# Topology Optimisation in Structural Steel Design for Additive Manufacturing
## 1 Introduction
### Metrics for Research Output in Topology Optimisation  
Performing a data analysis with the Scopus search tool (www.scopus.com) on 28 November 2020, it has been possible to observe that Topology Optimisation has been referred in scientific literature since the early 1980s, but not until the new millennium has the related scientific output been consistently increasing (Figure 3a). This fact can be related to the well-known recent computing power increase and massification, on which TO has a strong dependence. Furthermore, the ascendant trend has increased over the last 5 years, up to almost 1200 documents per year in 2020, during which more scientific and engineering disciplines have reportedly started employing TO more systematically. An interesting etymological approach lies in noticing an early word choice for _Topological Optimisation_ over _Topology Optimisation_ which, however, was not able to be employed in more than 10% of the analysed documents, over the recent years (Figure 4).  
Figure 3: Scopus search data analysis for **(a)**_Topology Optimisation_ and **(b)**_Topology Optimisation_ AND _Civil Engineering_, in Title, Keywords or Abstract in Research, Review, and Conference articles, on 28 November 2020.  
A different perspective is attained analysing the coexistence of TO and _Civil Engineering_ (Figure 3b), _Structures_ (Figure 5a), and _Steel and Connections or Joints_ (Figure 5b) in articles title, keywords or abstract. Among these three, TO and _Structures_ is the most common, even if under 2.5% of the total TO articles, and with a steady increasing trend. However, many Mechanical and Industrial Engineering documents use the keyword _Structures_. Furthermore, TO and _Civil Engineering_ have been practically not coincident until 2010 and, from there, yield a rather inconstant volume of documents not exceeding 10 per year. A similar conclusion can be drawn for the use of TO and _Steel Connections_ (or _Joints_), except for the fact that its modern employment seems to have started in 2005 and that it has not peaked above six documents per year. This suggests that the current TO magnification as an advanced engineering design method has not yet been brought to Civil and Structural Engineering comprehensively.  
Figure 6a as well as Figure 7a,b offer a brief insight on the field leading players. As a result, we observe [PERSON], [PERSON], and [PERSON] leading the list of most prolific authors. At the same time, the Dalian University of Technology, Danmarks Tekniske Universitet (DTU) and State Key Laboratory of Structural Analysis for Industrial Equipment are the  
Figure 4: Scopus search data analysis for _Topological Optimisation_ in Title, Keywords or Abstract in Research, Review, and Conference articles, on 28 November 2020.  
Figure 5: Scopus search data analysis for (**a**) _Topology Optimisation_ AND _Structures_ and (**b**) _Topology Optimisation_ AND _Steel_ AND _Connections_ OR _Joints_, in Title, Keywords or Abstract in Research, Review, and Conference articles, on 28 November 2020.  
most productive research centres. The National Natural Science Foundation of China is the primary funding agent for the research on this topic. It is well ahead of the US National Science Foundation and not matched by the remaining entities.  
As depicted in Figure 6b, Research Articles account for almost two-thirds of the analysed documents, with Conference Articles making one-third and leaving Conference Reviews and Journal Review Articles with 2.3% and 1.0% of the literature volume, respectively. This suggests a need for systematic reviews on the topic so that the literature is consolidated as a whole and sectorial reviews help each research discipline adapt and incorporate recent advances in TO, which is being developed in other disciplines.