# Multi-Directional Shape Change Analysis of Biotensegrity Model Mimicking Human Spine Curvature
## 4 Numerical Examples
### Total Computational Step  
Figure 6 shows the total computational step for all cases with target displacements in the uni-directional mode. The total computational step increases with increase of target displacement (i.e., 200 mm, 400 mm and then 600 mm). The highest total computational step is found in series Zp for all of the spine biotensegrip models, SB1, SB2 and SB3. In most cases, the lower total computational step is observed in SB1 followed by SB2 and, lastly, in SB3, except series Yn and Zp, involving target displacement of 400 mm and 600 mm, where no specific trends are observed.  
Figure 7 shows the total computational step for all cases with target displacements in the bi-directional mode. Similarly to the uni-directional mode, the increasing trend in the total computational step is found to be dependent on the magnitude of target displacement. In addition, the trend where SB1 has lower total computational step, followed by SB2 and later SB3 is observed in most of the analysis cases of XY200 and XY400. The total computational steps are comparable for all series (i.e., XpYp, XnYn, XpYn and XnYp) at target displacement of 200 mm and 400 mm, whereas there is no specific trend for target displacement of 600 mm. It can be seen that the analysis cases with target displacement of 600 mm show obvious increment in the total computational step. There is an exceptionally high total computational step in the analysis case XnYn600 for SB1 compared to other models in series XY600.  
Since all SB1, SB2 and SB3 models show similar patterns for the total computational step in the tri-directional mode, only SB2 is chosen for discussion. As can be seen in Figure 8, the total computational step in series XY400 is noticeably greater than series XY200 in both series Z and Zp (i.e., Zp200, ZP400 and Zp600). When the z target displacement increases in series Zp, the total computational step increases. However, the total computational step does not depend on the x,y,z- target displacement magnitude in series Zn. The total computational step for series Zn is significantly lower compared to series Zp, and they are comparable between series XY200 and XY400. An exceptional high total computational step in XnYp200 Zp400 (958) compared to other series XY is also demonstrated in SB1 (736) and SB3 (737).  
Figure 6: Computational steps in series dealing under the uni-directional mode.  
A direct relationship between the number of total computational steps and the target displacement magnitudes is observed. A strict limit specified for the forced elongation through the specification of \(\mathrm{d_{cl}}\) (see Equation (15)) in the algorithm results in larger total computational steps in cases with larger target displacement magnitudes. This also explains the reason for the larger number of computational steps in SB models that demonstrate pure axial deformation (i.e., series \(\mathrm{Zp}\)) than the bending deformation (i.e., series \(\mathrm{Zn}\)), since most cables required substantial positive forced elongations for the extension. A higher value of \(\mathrm{d_{cl}}\) may be applied in order to reduce the total computational steps. Meanwhile, attention should be paid to the accuracy of the solution.