# An Optimization Workflow in Design for Additive Manufacturing
## 3 Case Study  
The proposed workflow was applied to the remodeling of a piston rod. Reducing the weight of a piston rod while maintaining the mechanical performance is an important goal, especially in competitions in the automotive fields, but also in the industry where weight reduction leads to less inertia and to a reduction of energy consumption. The part is currently produced with a pressure die-casting process and is intended to be produced with the Selective Laser Melting (SLM) powder bed fusion AM technology. The material is an aluminum AlSi10 Mg with properties as in Table 1.  
Overall dimensions, loads, and constraints applied to the piston rod are shown in Figure 3a,b, respectively. The loads and constraints are summarized in Table 2.  
The topology optimization of the design space was performed in SolidWorks 2019 (Dassault Systemes) using the SolidWorks Simulation module; the software adopts the SIMP method for solving the optimization problem. The \"best stiffness to weight ratio\" goals was set, using the constraint of a final mass equal to 25% of the original part. The symmetry of the final part with respect to the YZ and ZX plane was imposed. Figure 4a shows the mesh resulting from the topology optimization. This mesh was then used as a starting point for the manual remodeling phase, performed in Inspire Studio CAD 3D software (Altair), as in Figure 4b. The size optimization section of the workflow was performed in Rhinoceros 6 (Robert McNeel & Associates) inside Grasshopper environment. The design space was filled with a conformal wireframe based on the simple cubic unit cell; the number of instances is 10, 4, and 15 along the \(x\)-, \(y\)-, and \(z\)-axis, respectively, and the minimum element size equals 3 mm. The FE beams model was set-up using Karamba3D plugin [74]. The loads and the constraints were directly applied at the nodes of the beams placed at the interface between the design space and the big and small rod's ends; the 7.5 kN load was equally distributed on each node of the upper part of the wireframe, so as the rotation and translation constraints on each node of the lower and upper part of the wireframe. The target utilization ratio was set to (90 \(\pm\) 1)% with respect to the yield strength. The upper and lower bound for the diameter of the beams were defined as 1.5 mm and 0.5 mm, respectively. Figure 5 shows the conformal wireframe and the utilization ratio of the optimized structure. Some beams do not reach the required utilization ratio; indeed, they present a utilization ratio lower  
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than the target because the optimized diameter was smaller than the minimum allowable size (i.e., 0.5 mm), so, being assigned the 0.5 mm diameter, they are under-utilized. The lattice structure was then modeled adopting the mesh approach and the Catmull-Clark subdivision surface algorithm. As can be seen in Figure 6, smooth surfaces are obtained, especially at nodal points. Then, the two models obtained from the topology and the size optimization were validated through FE analyses in Ansys Mechanical 2019 R1. The parts were meshed with tetrahedron elements using an element minimum size of 0.1 mm and an element maximum size of 1 mm. The meshing method is patch-independent and includes automatic  
Figure 4: Topology optimization: (**a**) SolidWorks Simulation result (mesh), (**b**) Inspire Studio manual remodeling result (NURBS). Figure 5: Size optimization: (**a**) wireframe model, (**b**) utilization ratio of the optimized structure (compression is positive). Figure 6: Modeled lattice structure: (**a**) lattice connected to the piston rod’s ends, (**b**) detail on the smooth surfaces at nodal points. refinement in curvature and proximity. The symmetry of the topology optimized part with respect to the ZX and YZ plane was exploited to simulate only one quarter of the model.