Transcript Document 7408345

Structural Reliability Considerations
for Lunar Base Design
Florian RUESS & Benjamin BRAUN
HE2
Habitats for Extreme Environments
www.he-squared.com
Rutgers Symposium on
Lunar Settlements
3-8 June 2007
New Brunswick, NJ
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Contents
I.
Motivation
II.
Structural Concepts
III. Structural Reliability
IV. Example
V.
Conclusions
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Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
I. Motivation
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
NASA Constellation Program
The Vision for Space Exploration
Photo: NASA
Goals on the Moon:
Science, Exploration Preparation, Eventual Settlement…
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Everybody wants to go to the Moon
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
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
II. Structural Concepts
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Structure Classification
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
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Structural Concepts
Focusing on second generation habitats, most proposed
concepts can be divided into:
• inflatable structures
• cable structures
• rigid structures
Photo: NASA
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Rigid Structures
Advantages:
• experience
• robustness
• all-in-one concept possible
Disadvantage:
Photo and concept: Schroeder et al.
• relatively large volume + mass
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
A Tied-Arch Shell Structure
Concept by HE2 and H. Benaroya
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Structural Design on the Moon
Scope of existing design standards exceeded
Many more uncertainties exist
► resistances, e.g. new materials
► loads, e.g. micrometeoroid impacts
Global safety factor concept
Reliability-based concept
• easy to apply
• complex to use
• uneconomic
• efficient
• actual reliability unknown
• quantitive measure of safety
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
III. Structural Reliability
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Classical vs. Structural Reliability
Technical components
Structural systems
• large numbers, same type
• unique components
• single failure mode
• different failure modes
• relative failure frequencies
• rare failures
© KMJ
Characteristics of the reliability analysis
1000 hours / life
• failure due to ageing
• failure due to extreme events
• estimation of life-time
• measure of safety
probabilistic modeling of
time until failure
► failure rate
probabilistic modeling of
resistances and loads
► reliability index b
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
How to picture the reliability index ?
Probabilistic models for the uncertain
► resistance R
► load S
fM (x)
failure
Probability of failure:
probability density function
of the safety margin M
safe
PF  PM  R  S  0 



 f x  f x  dx  
R
S

f M x  dx

M
In case of two N-distributed variables:
 x  M
PF  
 M

  b


x
-3,5
-2,5
-1,5
-0,5
0,5
bM
1,5
2,5
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
3,5
4,5
5,5
6,5
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Limit state functions
In the general case:
functions of several random variables x
R – S = fR(x) – fS(x) = g(x)
u2
safe
g(u) > 0
Limit state function g(x) can be
u1
► linear
failure
► nonlinear
g(u) < 0
Normalisation of the
random variables x:
g(x) → g(u)
g(u) = 0
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Limit state functions
In the general case:
functions of several random variables x
R – S = fR(x) – fS(x) = g(x)
g (u) = 0
u2
safe
g(u) > 0
Limit state function g(x) can be
► linear
u1
b
failure
► nonlinear
g(u) < 0
a - vector
Normalisation of the
random variables x:
g(x) → g(u)
g(u) = 0
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
How safe is safe enough ?
b
Pf
2.33
10-2
3.09
10-3
3.72
10-4
Level of safety depends on
• Societal acceptance
• Costs
Structural codes
on Earth
• Failure consequences
• injuries
4.27
10-5
?
4.77
10-6
Target reliabilities
on the Moon
• loss of life
• economic loss
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
IV. Example
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Example Calculation
Internal pressure

N M

 fy
A W
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Example Calculation
Regolith cover

N M

 fy
A W
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Assumptions for random variables
Random variable
Mean value
Coefficient of
variation (COV)
Yield strength fy
54.1 kPa
0.07
Internal pressure int
69.0 kPa
0.30
Regolith cover reg
8.3 kPa
0.12
Cross section A
nominal value
0.03
Section modulus W
nominal value
0.04
(aluminium fy,nom = 50 kPa)
Limit state function g(x)
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Calculation results
• Target reliability b = 4.77
u2
g (u) = 0
• Iteration result for a - values:
safe
afy
aint
areg
- 0.797
0.382
u1
b
failure
0.280
aA
- 0.212
aW
- 0.308
a - vector
g(u) = 0
► Determination of required cross - sectional properties
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Savings in Structural Mass
on Earth
100 %
73 %
Global safety factor
gglob = 5.0
gglob = 4.0
40 %
30 %
Reliability-based
LRFD
Pf = 10-6, gglob  2.6
Pf = 10-4, gglob  2.1
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
V. Conclusions
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Conclusions
• Reliability-based framework most appropriate
• Agreement on target reliabilities necessary
• Further steps should include …
• Influence of system redundancy
• Consideration of maintenance strategies
• Collection and statistical evaluation of data
I. Motivation – II. Structural Concepts – III. Structural Reliability – IV. Example – V. Conclusions
Ruess / Braun - Structural Reliability Considerations for Lunar Base Design
Thank you for your attention
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