Strength Analysis - Finite Element Analysis for Satellite Structures - page 196

is calculated directly by reading from the typical constant life diagram related to
the equivalent material of AMg6 aluminum alloy shown in Fig. 4.55 , and based on
the same criterion described in Sect. 4.12 . The number of cycles (n th ) corre-
sponding to the operational life time of the satellite is calculated by first calcu-
lating the satellite draconian period (T dr ), which is the time interval for completing
one orbital cycle (revolution), calculated from the following relationship:

8
<

9
=

2
4

3
5

1 e ð Þ 2
1 þ e cos ð u x Þ

2 5

2 sin 2 ð i Þ

Þ 2 þ

T dr ¼ 2p

e e

ð

p a 2 1

l e

Þ 2

: ;

l e a 2 1 e 2

ð

Þ 3 ð 1 þ e cos ð u x Þ

1 3 sin 2 ð i Þ sin 2 ð u Þ

ð 1 e 2 Þ

where:

• a: the major semiaxis ( = R e ? h)
• R e : the mean earth radius, ( = 6378.14 km)
• h: the satellite altitude
• l e : the gravitational constant of the earth, ( = 3.986005 9 10 5 km 3 /s 2 )

• e e : the earth oblateness parameter, ( = 2.6333 9 10 10 km 5 /s 2 )

• i: inclination
• e: eccentricity
• u: the argument of latitude
• x: the argument of perigee

For Small Sat, the following parameter values are taken in the calculations,
h = 668 km; i = 98.085 o ; e = 0.001; u = 0; x = 0. By substituting these values
into the previous equation, the draconian period for Small Sat is found to be:
T dr = 5881.9 s
The number of cycles (n) corresponding to the operational life time is then:
n th = T opr

T dr
where: T opr is the operational life time of the satellite, which equals to 5 years.
T opr = 5 9 365 9 24 9 60 9 60 = 157.86 9 10 6 s

Hence, n th = 26808 cycles
The thermal damage at the critical points is calculated by the relation:
D thermal ¼ n th
N th
The overall fatigue damage at the critical points is calculated by the following
relation:

D overall ¼ D dynamic þ D thermal

Table 4.32 lists thermal and overall fatigue damage calculations for the critical
points located in the basis unit block module.