamic load of a container placed on a flat wagon. For computer simulation of the dynamic load of a flat wagon with containers based on the suggested solution, we used the CosmosWorks package [44; 45; 46; 47]. The calculation was done using the finite element method. Spatial isoparametric tetrahedra were used to build the finite element model. The optimal number of finite elements was determined by the graphical and analytical method [48; 49; 50; 51]. The number of nodes was 302,512 and the number of elements was 883,801. The maximum element size was 100 mm, the minimum size was 20 mm. The design scheme considered that the carrying structure was affected by the vertical load of the container gross weight \(P_{gw}\), the tension of chain binders \(P_{f}\), the wind load \(P_{w}\), as well as the horizontal load of the container on superstructure \(P_{h}\), due to fluctuations of the flat wagon (see  
Figure 5: Accelerations applied to the container during transportation on a railway ferry.  
Figure 6). Since the chain coupler has certain angles of inclination relative to the wagon when securing, when creating the computational scheme, the load that is transmitted to the supporting structure of the flat wagon through the chain coupler is laid out in three components. At the same time, the angle of inclination of the chain coupler was taken into account: in the plane YZ, the angle of inclination was \(30^{\circ}\), for XY and XZ it was \(60^{\circ}\).  
The container was subjected to the vertical static load \(P_{5}^{c}\), the horizontal load in the areas of interaction with superstructures \(P_{ht}^{c}\), as well as the wind load on the side surface \(P_{w}^{c}\).  
Fixing the model was carried out in the areas where it rests on the bogies as well as the working surfaces of mechanical stop-jacks. To do this, the model was fitted with pads, the area of which was equal to the area of the working surfaces of the stop-jacks. The carrying structure material was 09G2S [52; 53; 54]. Between the interaction zones of the container and the superstructures of the flat wagon, we established a viscous linkage with a coefficient of viscous resistance 1.2 kN-s/m. The results of calculating the acceleration of a container placed on a flat wagon, taking into account different roll angles of a railway ferry, are shown in Figure 7. The maximum acceleration in this case affected the upper part of the containers along the central axis of the symmetry of the load-bearing structure of the flat wagon and was about 2.6 m/s\({}^{2}\).  
Figure 6: Design scheme of the load-bearing structure of the flat wagon with a container.  
Figure 7: Distribution of acceleration fields relative to the load-bearing structure of a flat wagon with containers.  
The accelerations acting on the container obtained by theoretical and computer modelling are shown in Figure 8, which shows that the maximum percentage of discrepancy between accelerations was 17.7% at the roll angle 10\({}^{\circ}\).  
Thus, given the viscous connection between the flat wagon and the container during transportation on a railway ferry, it becomes possible to reduce the dynamic load of the container supporting structure and improve the safety of sea transport.  
The F-criterion was used to check the adequacy of the mathematical and computer models developed by the authors. The roll angle of the railway ferry was taken into account as a variation parameter (5\({}^{\circ}\)-30\({}^{\circ}\)). If the value of the dispersion adequacy S\({}_{\text{a}}\) = 6.0 and the dispersion reproducibility S\({}_{\text{y}}\) = 4.21, the calculated value of the criterion was F\({}_{\text{p}}\) = 1.41, which was less than tabular F\({}_{\text{t}}\) = 4.53. Hence the hypothesis of adequacy was not rejected.  
In the future, it is planned to conduct a physical experiment aimed at studying the dynamic load of a container placed on a flat wagon during transportation by sea.