## 2 Design and Methodology
### Mesh and Study Validation  
Since there is a discrepancy in the structure design dimensions (from 0.5 mm (minimum side size) to 50 cm (maximum side size)), a custom mesh is used in the study to ensure accurate results. The minimum and maximum element sizes are set to 0.1 and 2 cm, respectively. Other element size parameters are important to mention such as the maximum element growth rate of 1.4, a curvature factor of 0.4, and a resolution of narrow regions of 0.7. A smooth transition to interior mesh is selected and the number of boundary layers is defined to be 15 with a factor of 1.2. A high-quality mesh and reliable outcomes are guaranteed by the specified element size and boundary layer parameters. (Figure 2). Seven mesh studies with varying qualities are developed and simulation data are collected for each study for a fixed load magnitude and position to assess mesh quality and simulation accuracy. The study's parameters details are shown in Table 1.  
The values of the potential difference measured by the sensors L2 and R2 are given in Figure 3. One can notice that the voltage values for each of these sensors are fluctuating for Studies 1 to 4 with an average error of 23.35%. However, in Studies 6 and 7, the voltage values of each sensor are converging to the same result with an average error of 1.1%. Considering this, we can verify the simulation outcomes based on the parameters established in Studies 6 and 7. We then proceed with our study using the same mesh parameters as in Study 6. \begin{table}
\begin{tabular}{p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt} p{56.9 pt}} \hline \hline
**Study** & \begin{tabular}{c} **Maximum** \\ **Element Size** \\ **(cm)** \\ \end{tabular} & \begin{tabular}{c} **Minimum** \\ **Element Size** \\ **(cm)** \\ \end{tabular} & \begin{tabular}{c} **Maximum** \\ **Element Size** \\ **(cm)** \\ \end{tabular} & \begin{tabular}{c} **Resolution** \\ **Element Size** \\ **(cm)** \\ \end{tabular} & \
\begin{tabular}{c} **Thickness** \\ **of Narrow** \\ **(rowth Rate)** \\ \end{tabular} &
\begin{tabular}{c} **Adjustment** \\ **Factor** \\ \end{tabular} \\ \hline
1 & 8 & 5 & 5 & 2 & 1 \\
3 & 5 & 2 & 2 & 2 & 1 \\
4 & 5 & 2 & 1.4 & 2 & 1 \\
5 & 3 & 1 & 1.4 & 2 & 1 \\
6 & 2 & 0.1 & 1.4 & 0.7 & 1 \\
7 & 2 & 0.1 & 1.4 & 0.7 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters details of different mesh studies. Figure 2: Design showing a good quality of structure mesh. One can observe that the highest value of stress is obtained when a 40 kg load magnitude is applied at a location far from the structure's fixed edge (x = 30 cm). The effect of the load position on the voltages provided by the sensors is shown in Figure 5. When the load is located at the structure's fixed edge (x = 0 cm), the highest voltage reading is provided by sensor L2 and negligible voltage readings are provided by the remaining sensors (L1, L3, R1, R2, R3). However, when the applied load is shifted from the structure's fixed edge, the voltage values provided by all sensors are obtaining higher with maximum voltage values measured by the closest sensor to the load location. As the load is displaced on the axis aligned with L2 and R2, these two sensors always provide the highest voltage values depending on the load position. The results are logical, since when higher stress is applied to the sensor's surroundings, a higher displacement of crystal atoms in the piezoelectric material of this sensor results in higher electric dipoles within the medium and, therefore, a greater charge potential difference. Thus, this can be considered as a validation of our study results, as sensors L1, L3, and R1, R3, are symmetrical and should provide similar values, which is confirmed in our results (see Figure 6). Figure 4: (a) [PERSON] stress distribution for a 40 kg load applied at x = 0 cm (edge of the structure); (b) [PERSON] stress distribution for a 40 kg load applied at x = 30 cm from the structure’s fixed edge.