# Topology Optimisation in Structural Steel Design for Additive Manufacturing
## 5 Topology Optimisation in Structural Design of Steel Elements and Joints  
### Steel Elements Design  
Structural design has been pushed into Topology Optimisation for several reasons. Not only does the technology availability in much user-friendlier tools [388] play a critical role in facilitating the centuries-old task of optimising structural design, but also external pressures drove structural engineers into TO. Such pressures have been found both upstream, with an architectural demand for shapes that can only be optimised with extreme computational resources [389; 390] and downstream, with the need for design processes able to foster Additive Manufacturing [391]. The former reasoning also explains why structural steel design has shown a particular prospect for successful TO applications [392]. The range of the applications includes Shape and Size Optimisation for steel members, as well as Topology Optimisation for the whole structural envelope. Furthermore, and unlike most of the other engineering disciplines, structural steel engineering still finds a preferred tool in Discrete Optimisation, over the Optimisation of Continua, for several problems with the macro-structures conceptual design. Among the members design, perforated beams and shear walls are particularly prone to TO. The former has been studied in depth by [PERSON] group at the University of Leeds [346], and the latter had a recent development in Bagherinejad [360], using commercial software. In both cases, a preliminary design with circular holes has been shown to evolve to a lattice-like geometry, with significant material subtraction in well-known less stressed areas. In a larger scale, floor diaphragm members have also been studied by [PERSON] et al. [393], to understand the optimisation possibilities under in-plane loading. Still, within the sectional optimisation domain, the Free Material Optimisation (FMO) method extension [394] provided a critical tool for plates, shells, and member's parts design, and an impressive Academia-Industry joint effort allowed developing the Sectional Optimisation Method (SOM), which enabled the design of optimised aluminium members, accounting for fabrication constraints, standards regulations, and local instability phenomena [341]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Programme** & **Nature** & **Runs on** & **Approaches/ Methods** & **Reference** & **Advantages** & **Disadvantages** \\ \hline GRAND (Ground structure analysis and design) & Freeware & MATLAB & Discrete Optimisation & [385; 386] & Freeware. & Constrained to the optimisation of ground & Constrained to the optimisation of ground & Constrained to the structures. \\  & & & & & & & \\ GRAND (Ground structure analysis and design) & Freeware & MATLAB & Discrete Optimisation & [387; 386] & Freeware. & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\ [PERSON]’s truss optimisation code for Mathematica & Freeware & Mathematica & Discrete Optimisation & [387] & Freeware. & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\  & & & & & & \\ \hline \hline \end{tabular} \({}^{(a)}\) Based either on publicly available information or on personal communications with the companies’ contacts (which can be disclosed).  
\end{table} 
Table 5: _Cont._Concerning structural systems and trusses optimisation, recent improvements include multi-objective optimisation techniques [395], Differential Evolution Algorithms [267], quantile regression for fostering the use of (discontinuous) I-beam cross-sections as design variables [396], and developments with the Interior Point method for non-linear and non-convex truss optimisation problems [397]. However, one of the most impressive developments can be found by [PERSON] et al. [398], a near-optimal truss design based on the homogenisation-based continuum TO. Practical applications of truss optimisation to bracing the systems design have some interesting contemporary examples in [399; 400; 401; 402; 403]. Therefore, high-rise buildings are an ideal ground for employing truss optimisation methods [106].