This document summarizes a finite element study of the self-deflection of large mirrors mounted with different kinematic mounts. The objectives were to accurately model self-weight deflection using analytical and finite element analysis methods, and to examine different mount designs. Basic ring and 3-point mounts were modeled and showed good agreement between analytical and FEA results, within 3%, for ring mounts. Future work proposed varying gravity vectors, modeling a complex whiffletree mount, and optimizing a low-density mirror to reduce deflection.

1. Finite Element Study of the Self-Deflections
in Large Mirrors Subject to Kinematic
Mounts
Tina Li
University of Hawaiʻi at Mānoa
May 6th, 2016
1

2. Agenda
• Problem and Objectives
• Methodology
• Verification of Basic Mounts
• Summary
• Future Work
2

3. Deflection of Large Mirrors
3
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

4. Importance
• Finding water
• Discovering the age of the universe
• Uncovering black holes
• Understanding and learning about:
• Dark energy and dark matter
• Seasons on other planets
• Exoplanets
4

5. Solutions for Reducing
Deflection
5
Mount design
Thin, lightweight
mirrors
Active/adaptive
optics
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

6. Objectives
• Main: To accurately model the self-weight
deflection of large mirrors on various mounts
• To examine the accuracy of different methods
to calculate deflection
• Analytical
• Finite Element Analysis (FEA)
6
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

7. Methodology
7
Basic
mounts
Ring mount
3-point
mount
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work
Complex
mount
Whiffletree
mount
Verification

8. Verification between
Analytical and FEA
8
?
Analytical FEA
=
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work
• Ring mount
• Roark’s (2012)
• 3-point mount
• Vukobratovich (2008)
• William and Brinson (1974)

9. 9
Basic
• Ring mount
• 3-point mount
Complex
• Whiffletree mount
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

10. Verification: Ring Mount
• As the aspect ratio for the mirror increases:
• Shear will become negligible
• Bending stress will be governing
10
% Difference FEA to Analytical
Aspect ratio = 8 Aspect ratio = 16
w/o shear w/ shear w/o shear w/shear
Simply
supported
8.6% 2.7% 0.8% 0.5%
Fixed 21.6% 2.7% 4.4% 2.7%
Aspect ratio (AR) = diameter
thickness
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work
AR = 8 AR = 16
q

11. Verification: Ring Mount
11
Simply Supported Fixed
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

12. Verification: Ring Mount
• Vertical axis (0˚ to the zenith direction)
• Simply Supported (~3% difference)
• Fixed (~3% difference)
12
Analytical FEA
m
m
m
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

13. 13
Basic
• Ring mount
• 3-point mount
Complex
• Whiffletree mount
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

14. Verification: 3-point Mount
14
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

15. Contributions
• Comparing numerical solutions (FEA)
• COMSOL
• SolidWorks
• ANSYS
• PLOP
• Comparing various analytical solutions (3-point mount)
• Vukobratovich
• Williams and Brinson
• Modeling 3-point mount
• Ring mount corroboration
• 3-point mount verification
15
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

16. Summary
Verification achieved
Deflection starts to
diverge at AR 8-10
•Due to deflection from
localized stress and
shear stresses
16
3-point
Mount
Achieved
corroboration
Limitation in
analytical
equation
Ring
Mount
Experiment
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

17. Future Work
• Obtain and analyze results from experiment
• Varying gravity vectors
• Investigating the whiffletree mount
• Optimizing a low density mirror
17
Problem and
Objectives Methodology
Verification
of Basic
Mounts
Summary Future Work

18. Acknowledgements
• Mark Chun and A Zachary Trimble
• Akamai Workforce Initiative
• Akamai is led and managed by the Institute for Scientist & Engineer Educators at the University of California Santa
Cruz, in partnership with the University of Hawai‘i Institute for Astronomy. Funding for the 2015 Akamai Internship and
Mentor Program is provided by: Thirty Meter Telescope International Observatory, THINK Fund at the Hawaii
Community Foundation, University of Hawai‘i System, University of Hawai‘i at Hilo, National Science Foundation
(AST#1347767), and National Solar Observatory.
• Institute for Astronomy at Hilo
• College of Tropical Agriculture and Human
Resources (CTAHR)
• Undergraduate Research Opportunities
Program (UROP)
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19. Questions?
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