1. Florian RUESS & Benjamin BRAUN Structural Reliability Considerations for Lunar Base Design Rutgers Symposium on Lunar Settlements 3-8 June 2007 New Brunswick, NJ HE 2 Habitats for Extreme Environments www.he-squared.com

2. Contents Ruess / Braun - Structural Reliability Considerations for Lunar Base Design I.Motivation II.Structural Concepts III.Structural Reliability IV.Example V.Conclusions www.he-squared.com

3. I. Motivation Ruess / Braun - Structural Reliability Considerations for Lunar Base Design I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

4. NASA Constellation Program Ruess / Braun - Structural Reliability Considerations for Lunar Base Design The Vision for Space Exploration Goals on the Moon: Science, Exploration Preparation, Eventual Settlement… Photo: NASA I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

5. Everybody wants to go to the Moon Ruess / Braun - Structural Reliability Considerations for Lunar Base Design The European Aurora program intends to sends humans to the Moon by 2024 China’s Chang’e program plans human missions to the Moon after 2020 Russia, India, Japan and many others also have lunar ambitions Photo: ESA I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

6. II. Structural Concepts Ruess / Braun - Structural Reliability Considerations for Lunar Base Design I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

7. Structure Classification Ruess / Braun - Structural Reliability Considerations for Lunar Base Design first generation: pre-fabricated and pre-outfitted modules like the ones for the ISS second generation: locally assembled structures after a certain presence on the Moon as been established third generation: structures exclusively made from local materials I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

8. inflatable structures cable structures rigid structures Structural Concepts Focusing on second generation habitats, most proposed concepts can be divided into: Photo: NASA Ruess / Braun - Structural Reliability Considerations for Lunar Base Design I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

9. Rigid Structures Advantages: experience robustness all-in-one concept possible Disadvantage: relatively large volume + mass Photo and concept: Schroeder et al. Ruess / Braun - Structural Reliability Considerations for Lunar Base Design I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

10. A Tied-Arch Shell Structure Ruess / Braun - Structural Reliability Considerations for Lunar Base Design Concept by HE 2 and H. Benaroya I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

11. Structural Design on the Moon Ruess / Braun - Structural Reliability Considerations for Lunar Base Design Many more uncertainties exist ► resistances, e.g. new materials ► loads, e.g. micrometeoroid impacts Global safety factor concept complex to use efficient quantitive measure of safety Reliability-based concept easy to apply uneconomic actual reliability unknown Scope of existing design standards exceeded I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

12. III. Structural Reliability Ruess / Braun - Structural Reliability Considerations for Lunar Base Design I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

13. Classical vs. Structural Reliability Ruess / Braun - Structural Reliability Considerations for Lunar Base Design © KMJ Structural systems unique components different failure modes rare failures Technical components large numbers, same type single failure mode relative failure frequencies 1000 hours / life failure due to extreme events measure of safety probabilistic modeling of resistances and loads ► reliability index  Characteristics of the reliability analysis failure due to ageing estimation of life-time probabilistic modeling of time until failure ► failure rate I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

14. safefailure f M ( x ) x MM MM probability density function of the safety margin M How to picture the reliability index ? Ruess / Braun - Structural Reliability Considerations for Lunar Base Design Probabilistic models for the uncertain ► resistance R ► load S Probability of failure:  In case of two N -distributed variables: I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

15. Limit state functions Ruess / Braun - Structural Reliability Considerations for Lunar Base Design ► linear u1u1 u2u2 ► nonlinear Limit state function g(x) can be In the general case: functions of several random variables x R – S = f R (x) – f S (x) = g(x) Normalisation of the random variables x : g(x) → g(u) safe g(u) > 0 failure g(u) < 0 g(u) = 0 I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

16. Limit state functions Ruess / Braun - Structural Reliability Considerations for Lunar Base Design ► linear u1u1 u2u2 ► nonlinear Limit state function g(x) can be In the general case: functions of several random variables x R – S = f R (x) – f S (x) = g(x) Normalisation of the random variables x : g(x) → g(u) g(u) = 0 safe g(u) > 0 failure g(u) < 0 g (u) = 0   - vector I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

17. How safe is safe enough ? Ruess / Braun - Structural Reliability Considerations for Lunar Base Design 4.77 4.27 3.72 3.09 2.33 10 -6 10 -5 10 -4 10 -3 10 -2 PfPf  Structural codes on Earth I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions Target reliabilities on the Moon ? Level of safety depends on Societal acceptance Costs Failure consequences injuries loss of life economic loss

18. IV. Example Ruess / Braun - Structural Reliability Considerations for Lunar Base Design I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

19. Example Calculation Ruess / Braun - Structural Reliability Considerations for Lunar Base Design I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions Internal pressure

20. Example Calculation Ruess / Braun - Structural Reliability Considerations for Lunar Base Design I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions Regolith cover

21. Assumptions for random variables Ruess / Braun - Structural Reliability Considerations for Lunar Base Design Random variable Yield strength f y (aluminium f y,nom = 50 kPa) Internal pressure  int Regolith cover  reg Cross section A Section modulus W Mean value 54.1 kPa 69.0 kPa 8.3 kPa nominal value Coefficient of variation (COV) 0.07 0.30 0.12 0.03 0.04 Limit state function g ( x ) I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

22. Calculation results Ruess / Braun - Structural Reliability Considerations for Lunar Base Design Target reliability  = 4.77 I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions u1u1 u2u2 g(u) = 0 safe failure g (u) = 0    - vector Iteration result for  - values: ► Determination of required cross - sectional properties - 0.797 0.382 0.280 - 0.212 - 0.308  f y   int   reg  A  W

23. Savings in Structural Mass Ruess / Braun - Structural Reliability Considerations for Lunar Base Design P f = 10 -4,  glob  2.1 100 %40 %73 %30 % Global safety factorLRFDReliability-based on Earth  glob = 5.0P f = 10 -6,  glob  2.6  glob = 4.0 I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

24. V. Conclusions Ruess / Braun - Structural Reliability Considerations for Lunar Base Design I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions

25. Conclusions Ruess / Braun - Structural Reliability Considerations for Lunar Base Design Reliability-based framework most appropriate Agreement on target reliabilities necessary I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions Further steps should include … Influence of system redundancy Consideration of maintenance strategies Collection and statistical evaluation of data

26. Ruess / Braun - Structural Reliability Considerations for Lunar Base Design Thank you for your attention www.he-squared.com