## 3 Materials and Methods
### Design Evaluation  
A vital shortcoming of data-driven generative design methods (e.g., GANs) is the inability to test the suitability of the resulting designs for the design purpose. Generative models are trained using the probabilistic distribution of the training set. Therefore, the generated data reflect the general characteristics of the training dataset in terms of form and function. For generative models to generate designs with superior functional properties, the training data must have superior design properties. The concept of functionality in structural components can be defined as the load carrying capability of components during operation. Physics-based approaches such as finite element analysis (FEA) are used to determine a component's functional (strength) properties in engineering design. FEA is a numerical analysis method that attempts to predict the mechanical behavior of the part and assembly under operating conditions [50].  
In this study, a static structural analysis was performed on the workpieces using CATIA. The models were discretized with tetrahedral elements using the patch confirming technique, ensuring that the mesh size did not affect the results, and the mesh was refined and validated until variations were reduced to less than 8%. The analysis includes a comprehensive elasto-plastic analysis of strain behavior beyond the elastic limit using the Newton-Raphson method detailed in Equation (3):  
\[\Big{[}K^{T}\Big{]}\{\Delta u\}=\{F\}-\{F^{nr}\} \tag{3}\]where \(K^{T}\) is the stiffness matrix, \(\Delta u\) is the displacement matrix, and \(\{F\}-\{F^{ur}\}\) is the force instability matrix.  
This study focused on the post-yield behavior of AlSi10 Mg materials modeled with a bilinear stress-strain relationship to reflect hardening after the yield point. Material properties included a yield strength of 270 MPa and a tangent modulus of 5 GPa. Boundary conditions fixed the workpieces in small holes, and a 150 N bearing force was applied to the large hole.  
In this study, we aimed to develop design concepts with a high strength-to-weight ratio using a data-driven generative design method. The generated designs were evaluated in a design-simulation environment, and their mechanical properties were determined. The von Mises values of all concept designs under the same conditions (boundary conditions, mesh size, material properties, load, etc.) were determined autonomously. Von Mises is the equivalent stress, which shows how much stress a material can carry without exceeding the elastic limit.  
A preliminary mesh optimization study was performed on a subset of approximately 10 samples to determine the optimal mesh size. This preliminary study involved repeating the analysis with different network sizes and observing the results until a point was reached where the analysis results were independent of network size. The mesh size that met this criterion was then used equally across all designs in our automated analysis process.  
In this study, the design concepts analyzed were ranked according to their von Mises values, and the designs that fell in the 50% percentile were determined. High-performance concept designs were converted into voxel format to be added to the training set. A random 3D model was removed from the training set as much as the data were added to the initial dataset. Thus, the average functional performance of the training dataset was increased. Creating the training set, training the GAN model, evaluating the generated design concepts, and adding high-performance concepts to the training set constituted the functional generative design cycle. This cycle did not diminish the diversity of the dataset; rather, it enhanced the dataset by incorporating designs that not only exhibited aesthetic and geometric variety but also demonstrated improved mechanical properties. The cycle continued until part of the training set consisted of GAN-generated models. Thus, design concepts with high strength could be generated.