## 3 Results and Discussion
### Compressive Properties  
The compressive properties of the proposed structures were investigated using both finite element analysis (FEA) and experimental methods. For the simulation, quasi-static compression was applied to the bottom surface of different structures while a displacement-controlled loading was directed downward along the central axis at the upper end. Grid convergence tests were conducted simultaneously in order to obtain force-displacement curves and maximum compressive loads [36; 37]. To ensure the accuracy of the FEA results, a hexahedral element (Solid186) of 1 mm size was used in the simulation. The FEA model consisted of 595,700 nodes and 101,700 elements. In the experimental setup of our compression tests, friction-free boundary conditions were employed to ensure a uniaxial stress state during loading. Specifically, polyethylene sheets were interposed between the sample and the loading platens to minimize lateral confinement near the loading platens. This approach was adopted to accurately measure the compressive strength and avoid any potential influence on the stress distribution within the sample due to frictional forces at the boundary. It is widely acknowledged that the type of contact between the specimen surface and loading surface plays an instrumental role in the stress distribution, behavior under loading, and ultimately the compressive strength of the sample. For instance, using a rough surface, such as fine-grained sandpaper, at the loading platen as a boundary can result in increased friction and hinder the lateral expansion of the sample, thus inducing a confining stress near the loading platen. Moreover, placing a rough surface as a boundary condition \begin{table}
\begin{tabular}{c c} \hline \hline
**Material Name** & **R4600 Resin Material** \\ \hline Density (g/cm\({}^{3}\)) & 1.3 \\ Young’s modulus (MPa) & 2600 \\ Poisson’s ratio & 0.42 \\ Elongation at break & 10\% \\ Tensile strength (MPa) & 47 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Material properties of R4600 resin material. Figure 2: Additively manufactured tubes. may alter the mode of failure of the sample under certain circumstances. Conversely, adopting friction-free boundary conditions can mitigate these issues and help achieve a more accurate characterization of the compressive properties of the sample [38; 39]. Taking BS-7 as an example, the compression finite element model is illustrated in Figure 3. Because the quality of the simulation models in this study is the same, according to the definition of the lightweight coefficient, there is only a one-coefficient relationship between the maximum load and lightweight coefficient, and thus the simulation results only yield the maximum load value (Table 2). Figure 4 depicts the compressive properties of different BSs. From Figure 4a, it can be found that with the increase of displacement, the compression forces of the three sample values and the simulated values of BS-7 gradually increase, and then reach the maximum value when the displacement is about 4 mm, and finally gradually decline; that is, they all have the same compression change trend. Table 2 illustrates that the FE analysis results of BS-7 agreed with the test results well, and the maximum error is less than 8%. All the results demonstrate that the designed FE model is sufficiently accurate with the experiment samples. This indicates that the derived theoretical model can effectively predict the compression performance of other BSs. The finite element model can effectively and accurately reflect the experimental data and can be used for further study.