In recent years, astronomical observations made with space telescopes have dramatically increased our understanding of the history of the universe. In particular, the cosmic Background Explorer (COBE) and the Hubble Space Telescope (HST) have yielded observations that cannot be achieved at ground-based observatories. We now have views of the universe before galaxies existed (from COBE) and views of young galaxies (from HST). But none of the existing observatories can provide views of the period in which the galaxies were born, about 100 million to one billion years after the "big bang". NASA expects the Next Generation Space Telescope (NGST) to fill this gap. An investigation into the structural modeling of the primary mirror of the NGST, its methodology and results are presented

Boulet, J. A. M.

English

NASA Technical Reports Server

-4. _,_' - .... ,_' i _-_-_
1997 NASA SUMMER FACULTY FELLOWSHIP PROGRAM
MARSHALL SPACE FLIGHT CENTER
THE UNIVERSITY OF ALABAMA IN HUNTSVILLE
STRUCTURAL MODELING OF THE NEXT GENERATION SPACE TELESCOPE'S
PRIMARY MIRROR
Prepared by:
J. A. M. Boulet, Ph. D.
Associate Professor
Department of Mechanical and Aerospace Engineering and
Engineering Science
University of Tennessee, Knoxville
MSFC Colleagues:
Max Nein(PS02)
Larry Craig (ED25)
Dave Jacobson (EJ31)
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https://ntrs.nasa.gov/search.jsp?R=19990010004 2020-06-18T00:46:38+00:00Z
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STRUCTURAL MODELING OF THE NGST
Introduction
In recent years, astronomical observations made with space telescopes have
dramatically increased our understanding of the history of the universe. In particu-
lar, the cosmic Background Explorer (COBE) and the Hubble Space Telescope (HST)
have yielded observations that cannot be achieved at ground-based observatories.
We now have views of the universe before galaxies existed (from COBE) and views
of young galaxies (from HST). But none of the existing observatories can provide
views of the period in which the galaxies were born, about 100 million to one billion
years after the "big bang." NASA expects the Next Generation Space Telescope
(NGST) to fill this gap.
Although several preliminary designs have been proposed for the NGST, the
current focus of NASA's effort is the design proposed in 1996 by a NASA team with
members at Goddard Space Flight Center (GSFC), the Jet Propulsion Laboratory (JPL),
and Marshall Space Flight Center (MSFC). This design is depicted in Figure 1. The
salient features of the design are the inflatable sunshade (to keep the mirror's tem-
perature at about 40 K), the large segmented primary mirror, the central mast sup-
porting the secondary mirror, and the remaining optics and other instruments
placed between the primary mirror and the sunshade. The primary and secondary
mirrors, together with their supporting structures, are referred to as the optical tele-
scope assembly (OTA).
Figure 1. NASA (GSFC, JPL, MSFC) Preliminary design for the NGST.
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Because the primary mirror, which is eight meters in diameter, is to be
launched by an existing vehicle, the mirror cannot be made in one piece. In the cur-
rent design, the mirror is made of nine segments. These include a central octagon,
itself containing a central circular hole, and eight movable petals. For launch, four
of the petals fold toward the front of the mirror and the other four fold toward the
back, as shown in Figure 2. On orbit, the petals are opened and the mast holding the
secondary mirror is extended, as seen in Figure 3. Each petal is supported by its own
reaction structure, depicted in Figures 2 and 3 as a second layer of material in each
petal.
Various materials have been proposed for the primary mirror, including
beryllium, nickel, silicon carbide, and glass. The first three of these are sufficiently
stiff so that the mirror portion of each petal need be supported only at three points.
But a glass mirror would be so flexible as to require support at about 150 points per
petal. In what follows, we discuss the ability of cklrrent modeling techniques to pre-
dict the behavior of a glass primary mirror.
Current structural models of the NGST primary mirror are based on the finite
element method (FEM) and incorporate triangular, flat-plate elements. Models are
analyzed with standard computer codes such as NASTRAN and EAL. The discus-
sion below is focused on two specific aspects of what could be called, in general, val-
idation of the models used in these codes. Are the models sufficiently accurate for
the current design of the glass primary mirror? For what aspects of the glass design
have the codes been validated? If the codes converge to some "best" analysis as the
finite element mesh is refined, how accurate are the results of that "best" analysis?
The launch of any space telescope would be preceded by a program of testing,
which would be used to validate (or invalidate) modeling. But successful validation
through testing requires that the tests include measurements that can be used to as-
sess the accuracy of all aspects of the modeling that have not been otherwise vali-
dated. Answers to the questions posed above are needed to insure that testing pro-
grams measure only that which needs to be measured.
Structural models of the NGST's primary mirror should accurately predict
both stress and deformation. Accurate stress prediction is needed to prevent the loss
of structural integrity. Accurate deformation prediction is needed to insure accept-
able optical performance, which is characterized by waveform error. Optical model-
ing techniques predict this error using detailed predictions of the mirror's deforma-
tion. If the structural models do not accurately predict the deformation, the optical
