# Modelling Upholstered Furniture Frames Using the Finite Element Method
## 3 Results and Discussion
### Bed Edge Stiffness and Strength  
The analyses revealed that the applied loading method and subsequent deformation of frame elements resulted in stress values consistent across all variants of frames within a given group, regardless of the material used. These stress levels, if nearing the material's strength limits, could compromise the structural integrity of individual components and the entire frame. However, simulations indicated that normal stresses at critical points (e.g., near maximum deflection) remained below the material's bending strength. For these analyses, a constant load was applied throughout. Displacement (deflection) in the direction of the load was considered a direct measure of stiffness. It was observed that increased deflection corresponded to reduced stiffness of the structure. Figures 5-7 present displacement and normal stress maps for all analysed bed frame models constructed from various raw materials. Table 2 summarises the exact values of normal stresses and displacements for all models. The highest stiffness was observed in frames made from Scandinavian pine wood. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{2}{c}{**Frame**} & \multirow{2}{*}{**Species**} & \multirow{2}{*}{**Land (Habitat)**} & **Strength** & **Normal** & \multirow{2}{*}{**Deflection**} \\ \cline{3-5} \multicolumn{2}{c}{**Version**} & & & **Class** & **Stress** & & \\ \hline \multicolumn{2}{c}{} & & \multicolumn{2}{c}{**EN 338**[64]} & **MPa** & **mm** \\ \hline \multicolumn{2}{c}{} & & \multicolumn{1}{c}{Poland} & C24 & 13.9 & 12.0 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 13.9 & 9.5 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C24} & 13.9 & 9.8 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{Scandinavia} & C30 & 13.9 & 9.7 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{Eastern Europe} & C24 & 13.9 & 9.8 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 13.9 & 9.7 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C24} & 13.8 & 10.7 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 13.8 & 11.1 \\ \hline \multicolumn{2}{c}{} & & \multicolumn{1}{c}{Poland} & C24 & 14.5 & 11.8 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 14.6 & 9.4 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C24} & 14.6 & 9.6 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 14.6 & 9.5 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C24} & 14.6 & 10.5 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 14.6 & 11.4 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C24} & 14.6 & 10.6 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 14.6 & 11.0 \\ \hline \multicolumn{2}{c}{} & & \multicolumn{1}{c}{Poland} & C24 & 8.0 & 3.8 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 8.0 & 4.1 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C24} & 8.1 & 3.4 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 8.1 & 3.2 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C24} & 8.0 & 4.8 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 8.4 & 4.4 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C24} & 8.0 & 4.2 \\ \multicolumn{2}{c}{} & & \multicolumn{1}{c}{C30} & 8.0 & 4.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Normal stresses and deflection (displacement) of the long frame (edge) of bed version A1 W3. Figure 5: Mesh (computational) model of the A1 W3 version bed frame with the distribution of the displacement (deflection) map of the bed frame (edge) in the direction of external load action. Figure 6: Mesh (computational) model of the A1 version of the bed frame with the distribution of the displacement (deflection) map of the bed frame (edge) in the direction of the external load. In analysing the stiffness of all the frames constituting the bed edge, it should be stated that in the case of both the A1 and A2 frame constructions, the most rigid bed edge in most cases is an element made of pine wood from Scandinavia.