# Topology Optimisation in Structural Steel Design for Additive Manufacturing
## 1 Introduction
### Topology Optimisation Modern Age  
Formerly described developments were only made possible by the advances on the homogenisation method, by [PERSON] and [PERSON] in 1988 [21; 22] and [PERSON] and [PERSON] [23]. In simple terms, the homogenisation method is deemed to solve a material distribution problem, as previously formulated by [PERSON] and [PERSON] [24; 25; 26; 27], considering either only two states: The presence or the absence of the structural material. A more profound explanation and interesting example can be found in [PERSON] and [PERSON] books [28; 29]. The homogenisation method, along with [PERSON]'s Method of Moving Asymptotes (MMA) [30], became the basis of most of the following applications, developments, and TO commercial software. However, in 1993, [PERSON] and [PERSON] [31] proposed the so-called Evolutionary Structural Optimisation (ESO) procedure as a possibility for simplifying TO computations by mimicking natural evolutionary processes in Finite Element Analyses (FEA). This led to significant criticism from many other researchers after some shortcomings were identified [32; 33; 34; 35]. As the discussion proceeded on the ESO method, justifications were debated, and enhancements have been proposed [36; 37; 38; 39; 40]. However, the results of evolutionary methods continue to drive some intense discussions in Academia [41]. Fundamental studies on methods and approaches continued with the work by [PERSON] and [PERSON] [42] on the continua TO under stress constraints, as well as in related numerical issues [32; 43]. After these fundamental works, TO had a significant growth as a discipline, and the distinction between its two significant sub-fields, the Discrete Optimisation and the Optimisation of Continua became less evident. While the first of those two concepts is deemed to optimise a finite number of known elements and is preferred in several practical applications [44], the second unrestrictedly optimises topology within a solid. Meanwhile, applications-focused research flourished, with optimisation early works being published in materials design [45], compliant mechanisms [46; 47], electronics [48], connections positioning and design [49], buckling phenomena and truss design [50; 51][52], and alternative approaches for the ribbed plate problem [53]. The new millennium brought significant progress in TO algorithms but also in modelling and freely or cheaply accessible software, such as [PERSON]'s MATLAB code [54; 55] or the Karamba plug-in for the Grasshopper environment [56]. Discrete Optimisation had some essential developments, both with algorithms development [57] and practical applications [58; 59]. The former depicts an interesting option for Discrete Optimisation in the automotive industry and a good \"how-to\" example. However, significant numerical problems can arise when node positioning is also considered an optimisable parameter [60]. Within the Optimisation of Continua, many valuable works could be highlighted. Yet, one cannot omit important developments in filters [61; 62], projection methods [63; 64],computational methods [65; 66; 67], as well as in the controversy evolutionary approach for continua [68]. Furthermore, practical methods, such as [PERSON] et al. 's useful model with global and local levels of intervention [69], as well as applications in form-finding [70], stiffened plates [71], and TO under load position uncertainty [72], proved the suitability of TO methods for industrial execution. In fact, all the former offer solutions and examples for managing essential aspects of the TO application to structural steel design. Concomitantly, automotive research centres developed several in-house tools and approaches to introduce TO in industrial Computer-Aided Engineering (CAE). Some examples can be found by [PERSON] et al. [73], [PERSON] et al. [74], [PERSON] et al. [44], [PERSON] and [PERSON] [75], and [PERSON] et al. [76]. For the TO applications to leverage AM, several notorious works were published from 2010 on. [PERSON] et al.