Strength Analysis - Finite Element Analysis for Satellite Structures - page 154

X n j
N j

¼ 1

where n j is number of cycles applied at a load corresponding to a lifetime of N j .

4.12.3 Performing a Fatigue Damage Calculation

The procedure of a fatigue damage calculation of Small Sat structure due to
mechanical dynamic vibrations consists of the following steps:

1. Run a modal analysis to determine the resonance frequencies of the satellite
structure. This step is done in Sect. 4.10 .
2. Run a harmonic analysis to calculate the fully reserved stress distribution
amplitudes at each selected resonance frequency (the first 15 sorted modes)
for every loading phase during transportation and launch. This step is done in
Sect. 4.11 .
3. Run a static analysis of the satellite model to determine the mean stress dis-
tribution of the cyclic stress during transportation and launch. This step is done
in Sect. 4.9.4 .
4. Define the most critical points at each structural module where there are
maximum resultant stresses during any loading phase. These points are rep-
resented in Figs. 4.47 , 4.48 , 4.49 and 4.50 . Be sure that the maximum resultant
stress at any critical point does not exceed the yield stress of AMg6 aluminum
alloy (150 MPa).
5. Calculate the number of cycles n j corresponding to each loading phase and
selected resonance frequency. It is calculated from:
n j ¼ X f j t j

6. Where f j is the resonance frequency and t j is the corresponding time duration of
applied load in each phase.
7. The satellite mechanical loads in Appendix A, Tables A.3, A.5, A.7, and A.12
represent the durations of dynamic vibrations affecting the satellite during rail,
road, and air transportation and launch vehicle flight, respectively. The duration
of each loading phase has been mentioned before in Sect. 4.11.2 . If there is
more than one selected resonance frequency located in the same frequency
band in any loading phase, the corresponding time duration should be equally
divided among the common frequencies. Table 4.18 lists the number of cycles
n j corresponding to each loading phase and selected resonance frequency.
8. Calculate the time life cycles N j corresponding to each loading phase and selected
resonance frequency. This is calculated directly for any given stress ratio by
reading from the typical constant life diagram corresponding to the material of
the primary structural modules, which is AMg6 aluminum alloy. Unfortunately,
this alloy has not available fatigue behavior data, but it is equivalent to 6061-T6