Table 1. Geometric comparison between physical specimens (PS) and modified Dynamic Relaxation (mDR) results in mm.
| Unit Module (Fig. 6D,I) | Grid Conf. (Fig. 7A,G) | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Retracted |
Extended |
7A |
7G |
|||||||||
| PS | mDR | % | PS | mDR | % | PS | mDR | % | PS | mDR | % | |
| l1 | 80.5 | 80.1 | 0.50 | 50.0 | 49.0 | 2.02 | 88.5 | 90.1 | 1.79 | 55.0 | 54.4 | 1.10 |
| l2 | 64.0 | 64.7 | 1.09 | 64.0 | 63.5 | 0.78 | — | — | — | — | — | — |
| h | 16.5 | 16.7 | 1.20 | 30.5 | 29.9 | 1.99 | 48.0 | 49.8 | 3.68 | 62.0 | 63.9 | 3.02 |
With the mDR simulation, the equilibrium states of the grid-based hierarchical designs are found when the total energy drops below ξ = 10−13 (Fig. 7D–F and J–L). This is achieved for each structure in under 1000 iterations. As shown in Table 1, mDR predicts the nodal coordinates within ±5 of both the square modules and the tiled grid structures.