## 3 Design of Recyclable Corrugated Vibration Isolation Box
### Study on Scaled Test Model
#### 3.1.2 Numerical Analysis for Assessing the Durability of the Internal Lattice Structure  
The strengths of the scaled test models were obtained by three-point bending tests for the design of the BCCB Trench prototype, and the numerical analysis phase was started to evaluate the durability of the internal lattice structure. Using the data obtained from the laboratory tests, a model validation study was carried out using the finite element method. The validated model enables modification of the internal frame design of the prototype without the need for additional experiments. Thus, the strength of the BCCB Trench can be increased when it is necessary to work on soils with lower bearing capacity than the sample soil in the current study or in deeper excavations. The material properties of the Scaled Model-4, which can withstand the lateral soil pressure calculated with the soil properties of the test area and has the lowest impedance, were entered into SAP2000 (v20) software [48], and load definitions were made by providing boundary conditions suitable for 3-point bending tests, and the model was created. The cardboard and balsa layers of the specimen were defined as plate elements in the Shell Section Layer Definition section. In the experimental studies, the force of 0.698 kN, which is the maximum force value that the Scaled Model-4 can carry, was applied vertically to the top plate center point of the specimen. In order to determine the ideal finite element size for the plate element to transfer the load, the mesh density was first investigated, and it was found that the solution moved away from the solution as the number of finite elements decreased (Table 2). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Scaled Model**} & **Dimension** & **Internal Frame** & **Max. Force** & **Max. Displacement** & **Max. Shear** & **Density** \\  & **(cm)** & **Type** & **(N)** & **(mm)** & **Stress (N/mm\({}^{2}\))** & **(kg/m\({}^{3}\))** \\ \hline
1 & 20 \(\times\) 40 \(\times\) 6.2 & Balsa & 2414.06 & 17.59 & 1.54 & 179 \\
2 & 20 \(\times\) 40 \(\times\) 4.2 & Corrugated & 501.56 & 15.50 & 0.68 & 130 \\
3 & 20 \(\times\) 40 \(\times\) 6.2 & Corrugated & 940.63 & 23.13 & 0.58 & 134 \\  & & Cardboard & & & & \\
4 & 20 \(\times\) 40 \(\times\) 4.2 & Corrugated & 698.44 & 23.99 & 0.95 & 123 \\  & & Cardboard & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparative results of 3-point bending test. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{2}{c}{**Mesh Size**} & \multirow{2}{*}{**Number of Elements**} & **Upper Plate Midpoint** \\
**a (mm)** & **b (mm)** & & **Displacement (mm)** \\ \hline
8.35 & 10 & 960 & 27.84 \\ \hline
16.7 & 20 & 240 & 26.72 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimization of the mesh density. The optimum result was obtained by solving the model using a 40 \(\times\) 3.4 mm mesh. The variation of top plate midpoint displacement values according to the number of finite elements is given in Figure 6.  
Once the optimal number of finite elements was determined, the suggested model underwent analysis. The displacement at the upper plate's midpoint of the specimen measures 25.09 mm (Figure 7). The maximum shear stress value was found to be 0.001245 kN/mm\({}^{2}\). \begin{table}
\begin{tabular}{c c c c} \hline \multicolumn{2}{c}{**Mesh Size**} & \multicolumn{1}{c}{**Upper Plate Midpoint**} \\ \hline
**a (mm)** & **b (mm)** & **Number of Elements** & **Displacement (mm)** \\ \hline
33.4 & 40 & 60 & 25.09 \\ \hline
100.2 & 200 & 4 & 12.69 \\ \hline
200.4 & 400 & 1 & 0 \\ \hline \end{tabular}
\end{table} 
Table 2: _Cont._  
Figure 6: The variation of top plate midpoint displacement values according to the number of finite elements. Figure 7: Analyzing the model of Scaled Model-4 in SAP2000 software. The load-displacement curves obtained with the finite element model and the load-displacement curves of the experimental results were compared (Figure 8). The numerical results matched the experimental results by 95%.