## 3 Results
### Case Study 1--Cantilever Bar Bending  
The first case is the optimization of loading the steel bar. This is a standard example of topology optimization and this problem has been solved analytically [26]. The structural optimization algorithm is used to obtain the input for the feature recognition algorithm, which was proved to provide the optimal solution [4]. It is important to note that the examples in the comparison with the literature were performed on extruded 2D optimization results. This case study is performed for a true 3D object with an optimization domain with one dimension restricted. The input for the optimization was created in CAD software using the following parts: optimization domain--box 20 mm \(\times\) 500 mm \(\times\) 1000 mm; bar to be optimized--box 20 mm \(\times\) 20 mm \(\times\) 1000 mm centered inside domain; support area--box 1000 mm \(\times\) 1000 mm \(\times\) 2 mm; stressed area--box 20 mm \(\times\) 20 mm \(\times\) 2 mm. All parts modeled in CAD are visible in Figure 12. The parts for use with the structural optimization system were exported as STL files. The material of the optimized model was steel with \(\
u=0.28\), \(E=200\times 10^{9}\) Pa, \(\rho=7800\) kg/m\({}^{3}\). The yield strength for the material was assumed to be \(250\times 10^{6}\) Pa. The bar was stressed with a force of 40 kN perpendicular to the axis. For this, a test factor of safety = 3 was assumed and the max allowed von Mises stress was set to \(80\times 10^{6}\) Pa. Structural optimization was run for 300 iterations. It is important to note that this case study has been prepared to compare results with examples widely used as a benchmark for structural optimization and the implementation of the results is not possible. A shear force of 40 kN is applied to the area of 20 mm \(\times\) 20 mm and this alone would cause structural failure. The mesh from the structural optimization was directly used as an input for the feature recognition system. Refinement was run with the parameters displayed in Table 1. The refinement progress is shown in Figure 13. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Initial cylinder radius & 10 mm \\ Minimal Initial Element Size & 40 mm \\ Population & 5000 \\ Node Move Standard Deviation & 5.0 mm \\ Radius Change Standard Deviation & 1.0 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of feature recognition algorithm used in Case Study 1. Figure 12: **(a)** CAD screenshot displaying the input object—bar and optimization domain. **(b)** CAD screenshot displaying the stressed area (left), supported area (right) and optimization domain. The result of the feature recognition algorithms was imported into the CAD system and exported as an STL file, which was used in the solution verification (Figure 14). The numeric results are in Table 2. The boxplot of the surface von Mises stress is Figure 15. The reconstructed object is 0.3% lighter than the structural optimization result, so the algorithm produced an object of similar mass. The reconstructed object has a lower maximal surface von Mises stress and exhibits smaller deflection under load. The overall von Mises distribution is more concentrated (interquartile range \(19.97\times 10^{6}\) Pa in reconstructed vs. \(52.67\times 10^{6}\) Pa for reconstruction input), which suggests better distribution of load under stress in the reconstructed objects. This is because the compression/tension stresses dominate in this structure and the cylinder, which is the chosen structural element, carries those loads well. On the other hand, the von Mises stress is higher and a visual inspection of the FEM results shows excessive stress at the element connections (Figure 16). Those are the points where the bending moments concentrate. Disregarding the impossible load conditions, the implementation of the result would require manual strengthening of those points in CAD software to avoid structural failure.