# Topology Optimisation in Structural Steel Design for Additive Manufacturing
## 5 Topology Optimisation in Structural Design of Steel Elements and Joints
### Multiple Loading and Robustness  
Significant obstacles still limit the broader employment of TO in structural design. One of the most important is the susceptibility of optimisation results to loading patterns. Albeit, recent advances onto robust solutions, which show endurance to loading scenarios multiplicity [454] and extreme degrees of TO in structural design usually result in members that efficiently withstand a finite number of loading patterns used in the design, but may be inefficient for other loading patterns, even resulting in less intuitive and less visually appealing topologies. In fact, real structural design optimisation problems are deemed to fulfil the requirements of multiple objective functions [455; 456; 457; 458]. Under these circumstances, the TO use for structural engineering is impaired by three reasons: First, loading patterns can be very profuse, up to hundreds or thousands in complex structures. This is not necessarily a research problem, but a practical one since common computational methods are still not suited for delivering TO results for many loading patterns in a reasonable time. The second problem is related to the absence of accidental and unconventional loading patterns in regular structural design. Without it, the redundancy of structural members may become negligible and an unexpected collapse under non-conventional loading may occur. The last, and possibly most severe, set of problems is related to the current methods for TO under multiple alternating loads. Notwithstanding some recent advances, current methods still face the inconvenience of non-unique solutions [459] and local extrema, as well as the difficult to account for loads with very different scales of intensity [458]. Multiple-loading and multi-objective optimisations have been handled with a plethora of methods. Both deterministic or physically accurate, and uncertainty-based methods, including notorious fuzzy approaches, have been used [458]. Arguably, the Kreisselmeier-Steinhauser function (KS) stood out in the past decades, mostly in aeronautical engineering studies. Among recent advances, one can highlight the efforts to account for uncertainties in the loading intensity and position with the method by [PERSON] and [PERSON] [460], and the compliance-function-shape-oriented approach by [PERSON] [461] and precursory work [462], the generalized material interpolation scheme by [PERSON] et al. [463], as well as the RBTO approach by [PERSON] and [PERSON] [464]. Previously, [PERSON] et al. proposed one more option for multi-objective TO, employing the Normalized Exponential Weighted Criterion (NEWC) and the Fuzzy Multiple-Attribute Group Decision-Making (FMAGDM) theory [458]. Likewise, [PERSON] and [PERSON] introduced the use of the Transplanting Independent Continuous and Mapping Ideas into Materials with the Penalisation (TIMP) method for the TO of plate structures under multiple loading [465]. Its interesting feature lies in adding one more penalty function to a SIMP-like method. One very different advance can be found in the approach by [PERSON] et al. [466] to the wind loading complexity through integrating Computational Fluid Dynamics (CFD) models into a BESO method for TO. Much of this research is related to contemporary multiple loading. The problem of non-simultaneous multiple loading implies significant computational efforts to extend the analysis scope, integrate TO results, and deal with very significant practical issues. Works on dealing with alternating loads can be found early in the TO literature, including the 1970s [PERSON] work [467], but hardly can be considered solutions for the complexity of the currently analysed problem. Recent works with alternating loads include [PERSON] et al. 's Revolutionary Superposition Layout (RSL) method [468], as well as [PERSON] and [PERSON] contributions, [459; 467]. Furthermore, [PERSON] et al. managed to use a method to examine and overly stress paths and compose comprehensive layouts, optimized for several sets of loads [341], [469].