# Topology Optimisation in Structural Steel Design for Additive Manufacturing
## 1 Introduction
### Topology Optimisation in Civil and Structural Engineering  
Within civil and structural engineering, significant TO applications can be found in several sub-fields. While Discrete Optimisation of truss-like structures is, probably, the most straightforward application--and, indeed, has some early and interesting applications such as the Structural Topology and Shape Annealing (STSA) approach to transmission towers by [PERSON] and [PERSON] [82], the Mixed-Integer Non-Linear Programming (MINLP) approach to industrial steel buildings structural cost optimisation complying with Eurocode 3 (EC3) by [PERSON] and [PERSON] [83], the method for trusses optimisation by [PERSON] et al. [84] or the employment of genetic algorithms by [PERSON] and [PERSON] [85]--there are some works on the TO of structural systems under seismic loads. Such could be regarded as a surprise, since the seismic design is undoubtedly more complex and demanding compared with static loading common cases but may be explained by the resourcefulness of TO addressing complex issues which, otherwise, would hardly be efficiently solved with analytical means. Among the aforementioned works, one can highlight the steel frames optimisation by [PERSON] and [PERSON] [86], more recent studies of space structures under seismic loads with evolutionary approaches [87; 88], a comparison of different soft computing algorithms by [PERSON] and [PERSON], taking infrastructures lifelines as the study object [89], as well as [PERSON] et al.'s well-known mastery for innovative solutions, materialised in the use of TO for meeting significant seismic, aesthetical, budgetary, and regulatory demands for a specific building [90].  
The conceptual design of tall buildings gathered practitioners and researchers attention (as depicted in Figure 1b), leading to a more practical design process optimisation [91] or algorithms focused research [92]. Nevertheless, the systematic employment of TO for the conceptual design of tall buildings is particularly evident in the [PERSON], [PERSON], and Merill experience. As reported by [PERSON] with other SOM engineers and academics [93; 94; 95; 96; 97], such solutions were developed for impactful projects and competitions (Figure 1c).  
Steel sections and the connections design are two other sub-fields where TO has had an impact. Regarding the former, the [PERSON] group (Figure 2a) and [PERSON] et al. research on steel beams with web openings [98], [PERSON] et al.'s creative employment of evolutionary algorithms for pre-tensioned cable structures design [99], and [PERSON]'s book chapter on cold-formed steel members [100] must be referred. Regarding the latter, it is important to stress out the contributions by [PERSON] et al. [101] and [PERSON] [102] on the bolted steel connections geometric optimisation and stiffeners optimisation, respectively.  
The bridge design, on the other hand, has had lesser attention from the TO point of view. Nevertheless, [PERSON] et al.'s work on bridge design accounting for construction constraints with ESO algorithms [103] and [PERSON] et al.'s Bi-Directional Evolutionary Structural Optimisation (BESO) algorithms application to the bridge conceptual design (Figure 2b) [104] must be mentioned.  
Beyond steel design but still within structural engineering, concrete TO has had some landmarks, including [PERSON] et al.'s work on frame nodes [107], [PERSON] et al.'s fresh look into the classical concrete shell supported bridge design [108], [PERSON] et al.'s approach to TO for enhancing strut-and-tie models [109], and the use of TO by [PERSON] and [PERSON] [110] in the Carbon Fibre Reinforced Polymers (CFRP) reinforcement design for concrete slabs. Other civil engineering sub-fields for TO include the building's thermal behaviour design [111].