# Optimization of Sensor Positions and Orientations for Multiple Load Case Scenarios
## 3 Numerical Example  
In this study, a structure made of a composite matrix with 50% glass fiber and polyester is considered as the numerical example. The material consists of the properties shown in Table 1. A fine mesh consisting of 20-noded hexahedral elements was used in the FEM model shown in Figure 7.  
The geometrical dimensions of a composite structural model are shown in Figure 8.  
For strain-based optimization, the displacement boundary conditions are applied on the bottom side of the structure (Figure 9) as follows: zero displacement (A) was applied to the surface labeled 'A' to constrain movement along the x-axis, zero displacement (B) was applied to the edge marked 'B' to constrain movement along the y-axis, and zero \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameters** & **Values** & **Units** \\ \hline Young’s modulus & 13,000 & (MPa) \\ Poisson’s ratio & 0.30 & - \\ Thermal conductivity & 0.94060 & (W/m\({}^{\circ}\)C) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The material properties used in the numerical example. Figure 6: Flowchart of the optimization algorithm. FEM Data and Sensor Placement Area of the Structure_  
In this study, ANSYS Workbench 2022 R2 was used to simulate the composite structure [29]. The load case data used in the optimizations were obtained from FEM computations. The composite structure was discretized into about 130,000 (20-noded hexahedral) elements (see Figure 7), resulting in a total of about 600,000 nodes with strains or temperature values for each parameter under every load case. In strain-based optimization, the strain tensors were evaluated for each load case. From the FEM results, it has been determined that the maximal values of equivalent strains or temperatures are obtained from the shaded area of the structure shown in Figure 11. Therefore, the shaded area of the structure was considered for sensor placement optimization. Figures 12 and 13 show the behavior of the composite structure when seven different mechanical and thermal loadings are applied. In Figure 12, each load case, with the same 100 N force, has a unique strain field and maximum strain location depending on the load position. This spatial variation shows the extent to wh  
Figure 11: Sensor placement area of the structure. Figure 10: The locations of force applications on structural domain, shown in purple circles. localized and also directionally sensitive, due to complex interactions among the material geometry and boundary conditions. Some fields appear highly localized near the point of force application, while others demonstrate more diffuse heterogeneity of elevated strain, indicative of differences in stiffness of the loading path. The asymmetry in some of the distributions suggests stiffness gradients induced by geometry. Generally, there is no one point at which the samples experience peak strain in all the cases, validating the main point of this study. Placement of the sensor should sample those areas that involve multiple candidates for the maxima instead of one fixed spot. This is especially important since our strain sensor model is orientation sensitive, and thus positioning and angular alignment are critical factors to be considered. Figure 13 illustrates the map of the temperature distribution under applications of the Dirichlet boundary condition of 50 \({}^{\circ}\)C to the same locations. Another Dirichlet boundary condition of 25 \({}^{\circ}\)C was applied to the bottom surface. To all the other surfaces, a Neumann boundary condition was applied, assuming zero heat flux. Such thermal fields show a high gradient in the region around the heated zones, with maximal values of the temperature near the sources and decreasing values close to the fixed temperature boundary. The evolution of these temperature fields is controlled by the thermal conductivity of the material and by the boundary conditions, in particular by the insulating sidewalls that reduce the lateral heat flow and favor that in the vertical direction.