## 4 Results and Discussion
From this analysis as well as the qualitative evaluation, it can be concluded that the developed optimization method produces a visually modified design which also leads to a slightly increased stiffness for the same volume due to the targeted redistribution of material. Therefore, the quantitative evaluation supports the assumption already made on the basis of the qualitative results that the described procedure is plausible and purposeful even with the increased stiffness of only 1% under the given parameters and load case. In order to examine the optimization history in addition to the final results, the progression of compliance up to convergence was analyzed (see Figure 9). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Developed Optimization** & **Standard Topology** \\  & **Method** & **Optimization** \\ \hline Final volume [\%] & 65.83 & 65.69 \\ \hline Strain energy [m] & 350.247 & 348.598 \\ \hline Required iterations [–] & 39 & 37 \\ \hline Contour/Interface/Hatching area [\%] & 37.77/7.68/54.55 & 30.86/7.58/61.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quantitative evaluation of the two resulting designs. It is noticeable that both the standard topology optimization and the developed optimization method have a very similar optimization history, and no divergence or severe discontinuities in the compliance are generated by adjusting the fictive densities. Furthermore, it can be seen that approximately the same number of iterations are required to generate the two very different designs. The observation of the optimization history thus allows the assumption that no significant disturbance in the convergence is introduced by the adjustment of the fictive densities, whereby the developed optimization method also generates an optimized design in a targeted manner. Therefore, the assumption is made that the presented optimization method can be used as a basis for extensions. In the following, based on the results of a stress analysis and by examining the final design, the necessary and plausible extensions of the presented optimization method are discussed. In addition to the findings regarding the volume-specific stiffness, the static FE analysis can be used to analyze the prevailing stresses. Here, 230 MPa was defined as the critical stress, since this can be assumed to be the yield stress and thus the limit of plastic deformation for the applied material. All elements exceeding this stress value are colored gray in Figures 10 and 11 right. It can be seen that especially the load application and the clamping regions exceed the value of 230 MPa. Furthermore, the elements at the bottom of the two beams, where a high stress due to bending is present, exceed 230 MPa. This follows primarily from the load itself and is mainly due to the selected displacement \(d\). This displacement was chosen arbitrarily, since its value for an optimization purely for stiffness has no influence on the result. Rather, it is intended to show, on the basis of the stress evaluation, that an abrupt stress progression occurs across the porous areas (see black marking in Figures 10 and 11 right) which is caused by their different Young moduli. The contour area exhibits the highest stress and the interface area the lowest. This correlates with the Young modulus, since the higher Young modulus causes a higher stress at the same load. If the limit of 230 MPa is now applied, it is possible that this limit will not be exceeded in a standard topology optimization in which the three porous areas are not taken into account. However, if the porous areas from the SLM are subsequently transferred to the design and evaluated in a static FE analysis, the critical stress of 230 MPa may be exceeded due to the higher Young modulus in the contour area. Therefore, it is obvious that this critical stress should already be taken into account directly in the optimization method. This can be conducted, for example, by defining a global strength constraint.