## 1 Introduction  
For ultra-lightweight applications, composite materials are often the preferred choice in the material selection process due to their superior strength-to-weight ratio. In addition, continuous fiber reinforcements are known to significantly outperform discontinuous reinforcements (short fiber, nanofibers and particles) [1, 2, 3, 4]. Traditional manufacturing processes, such as manual layup, are well established for Continuous Fiber Composite (CFC) manufacturing. However, among other disadvantages (material waste, expensive manufacturing holds), the traditional processes are limited in terms of achievable geometrical complexity [5]. In contrast, Additive Manufacturing (AM) enables the fabrication of parts with complex geometries and various infill patterns [6]. It is particularly attractive for the manufacturing of customized parts and small series. Substantial Research & Development efforts have been dedicated to the development of AM technologies for CFC over the last years. The most common AM technology for the fabrication of CFC, essentially due to its low associated costs, is Continuous Filament Fabrication (CFF). Research in CFF hasaddressed the following issues: material extrusion process [7; 8], printable materials and their mechanical properties [9; 10], infill patterns and their influence on energy absorption [11], environmental effects [12], process parameters [13; 14; 15; 16], fiber placement, printing path design [17], and lightweight applications [18; 19; 20]. The technological trend in CFF is now going towards true 3D printing with multi-axis devices. Early examples of true 3D printed CFC components are lattice sandwich core structures [21; 22]. True 3D systems range from low-cost devices to systems with up to 12-axis of motion and multiple industrial robotic arms [23; 24; 25; 26; 27; 28]. They offer various advantages. The relative movement between the print head and the print bed helps reduce support material [29] and increase printing speed. Both reduce the overall printing time [30]. Furthermore, it enables non-planar 3D printing, which offers two essential benefits. Namely, an increase in the surface quality of the printed components and the possibility of material deposition in 3D curves [23]. Non-planar 3D printing opens up the possibility of optimizing the fiber direction in the plane and the 3D space, allowing for the creation of much stronger components. Before printing, a slicer divides the part geometry (stl.-file) into successive layers in the height direction. The layers are then printed one after the other. This limits the deposition paths to 2D planes, resulting in one direction (perpendicular to the plane) being much weaker than the in-plane directions, essentially due to interlayer adhesion and delamination issues. The weak direction exists for both reinforced and unreinforced materials. [PERSON] et al. [31] quantified this anisotropy for an ABS filament. [PERSON] et al. [32] found better structural integrity for PA12 nylon when filaments are aligned with the direction of applied stresses. Multi-axis 3D printing enables, in contrast, to deposit filaments along 3D paths. For instance, in the case of a pressure cap, fiber deposition along the cap curvature becomes possible, resulting in a much stronger part. For polymers, [PERSON] et al. [33] showed the benefit of stress-tensor-aligned deposition paths using a 5-axis printer. They fabricated vessel pressure caps with optimized 3D deposition paths, which had three to five times the strength of the layer-wise manufactured parts. This strength improvement results from the utilization of manufacturing-induced anisotropy (the polymer itself has isotropic material properties). In the case of the pressure vessel cap, it is possible to optimize the fiber direction analytically. However, for the optimization of components with more disordered stress distributions, numerical tools are needed.