## 5 FEM Numerical Tests of the Strength of the Basic Platform and Sets in the Design Version
### Multi-Variant FEM Numerical Analyses in Shell-Beam Models  
At the stage of designing the structure, multi-variant tests of 10-foot platforms were carried out in simplified models with the use of limit operating loads, with different methods of loading the load with the maximum value of \(\mathrm{Q_{max}}=100\) kN. In Variant 1 of the FEM analysis, in the shell-beam models, the case of loading the model of the platform placed on the horizontal surface of the ground with the \(\mathrm{Q_{max}}\) load was represented. Variant 2 corresponds to the rope lifting of the above-mentioned load using a four-section, symmetrical sling. In Variant 3, the lateral lifting of the platform with the use of forklift devices was recreated. In Variant 4, a critical case of loading logs using a hook device with boundary conditions and reduced loads was defined, which is shown in Figure 6. Loads from hook lifting determined as a result of MBS dynamic analyses in the model of the basic 10-foot platform were applied to the end carriage in the nodes of mounting the handle cooperating with the hook of the lifting device in the form of the component forces: vertical \(\mathrm{S_{y}}\) and horizontal \(\mathrm{S_{x}}\) (Tables 1 and 2). In each load variant, the dead weight of the platform was also taken into account. The support and reduced load conditions used in multi-variant models 1-4 are discussed in detail in Section 6.1, on the example of FEM solid-shell models of the platform, in which the components of the platform's movable connections were more precisely represented. Figure 10: Three-dimensional numerical model of the platform used in multi-variant FEM analyses: Boundary conditions: 1—supports—non-movable articulated constraints; 2—vertical constraints; 3 and 4—model of an equivalent load on the structure with its own weight and load with the weight of 100 kN distributed continuously on the crossbeam of the bottom of the frame; 5—reduced loads modeling the operation of the hook; simplified discrete model of the end carriage wall rotating joint in the side of the frame; 6—beam elements; 7—RBE2 kinematic elements; 8—2D shell elements modeling the end carriage. The colors indicate the groups of elements used in the beam-shell model of the platform: red, yellow, green and navy blue—CBEAMS beam elements with different parameters, blue—2D shell elements. Table 3 summarizes the selected maximum results of multi-variant FEM analyses obtained in the shell-beam models of 10-foot platforms. The results presented in Table 3 were determined as part of quasi-static FEM analyses, in which Variants 1-4 were used, representing the limit operating loads, with different methods of loading the platform. Based on the comparison of the maximum values of displacements and reduced stresses, it was confirmed that the most unfavorable variant generating the maximum effort of the platform is Variant 4 of loads corresponding to the operation of lifting the platform with a load using a hook device. Numerical Tests of the Strength of the Platform-Container in the Prototype Version Including Removable Connections  
Based on the results of the numerical tests presented above, a structural design of the 10-foot platform was developed in the prototype version (Figure 14a), in which the areas of movable joints between the platform components were represented in detail. Appropriate 3D FEM models were built in which the areas of joints between the removable components of the platform-container were more precisely represented [34, 36]. The main components of the platform: frame, end carriage stiffeners, connections of the end carriage with the frame, braces, and stanchions were modeled using solid elements (Figure 14a). In this version of the 3D models, the shape of all components of the movable connections was represented, including holes cooperating with screw joints or pins. Fasteners in movable connections (marked 1-3 in Figure 9) were represented using RGB kinematic elements (7 in Figure 10, as in multi-variant models).