Civil Engineering Reference
In-Depth Information
listed in the printed output. Therefore, for each analysis set, the expansion pass
of every superelement structural module is done twice to calculate the real and
imaginary parts of the solution.
8. Review the results: The results data for fully reversed harmonic analysis of the
entire model and the expansion pass for each superelement module are the same
as the data for a basic structural analysis. All results are complex in nature, and
are stored in terms of real and imaginary parts because damping is defined.
4.11.4 Harmonic Response Analysis Results
As mentioned before, harmonic response analysis [
2
] is performed to calculate
peak stresses in the structural modules due to harmonic inertia loads. These
maximum stresses are used in fatigue damage calculations. Therefore, the output
results from the harmonic analysis must serve the fatigue analysis. The harmonic
tension stresses are responsible for dynamic fatigue failure. So the output results
from the harmonic analysis are the equivalent amplitude stresses (Von Mises) in
each structural module. For Small Sat harmonic analysis, the equivalent amplitude
stress at each point is calculated from the formula:
q
ð
r
R
Þ
2
þð
r
Imag
Þ
2
r
e
¼
where: r
R
and r
Imag
are the real and imaginary equivalent amplitude stress at the
point.
Harmonic loads do not act individually on structural elements, but they operate
simultaneously with quasi-static loads. Quasi-static loads comprise both static and
dynamic loads, and are applied at a frequency sufficiently below the first natural
frequency of the structure. Therefore, the quasi-static loads are independent of
time or very slowly, so that the dynamic response of the structure due to the
dynamic component is not significant.
The maximum stresses affecting the structure are a combination of the equiv-
alent amplitude stresses due to fully reversed harmonic loads and the equivalent
stresses from the static components of the quasi-static loads. Since the finite-
element model of Small Sat is linear, then superposition is applicable to calculate
the maximum stresses in each structural module. The equivalent stresses from the
static components of the quasi-static loads can be considered as the mean stresses
for the fatigue analysis due to dynamic loads. The satellite mechanical loads given
in Appendix A, Tables A.1, A.6, and A.8 show the quasi-static loads affecting the
satellite during road, rail, and air transportation and launch, respectively. The
mean stresses in each structural module can be calculated by performing static
analysis for the entire satellite model. The load factors used for the static analysis
are specified as follows:
Search WWH ::
Custom Search