## 4 Simulation Experiment and Mathematical Model Validation
### Finite Element Simulation of the Temporary Support Robot and the Floor  
To analyze whether the stresses on the TSR itself and the floor under stable support conditions meet the strength requirements, the stress characteristics of the floor and the TSR were simulated and analyzed using finite element analysis. In the finite element analysis process, the model constructed in Section 2.3 of the TSR was imported into the ANSYS Workbench 2023 R1 software, omitting non-load-bearing components such as support columns; small structures like lifting rings and mounting holes were ignored; the effects of rounded corners and welding on the load-bearing characteristics of the support were not considered; and equivalent loads were used to replace the column structure. The relevant parameters of the simulation model are consistent with those described in Section 4.1. According to the actual working environment of the TSR, appropriate parameters are selected, and the relevant parameters are shown in Table 4. Based on this, the automatic mesh generation function in the software was used to mesh the simulation models of the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline the distance from each hinge point on the top beams of & \\ support 1 and support 2 to the roof \(H_{1}\)/mm & 0.3 \\ the distance from each hinge point on the bases of & \\ support 1 and support 2 to the base \(H_{2}\)/mm & 0.3 \\ the distances from point A\({}_{1}\) to the tail end of support 1 \(L_{1}\)/mm & 2.8 \\ the distances from point A\({}_{2}\) to the tail end of support 1 \(L_{2}\)/mm & 2.8 \\ the distances from point A\({}_{3}\) to the tail end of support 1 \(L_{3}\)/mm & 1.2 \\ the distances from point A\({}_{4}\) to the tail end of support 1 \(L_{4}\)/mm & 1.2 \\ the distances from point B\({}_{1}\) to the tail end of support 2 \(L_{5}\)/mm & 2.9 \\ the distances from point B\({}_{2}\) to the tail end of support 2 \(L_{6}\)/mm & 2.9 \\ the distances from point B\({}_{3}\) to the tail end of support 2 \(L_{7}\)/mm & 1.2 \\ the distances from point B\({}_{4}\) to the tail end of support 2 \(L_{8}\)/mm & 1.2 \\ the vertical distance from the roof to the floor \(H\)/m & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Other parameters for the virtual prototype model. Figure 9: Value range of specific pressure \(P_{22d}\). TSR and its corresponding floor, resulting in a finite element model with 29,282 elements and 13,631 nodes for support 1, and a model with 25,762 elements and 11,204 nodes for support 2. When the TSR achieves a bottom pressure of 0.2 MPa, it can be calculated using the pressure formula and Equation (2) that the bottom pressure of support 1 on the roof is approximately 0.1 MPa. Similarly, when the TSR reaches a bottom pressure of 0.2 MPa, it can be calculated using the pressure formula and Equation (5) that the bottom pressure of support 2 on the roof is approximately 0.18 MPa. Based on the model shown in Figure 4, a simulation analysis of the load on the top beam was conducted, as illustrated in Figures 4 and 10. Figure 10 shows the simulation results under a uniform load of 0.1 MPa applied to the top beam of support 1, where Figure 10 represents the stress cloud diagram of support 1 and Figure 10 represents the stress cloud diagram of the floor under support 1. Figure 11 shows the simulation results under a uniform load of 0.18 MPa applied to the top beam of support 2, with Figure 11 representing the stress cloud diagram of support 2 and Figure 11 representing the stress cloud diagram of the floor under support 2. From Figure 10a, it can be seen that under a uniform load of 0.1 MPa applied to the top beam of support 1, the overall stress on support 1 is within the range of 121 MPa, which is below the yield strength of Q690. The peak stress is concentrated on the rib plate at the hinge between the top beam and the support cylinder, indicating that this part of the structure is more prone to damage under these conditions. The displacement of support 1 is within the range of 11 mm.