## 4 Results and Discussion  
In the following, the results are presented and discussed, which were obtained using the developed optimization method (see Figure 7) and a standard topology optimization (see Figure 8). If the results are considered qualitatively, it can be stated that both optimizations form a type of truss structure consisting of struts along the main load paths. This can be explained by the defined three-point bending load case. However, a closer look reveals clear differences. The standard topology optimization (see Figure 8 left) results in wide indentations in the lower corners and a large hole in the middle of the beam. In contrast, the developed optimization method (see Figure 7 left) results in both the indentations and the hole being much smaller. Instead, a type of hollow structure is created which is illustrated by the sectional view (see Figure 7 right). Furthermore, the results indicate that the developed optimization method tends to an increased number of thin struts compared  
Figure 8: Result of the standard topology optimization: overall design (**left**) and sectional view (**right**). Figure 7: Result of the developed optimization method: overall design (**left**) and sectional view (**right**). to the standard topology optimization, as can be seen, for example, in the corner of the clamping based on the three struts. This leads to the assumption that the developed optimization method maximizes the contour area of the resulting design. The assumption can be confirmed by the quantitative evaluation of the contour area, since the design of the developed optimization method has an approximately 7% bigger contour area compared to the design of the standard topology optimization (see Table 3). To obtain this quantitative evaluation, all hexahedral elements which have the material properties of the contour area are determined. The number of elements recorded this way allows the volume of the contour area to be estimated, since all hexahedral elements have the same size due to the simple geometry of the bending beam. The effect of the contour area maximization could be triggered due to two factors. Firstly, beginning with the first iteration, the three porous areas are considered in the FE model, and thus the outer surface (contour area) is improved along the print direction in the initial FE model. This leads to the assumption that the optimization algorithm thus does not eliminate the improved elements, resulting in the hollow structure. However, by observing the interior of the beam, it can be shown that the surface area is also increased there. Thus, the influence due to the consideration of the three porous areas from the first iteration onwards is estimated as small. Rather, the increase in surface area can be explained by the second factor, the material properties from Table 2. The Young modulus in the contour area is the highest and thus also has the highest material stiffness. This increased stiffness is preferred by the optimization algorithm and leads to a bigger contour area. This result allows the assumption that the described procedure within the developed optimization method can be classified as plausible and purposeful. In addition to the qualitative evaluation, it is important to perform a quantitative analysis as well. Therefore, a static FE analysis, in which the three porous areas including the material properties are transferred to the resulting designs, was performed and the strain energy calculated. Furthermore, the actual final volume as well as the required iterations was extracted. The resulting values are presented in Table 3.  
The developed optimization method leads to an increasing stiffness by extending the contour area. Therefore, the volume-specific strain energy \(\left[\frac{\text{mI}}{\text{mm}^{3}}\right]\) is evaluated which results in an approximately 1% higher value for the design of the developed optimization method.