SPINAL INJURY CONTROL - Injury Biomechanics and Control: Optimal Protection from Impact - page 200

160 ms was
divided into 20 subintervals. The first 15 partition points occurred with an
interval of 5 ms and covered a segment of 75 ms, whereas the remaining 5
points occurred with an interval of 17 ms. The control of Eq. (5.103) was
utilized as the initial approximation. To solve the constrained minimization
problem, MATLAB function fmincon was used. The results of the
optimization are presented in Figs. 5.12 and 5.13. Figure 5.12 presents
the optimal time history

For the further optimization, the time interval 0 ≤ t ≤

u s 0 (t) of the absolute acceleration of the seat
pan. There are two segments apparent in the plot on which the function
u s 0 (t) demonstrates different behavior. The duration of the first segment
is approximately 50 ms. This segment can be compared to the transient
segment of the function u s (t) of Eq. (5.101) for the two-degree-of-freedom
model (Fig. 5.10). On this segment, the function u s 0 (t) experiences rapid

changes. Beyond this segment, on the interval between 50 and 160 ms, the
deceleration of the seat pan is more uniform. Figure 5.13 shows the time
history of the magnitude of the spinal compressive force. The maximum

¯

3

2

1

0

0 25 50 75 100 125

Time (ms)

FIGURE 5.12 MADYMO-optimized time history of the absolute acceleration of the

seat pan.

3

2

1

0

0 25 50 75 100 125

Time (ms)

FIGURE 5.13 Optimal time history of the magnitude of the spinal compressive force
calculated on the basis of the MADYMO simulation.