## 5 Conclusions  
This work reviews TO methods for FRC structures applied to CF4. First, the study underlines the single-scale TO approaches that simultaneously or sequentially design fiber orientation and structural topologies. The study classified parameterizing techniques for anisotropic materials' topology optimization. Continuous parameterization schemes are considered for spatially varying fiber orientations and/or fiber volume fractions. In addition, these methods are amenable to CF4 and multi-axis material deposition technologies. Contrary to that, to attend to established manufacturable units, e.g., automatic fiber placement or automated tape layup, DMO is widely chosen to optimize composite laminates. The study further reports the usefulness of multi-scale TO for realizing FRC and extending it for variable fiber fraction structures. Moreover, it highlights emerging TO methodologies, such as feature-mapping, multi-component, and isogeometric optimization. The potential  
Figure 7: Typical cross-sectional view of a CF/PA6 filament by optical microscopy [15].  
applicability of these methods towards CF4 sets a new bar for designing FRC structures. Thus, we address the following main challenges in designing TO for anisotropic materials:  
_General applicability_: Most studies utilize the performance measure to minimize compliance and material distribution on a simple structure; thus, these methodologies still require validation for complex problems, such as bucking stability, compliant mechanisms, eigenvalue analysis, etc.  
_Solution dependency on an initial guess_: CFO methods are sensitive to starting guesses but are widely chosen for their simplicity and inherent attribute to the design of continuous fiber orientation. Taking the benefits of CFO and DMO provides a new direction to realize free-form FRC structures additively, but it still needs further improvement and research.  
_Multiple constraints_: Simple volume constraints integrated with manufacturing constraints, such as minimum curvature, fiber filament cut-out, feature size, etc., are essential to validate the optimization process and realizability of the printed part.  
_Revival of shape-based TO_: Several works adopt pixel- or voxel-based TO approaches due to their simple implementation but need not be a suitable choice to attain CAD-friendly design and not necessarily adapt to other FRC manufacturing units. Thus, emerging TO methodologies, such as feature mapping, isogeometric shape optimization, and multi-component methods, have been considered for the DfAM framework.  
_Three-dimensional printing of continuous FRCs_: CF4 is a young technology but has favorable attitudes toward designing structures' mechanical properties, such as tensile, flexural, compression, and impact properties. However, the printed parts' strength will always be lower than traditional methods due to the low fiber content, poor interface bonding force, void formation, and inevitable printing limitations. Thus, to improve the performance of given CF4 prints, a parallel investigation of the material and morphological properties of continuous FRCs must go hand-in-hand with the TO framework.  
Finally, the choice of the TO methods for designing complex FRC parts applied to CF4 requires various considerations; thus, this review highlights the different aspects of TO methods used for FRC structures to lay an essential foundation for researchers entering the field of the TO of additively manufactured continuous FRCs.  
Funding: Financed by the European Union--NextGenerationEU (Grant n\({}^{\circ}\) CN_00000023). The opinions expressed are those of the authors only and should not be considered as representative of the European Union or the European Commission's official position. Neither the European Union nor the European Commission can be held responsible for them.  
Institutional Review Board Statement: Not applicable.  
Informed Consent Statement: Not applicable.  
Data Availability Statement: Not applicable.  
Conflicts of Interest: The authors declare no conflict of interest.