###### Abstract  
Topology optimization offers a possibility to derive load-compliant structures. These structures tend to be complex, and conventional manufacturing offers only limited possibilities for their production. Additive manufacturing provides a remedy due to its high design freedom. However, this type of manufacturing can cause areas of different material properties in the final part. For example, in selective laser melting, three areas of different porosity can occur depending on the process parameters, the geometry of the part and the print direction, resulting in a direct interrelation between manufacturing and design. In order to address this interrelation in design finding, this contribution presents an optimization method in which the three porous areas are identified and the associated material properties are considered iteratively in a topology optimization. For this purpose, the topology optimization is interrupted in each iteration. Afterwards, the three areas as well as the material properties are determined and transferred back to the topology optimization, whereby those properties are used for the calculation of the next iteration. By using the optimization method, a design with increased volume-specific stiffness compared to a design of a standard topology optimization can be created and will be used in the future as a basis for the extension by a global strength constraint to maintain the maximum permissible stress and the minimum wall thickness. M 20221599 1  
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distribution in the defined design space until a given objective function is maximized or minimized. For this purpose, a fictive density \(\rho[i]\) is assigned to each element \(i\), whereby the Young modulus \(E[i]\) of each element is defined as follows [3]:  
\[E[i]=\rho[i]^{p}*E_{0} \tag{1}\]  
\(E_{0}\) describes the Young modulus of the initial material which is defined during the initialization of the topology optimization. Furthermore, the often used SIMP approach introduces a penalty factor \(p\) which leads to a continuous material distribution. In each iteration, the fictive densities and thus the Young moduli are systematically adjusted by the optimization algorithm until a defined convergence criterion is met [3]. A common objective function, for instance, is to maximize stiffness under a given volume reduction. In density-based topology optimization, a distinction can essentially be made between two optimization approaches for satisfying the objective function. In the controller-based approach, an optimality criterion is defined. Based on this criterion, the objective function is achieved in a given number of iterations and is therefore computationally efficient. In contrast, the sensitivity-based approach bases on the calculation and evaluation of sensitivities, whereby additional restrictions such as a minimum wall thickness, a strength constraint or demolding constraints can be taken into account [4]. An algorithm employed by commercial tools to adjust sensitivities within the topology optimization represents the method of moving asymptotes (MMA) [5]. In addition to density-based topology optimizations for a single material, there are also those for multiple materials [6]. The basic approach of such a multi-material topology optimization is to minimize the compliance while taking into account two constraints: the reduction in the total volume, and the maintenance of the respective volume limits of the materials to be combined. Thereby, the materials used can be freely arranged in the design space by the optimization. Another possible approach for single-material as well as multi-material topology optimization offers the level set method and has been a steadily growing research topic in recent years [7]. However, the result of a finite element (FE)-based topology optimization causes complex structures which usually cannot be produced with conventional manufacturing or only with additional effort and thus high costs [8].