# Development of Everting Tubular Net Structures Using Simulation for Growing Structures
## 3 Results
### Preliminary Study of Net Parameters  
In the first design step, the parameters of the net structure were investigated concerning the prospects for everting behavior and possible occurrence of critical loadings. The parameters are strongly linked to each other, due to the discrete nature of the net and amount of crossing points. With a given number of circumferential crossing points, the length of bars scales the angles between them and vice versa. At a given bar length, an increase of circumferential crossing points leads to changed angles between bars. On the other hand, with a given cylinder height, the number of crossing points in the cylinder axis direction changes bar lengths and angles. Hence, some parameters were fixed and the alteration of the main variable defines the remaining dependent parameters. The number of circumferential crossing points was set to \(n=12\), which results in a section angle \(\gamma=\frac{2\pi}{n}\) (Figure 9). The number of crossing points \(k\) in the cylinder axis direction was chosen to give a cylinder height of \(a\) near \(145\) mm, which reaches the maximum printable height. The cylinder radius was set to \(r=20\) mm. The angle \(\alpha\) between the bar and horizontal axis was chosen as the main variable. The angle \(\beta=90^{\circ}-\alpha\) between the bar and vertical axis and the bar length itself \(l=\left(\frac{\pi r}{n}\right)\cos\alpha\) results from the main variable and fixed parameters. The geometric model was built via Ansys APDL script, so that the crossing points were defined and connected with straight beam elements to structure the tubular geometry. With the script, the model was then transferred into LS-Dyna keywords. At the same time, load coordinate systems were defined to overcome the strict Cartesian restriction in LS-Dyna, which allows no general load definition in a cylindrical coordinate system. Figure 8: Exemplary evaluation using a regression line (dashed) (**a**); identified engineering stress–engineering strain curves of the tensile tests on round tensile bars (**b**) with a table of results for the [PERSON]’s modulus. Figure 9: Geometry model of everting structure: upper tube end with Cartesian coordinate systems for definition of cylindrical loads (**a**) and detailed view with dependent geometric variables (**b**). The angle \(\gamma\) between two horizontally neighboring crossing points describes the section angle with center of angle (not shown) that lies on the inner cylinder axis. Three variations 30\({}^{\circ}\), 45\({}^{\circ}\) and 60\({}^{\circ}\) of the main variable \(\alpha\) were modeled in LS-Dyna with beam elements (default type 1, Hughes-Liu with cross-section integration). Each bar consists of four beam elements (diameter of 1.7 mm) to account for the bending compliance of bars. The lower tube end nodes were fixed in all degrees of freedom, which models a clamping of the lower end. For the upper end nodes, a prescribed nodal translational in radial tube direction was applied for each node in the beginning of the simulation, using the already defined local Cartesian coordinate systems (Figure 9a). Additionally, a translational motion in the negative z-direction (toward the lower end nodes) completes the initial everting stage and allows for a further continuous everting progress. The beams use a purely linear-elastic material model (*MAT_002) with [PERSON]'s modulus of \(E=6\) MPa (6 N/mm\({}^{2}\)) (according to evaluation of tensile test above), density of \(\rho=2000\times 10^{-12}\frac{\mathrm{t}}{\mathrm{mm}^{3}}\) and a [PERSON]'s ratio of \(\
u=0.49\) according to hyperelastic characteristics of material. A self-contact of the tube was defined using a single beam element set within the contact-card *CONTACT_AUTOMATIC_GENERAL. Otherwise, excessive self-penetration would occur. The total simulation time was set to 2 s to ensure a nearly quasi-static loading condition. This leads to a negative axial motion with a velocity of the upper-end tube nodes of \(-400\)\(\frac{\mathrm{mm}}{\mathrm{s}}\) in the z-direction.