models may not accurately predict the optical performance. In that case, despite
maintaining its structural integrity, a space telescope could be a failure. It follows
that validation of the modeling, through testing or otherwise, should include vali-
dation of both stress and deformation predictions.
Two assumptions currently used in structural modeling of the NGST's pri-
mary mirror are (a) that shear deformation is negligible and (b) that deformation
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Figure 2. Launch configuration for the NGST's optical telescope assembly.
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Figure 3. Deployed (on-orbit) configuration for tke NGST's optical telescope assem-
bly.
r
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varies slowly with position over the surface of any petal. The validity of both these
assumptions was investigated during the period covered by this report. The inves-
tigation began with a brief literature search, which revealed little documented work
that would apply to these issues as manifested in the NGST mirror. This literature
search continues.
Methodology
Lacking applicable previous work, we conducted a preliminary investigation
of the two assumptions listed above by analyzing the simple models depicted in
Figures 4 through 7. Each model is an infinite beam with equally spaced support
loads. The support loads represent those that a mirror petal would experience on
orbit.
In Figures 4 and 5, the support loads are developed in reaction to a uniformly
distributed load applied to the beam. On orbit, such a load would not be present.
Rather, the predominant loading experienced by the supports would be created by
the mirror's tendency to deform in response to temperature gradients. If such gra-
dients were small, the support loads would vary slowly over the surface of the petal.
In that case, the deformation between the supports would be approximately the
same as that for the model shown in Figures 4 and 5.
In Figures 6 and 7, the support loads are assumed to be developed in response
to rapidly varying deformation of the mirror. For convenience, the support loads
are taken to be equal in magnitude and alternating in direction. This could only oc-
cur in response to large temperature gradients.
Results
Elementary beam theory (no shear deformation) leads to deformation pat-
terns illustrated in Figure 8. From the figure it is apparent that the peak-to-peak de-
formation expected for the model depicted in Figure 6 is about fifteen times larger
than that expected for the model depicted in Figure 4. This indicates that the as-
sumption of small temperature gradients is critical. If it is significantly in error, per-
formance of the mirror may not be as expected.
When elementary beam theory is combined with well-known analysis of
shear deformation, the deformation patterns for the two beam models are as shown
in Figures 9 and 10. These figures indicate that shear deformation will not be signif-
icant provided the mirror thickness remains less than about one-tenth the spacing
of the support loads. For the current glass design, this ratio is about 0.025. Hence, it
is unlikely that shear deformation will be significant in the NGST's primary mirror.
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Figure 4. Infinite beam with uniformly distributed applied load and equally spaced
supports.
Figure 5. Free-body diagram of one wavelength o: the beam depicted in Figure 4.
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P P P
Figure 6. Infinite beam with no applied load and equally spaced, self-equilibrating
support loads.
P/2 T P/2
P
Figure 7. Free-body diagram of one wavelength of the beam depicted in Figure 6.
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Figure 8.
f(0
F(0
0
0.5
--0.5
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/
I
/
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/
b
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.%
%
k
_ -L -;-- -
, %
• h
, k
• X
."/ I I I "",
-1 -0.5 0 0.5
Normalized deflections of beams depicted in Figure 4 (solid line) and
Figure 5 (nonuniformly dashed line), without shear deformation.
Figure 9.
0.04
f(_,____o.25,o)0.02
f(_,0.25,o.1)
0
f(_,_0.25,0.2)
O --- -0.02
I I I I I
--0.04 I I I I I •
-0.4 -0.2 0 0.2 0.4
Effect of shear deformation on beam d_picted in Figure 4. Poisson's ratio
is 0.25. The ratio of the beam thickness to the spacing between the sup-
ports varies from zero (no shear deforrr;ation) to 0.2
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Figure 10.
0.6
0.4
fNSD(_) 0.2
f SD (_' 0.25, 0.1) 0
fSD (_' 0.25, 0.2)
0 -0.2
! I I
I I I
- -0.5 0 0.5
Effect of shear deformation on beam depicted in Figure 6. Poisson's ratio
is 0.25. When the beam thickness is zero (solid line), there is no shear
deformation. The dashed lines show the deformation that would be
added to the solid line due to shear deformation when the beam thick-
ness is 0.1 or 0.2 times the spacing of the support loads.
Conclusions
Although shear deformations is not likely to be significant in the NGST's
primary mirror, the assumption of small temperature gradients is critical. If its va-
lidity cannot be verified, the current design should be pursued under the assump-
tion that large temperature gradients may exist.
Acknowledgement
The author would like to acknowledge the kind assistance and cordiality of
Max Nein (PS02), Larry Craig (ED 25), Dave Jacobson (EJ31), the entire ED25 branch,
and the staff of the Summer Faculty Fellowship Program. Without their help, this
work would not have been possible.
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Structural Modeling of the Next Generation Space Telescope's Primary Mirror

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