# Topology Optimization of an Aerospace Bracket: Numerical and Experimental Investigation
## 1 Introduction
At the same time, the optimization problem needs to be solved in a high dimensional space, which is generally a hard problem and becomes practically intractable when discrete/binary variables with multiple constraints are involved, thus rendering this discrete approach disadvantageous [16]. To address this challenge, [PERSON] proposed the solid isotropic material with penalization (SIMP) method in [18], which introduced a density function, the pseudo density variable \(\rho\), i.e., a continuous variable in [0, 1], and therefore allows the use of optimization procedures that were not applicable in the initial discrete setting. Furthermore, the penalization and density filtering techniques introduced by SIMP are equally significant, as they not only help in finding the desired optima, but they also smoothen any wiggles that may appear in the response functions due to the design parameterization on a finite element mesh. Filtering techniques have an especially positive effect on the convergence of a gradient-based topology optimization method. Note that the density-based approach employed in this work follows the SIMP method, wherein density is ultimately forced to approach 0 or 1 rather than varying continuously. The default ANSYS filtering algorithm is employed to this end. These techniques, along with the effect of the design parameterization, are discussed thoroughly in [19]. The level-set method, as previously mentioned, follows a different approach and although relatively newer, it receives continuous attention due to its additional benefits. LSM uses a flexible implicit description of the material domain. The structural domain is represented by the zero-level contour via a level-set function; see [20, 21, 22]. The well-defined and smooth structural boundary, which is retained throughout the optimization procedure, makes the LSM advantageous as no post-processing of the ragged boundaries resulting from density-based methods is required [20]. LSM in structural optimization has been noted by its pioneer users [23] as being able to naturally handle changes in topology, alongside a crisp and smooth interface representation resulting in solutions that are comparable to, or even better than, the ones achieved with SIMP and ESO [24, 25, 26]. In the pursuit of the full exploitation of the design freedom and manufacturing complexities which AM technology permits, topology optimization becomes of immense importance. Structural topology optimization produces complex geometries which are generally difficult to produce with conventional manufacturing techniques. Hence, it is common for researchers and engineers working with topology optimization to resort to AM techniques. However, some limitations of AM also need to be considered so that complex,topologically optimized designs of high quality can be achieved [27]. In modern manufacturing, a wide range of application objectives are achievable through the advantages and possibilities made feasible by integrating topology optimization and additive manufacturing. Research in this area reveals that creating high-performing, multi-functional, and lightweight products relies on a comprehensive approach which simultaneously considers materials, structure, manufacturing processes, and performance [13]. In their review of relevant technologies in industrial applications, the authors of [12] put forward two main reasons for pursuing the integration of topology optimization into AM: The first reason is that optimized components can be cost-effectively produced only through additive manufacturing techniques, as they are very complex and difficult to manufacture using conventional processes. The second consideration is the cost of both the product and the materials, which are directly related to the material and weight reductions that are achieved by both technologies.