## 3 Model Design  
To investigate the application of the developed optimization method and its effects on the resulting design, a three-point bending beam is used as an example load case. The example is intentionally kept simple because the contribution is focused on the method and its evaluation in the context of design finding. Therefore, a simple example helps to evaluate the plausibility of the results. The bending beam is clamped in a fixed-loose bearing at the bottom side edges and centrally loaded with a displacement \(d\) of 0.24 mm (2% of the maximum height) (see Figure 6). The sensitivity-based optimization approach, described in the previous chapter, is applied. Through the usage of such a sensitivity-based approach, the possibility is offered to consider additional boundary conditions in the future, such as a minimum wall thickness or a global strength constraint [17]. This is intended by the authors as a further development as well as an improvement of the optimization method and will be discussed in the following. The material properties (Young's modulus and Poisson's ratio) for the three porous areas which arise due to the chosen process parameters were characterized in material testing (see Table 2). For this purpose, in addition to CT analyses for detecting the porosity distribution, ultrasonic phase spectroscopy (UPS) and resonant ultrasound spectroscopy (RUS) were employed for the determination of the mechanical material properties [31]. The chosen material for characterization is AlSi10 Mg. In addition to the material properties, Table 2 also shows the thicknesses of the areas as they appear in the SLM in each layer plane. No explicit thickness is defined for the hatching area, since this results from the total volume without the contour and interface areas and thus always describes the remaining inner area (see Figure 1 left). In order to model each layer within the optimization method despite the small thickness, the global element edge length must not exceed the thickness of the interface area. Therefore, in this contribution, a global element edge length of 0.1 mm is defined. Hexahedral elements are applied as the element type, since, in comparison to tetrahedral elements, they do not have an artificial stiffening effect. Due to the lower computation time, a linear shape function is chosen. These chosen parameters result in a mesh consisting of 6.9 million \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Contour Area** & **Interface Area** & **Hatching Area** \\ \hline Young’s modulus [GPa] & 75 & 65.5 & 72.5 \\ \hline Poisson’s ratio [–] & 0.35 & 0.35 & 0.35 \\ \hline Thickness [mm] & 0.4 & 0.1 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Dimensions and material properties of the three porous areas. Figure 6: Three-point bending beam with dimensions, clamping and loading. hexahedral elements. By exploiting the symmetry of the load case, the number of elements can be halved and the calculation time accelerated. The overall goal is the maximization of the stiffness. Therefore, as the objective function of the optimization, maximizing the strain energy under a given volume reduction to a relative final volume of 60% is defined. Thus, the goal is a structure that retains as much internal energy as possible to withstand the defined deformation. In order to evaluate the resulting design from the presented optimization method both qualitatively and quantitatively, it is compared to the design from a standard topology optimization performed with only one set of material properties. For this evaluation, a static FE analysis based on the same FE model (e.g., the initial topology optimization mesh defined in _Initial FE model_) is performed. Therefore, for each of the two designs (resulting from the developed optimization method and the standard topology optimization), the three porous areas and thus their material properties are transferred to the FE model.