# An Optimization Workflow in Design for Additive Manufacturing
## 2 Design Workflow  
The proposed workflow helps the designer during the product development process of AM components, guiding him throughout decisions that allow to fully exploit AM potential. AM-related engineering requirements and technological constraints are considered in the first phases of the workflow and simulation tools are used to optimize and validate the geometric model. In particular, the workflow can be adopted during the embodiment design phase of parts in which the mechanical performance needs to be maximized and the weight needs to be as low as possible. Structural optimization approaches such as size and topology optimization perfectly suit this scenario. Figure 2 shows the proposed design workflow for AM. First, the design space is identified. The design space is a volume where the material distribution is going to be optimized; it can be obtained from an existing model or it can be specifically designed considering the maximum allowable size of the component. Then, two paths can be followed: the first one performs a topology optimization on the entire design space, whereas the second one performs a size optimization on a lattice structure. Regardless of the selected approach, a finite element (FE) model is created taking into consideration not only the \"usual\" boundary conditions such as the material, the loads, and the constraints but also the constraints and conditions strictly related to the design for AM. For instance, the technological constraints could include a limit for the inclination of the structure to avoid overhang angles (if required by the manufacturing technology) and the upper and lower limits for the most critical features, i.e., hole size, strut dimension, wall thickness, etc. Furthermore, since AM allows the production of complex geometrical shapes, it is easier to create parts resulting from multi-objective optimization; the optimization goals like targeted mass and natural frequencies, or desired heat exchanging properties can be considered as engineering requirements. Including this information in the first part of the workflow enables to obtain a design with the desired functionalities that is likely to be produced without the need of stepping back to the product development phase. If the topology optimization approach is chosen, the design space is discretized and a polyhedral mesh is obtained; then, the topology optimization is performed. During this process, the material is arranged inside the design space to find the best distribution of  
Figure 2: The proposed design workflow for additive manufacturing. Black blocks: steps related to the boundary conditions; green blocks: steps related to the topology optimization; blue blocks: steps related to the size optimization; red blocks: steps related to computer-aided engineering (CAE) simulation software. material under a set of boundary conditions and respecting the structural and dimensional performance requirements. According to the literature, several topology optimization algorithms can be used [38]. Homogenization methods use the mathematical theory of homogenization [39,40] to study a complex domain previously divided into microstructures, i.e., the finite elements, as a continuum domain made up of a virtual material called effective material [41]. Density methods consider the density as the only design variable for each finite element, and the variable can assume a value between 0 and 1; since the optimal solutions would consist of elements with values mostly between 0 and 1, the results would be far from a solid (1)-void (0) situation. The most popular numerical method for suppressing intermediate densities is the Solid Isotropic Microstructure with Penalization (SIMP) method, proposed by [PERSON] [42], which penalizes elements with intermediate densities exploiting a power law.