## 1 Introduction  
When considering applications of fused filament fabrication (FFF) additive manufacturing (AM) across the manufacturing, automotive and aerospace industries, the two most common thermoplastics employed are polylactic acid (PLA) and acrylonitrile butadiene styrene (ABS) [1]. Both PLA and ABS are reasonably strong and light, with the tensile strength of PLA typically 25-60 N/mm\({}^{2}\)[2; 3; 4; 5; 6] and that of ABS 30-40 N/mm\({}^{2}\)[1; 4; 7]. Considering that the densities of these materials tend to be 1020-1400 kg/m\({}^{3}\)[4; 6; 7], in terms of the strength-to-weight ratios shown in Table 1, PLA and ABS can typically outperform a variety of conventional materials; however, the lower stiffness and ductility of these polymer materials must be noted when considering deflection and deformation limits. Nevertheless, these mechanical properties indicate useful applications across the automotive, aeronautical and aerospace industries where weight optimization is important. Given the flexibility of form achievable through AM techniques, the present study examines the behaviour of elliptical cross-section tubes, the geometries of which have been recognized for centuries to possess unique analytical properties [8]. Hollow elliptical tubes formed from various materials have precedents in a variety of industrial applications including heat transfer ducts [9; 10], fluid conduits [11], fluid dynamics [12] and structural load-bearing members [13]. The cross-sectional geometries of such tubes are characterized by their maximum cross-sectional radius \(a\), their minimum cross-sectional radius \(b\) and their tube wall thickness \(t\), as shown in Figure 1. In addition to their aesthetic properties, elliptical sections have a mechanical advantage over their circular counterparts owing to having a stronger major axis of bending (axis y-y in Figure 1). Initial studies [14; 15] into the stability of thin-walled steel oval-shaped sections in compression provided an experimental basis for the resistance of such sections to local buckling. More recent analytical studies into the local buckling of steel [16; 17; 18], stainless steel [19] and aluminium [20] elliptical tubes have characterized elastic buckling modes and postbucking behaviour, with the dependence of postbucking behaviour on the cross-sectional aspect ratio \(a/b\) attested to. Studies into fibre-reinforced polymer elliptical sections have been conducted [21], but seemingly exclusively as a confining layer to an inner concrete core. It has been shown through numerical parametric studies that, with increasing aspect ratio, the postbuckling behaviour of slender steel elliptical tubes in compression [22] and bending [23] transitions from unstable imperfection-sensitive behaviour like that \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Material**} & \multirow{2}{*}{\begin{tabular}{c} **Strength** \\ **(N/mm2)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Elastic Modulus** \\ **(N/mm2)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Density** \\ **(kg/m3)** \\ \end{tabular} } & \multicolumn{1}{c}{
\begin{tabular}{c} **Normalised** \\ **Strength-to-Weight** \\ **Ratio** \\ **(km)** \\ \end{tabular} } \\ \hline Ultimaker PLA [6] & 50 & 2350 & 1248 & 4.08 \\ MCPP ABSX [7] & 39 & 1980 & 1030 & 3.86 \\ S275 steel & 275 & 210,000 & 7850 & 3.57 \\ S355 steel & 355 & 210,000 & 7850 & 4.61 \\ C40 concrete & 40 & 32,100 & 2400 & 1.70 \\ C24 timber & 24 & 10,800 & 550 & 4.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of PLA and ABS materials examined in the present study compared to other materials. Figure 1: Cross-sectional geometry of EHS showing dimensions and axes. observed in cylindrical shells to stable imperfection-insensitive behaviour like that observed in flat plates.