# Topology Optimization of an Aerospace Bracket: Numerical and Experimental Investigation
## 1 Introduction  
Over the years, the rapid growth and continuous developments in additive manufacturing (AM) have revolutionized numerous processes via enhanced rapid prototyping and mass production of intricate components, benefiting industries ranging from aerospace and automobiles, to military, dental, fashion, medical, jewelry, footwear, architecture, eyewear, construction, education, and food industries, among others [1]. Additive manufacturing provides unmatched possibilities to produce complex geometry with advantages such as minimal manufacturing cost for custom parts, rapid prototyping, less time consumption, optimal resource usage, reduced post-processing, and environmental friendliness [2]. The American Society for Testing and Materials, or ASTM ([[https://www.astm.org/](https://www.astm.org/)]([https://www.astm.org/](https://www.astm.org/)), accessed on 9 September 2023), defines AM as the process whereby materials are added to create components using data from a 3D model, usually by building one layer upon another, contrary to subtractive processes which remove material. Other terms used for additive manufacturing include additive fabrication; additive techniques; layer manufacturing; additive layer manufacturing; additive processes; and freedom fabrication [3]. Generally, ASTM classifies additive manufacturing processes into seven categories: material extrusion,vat photopolymerization, sheet lamination, binder jetting, directed energy deposition, material jetting, and powder bed fusion. These processes differ in the ways layers are deposited to form parts, as well as the printing materials that can be used [3]. Certainmethods, such as fused deposition modeling (FDM), selective laser sintering (SLS), and selective laser melting (SLM)--also known as direct metal laser sintering (DMLS)--produce layers by melting or softening the printing materials, while on the other hand, methods like stereolithography (SLA) use various technologies to cure and solidify liquid resins or other appropriate materials. Each of these methods has its own merits and drawbacks, and therefore finds applications according to the desired object's properties and usage scenarios. Furthermore, printing materials and their properties depend both on the AM method and the equipment used in each case. For example, powders intended for fusing must have the capacity for energy absorption; jetted binders must be able to be dispensed; and polymers must act in line with controlled activation [1]. At the same time, for every AM technique used, there are certain process parameters that must be carefully selected in appropriate value ranges to achieve the desired objectives. For a comprehensive review of the status, trends, and prospects of additive manufacturing, the interested reader is referred to [4; 5; 6; 7; 8]. Designers and engineers are constantly being challenged to develop products and processes that use less materials and energy while being both cost-efficient and less time-consuming [9]. However, realizing the full potential of additive manufacturing requires a paradigm shift in design methods; topology optimization (TO) is among the approaches that permit this change, since it allows the production of complex lightweight components with less material usage, but without sacrificing the resulting strength and mechanical properties. TO has been employed in several engineering processes, and engineers and designers continue to research and develop new and efficient approaches for incorporating TO into AM [10]. Although a precise mathematical definition of topology optimization does exist, a more practical descriptive definition from an engineering perspective states that, \"Topology optimization is a shape optimization method which uses algorithmic models to optimize material layout within a user-defined space for a given set of loads, conditions, and constraints\" [11].