(Advanced) Result Analysis

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The variation of flexibility is illustrated in the figure above. We can find that as the groove depth grows, the flexibility increases, while as the wall thickness grows, the flexibility decreases. Both variations are monotonous.

As shown in the figure, the load bearing capacity increases monotonously as the wall thickness grows. However, the variation of load bearing capacity about the groove depth is not monotonous: it initially increases, and then decreases. We believe the cause is that as the groove depth increases, then the arm of gravity and load increases while the forces themselves decrease. Because the wall of a relatively large thickness confines the airbags’ inflation, the forces decrease slowly when the groove depth is relatively small. So their product initially increases.

Besides, the deformation of airbags is confined, so the increasing forces' of the arm is confined while the forces always decrease as the groove depth increases. So their product has an extreme value, and then decreases. Because of the non-monotonous variation, the load bearing capacity reaches an extreme value at a certain groove depth under every fixed wall thickness (white line in the right figure). On its left side, the flexibility and load bearing capacity both increase as the groove depth grows. Thus, values in this region are not concerning because both properties can be better on the right side of the white line.

To get an explicit view of the load bearing capacity’s non-monotonous variation along with the groove depth, the performance of load bearing capacity under different fixed wall thickness are demonstrated in 2D plane in the figure below. From that, several conclusions can be drawn:

• As the wall thickness grows, the extreme point moves rightwards, so a deeper groove is required corresponding to a thicker wall for achieving maximum load bearing capacity.

• The curve corresponding to a 2mm wall thickness monotonously declines, with no extreme point. From the trend that the extreme point moves leftwards when wall thickness decreases, we can infer that when the wall thickness is less than a certain value, the extreme point has a minus groove depth. Therefore, an additional part at the intersection, instead of a groove, is required to realize a model with a thin wall.

• With a fixed groove depth, the load bearing capacity always increases as the wall thickness grows, but its rising range gradually reduces. So, it’s not effective to keep increasing the wall thickness when it’s already large. Instead, it is useful to increase the pressure.

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