EWEA 2011 Brussels, Belgium: Europe’s Premier Wind Energy Event Structural reliability analysis of rotor blades in ultimate loading K. C. Bacharoudis 1 , D. J. Lekou 2 , T. P. Philippidis 1 1. University of Patras, Dept. of Mechanical Engng & Aeronautics, Greece 2. Centre for Renewable Energy Sources, Wind Energy Division, Greece Brussels, 14-17 March 2011
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EWEA 2011 Brussels, Belgium: Europe’s Premier Wind Energy Event
EWEA 2011 Brussels, Belgium: Europe’s Premier Wind Energy Event. Structural reliability analysis of rotor blades in ultimate loading. K. C. Bacharoudis 1 , D. J. Lekou 2 , T. P. Philippidis 1 University of Patras , Dept. of Mechanical Engng & Aeronautics, Greece - PowerPoint PPT Presentation
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EWEA 2011 Brussels, Belgium:Europe’s Premier Wind Energy Event
EWEA 2011 Brussels, Belgium:Europe’s Premier Wind Energy Event
Structural reliability analysis of rotor blades in ultimate loading
K. C. Bacharoudis1, D. J. Lekou2, T. P. Philippidis1 1. University of Patras, Dept. of Mechanical Engng & Aeronautics, Greece2. Centre for Renewable Energy Sources, Wind Energy Division, Greece
Brussels, 14-17 March 2011
The objectives are:
• Reliability assessment of a given design (safety factors, Target reliability)
• New probabilistic design, sensitivity studies (Improve/optimize blade structural design)
• Sectional analysis based on thin wall multi cellular theory was performed by a numerical tool (THIN)
• Monte Carlo, Edgeworth expansion method and Response Surface method/Monte Carlo were used
• Stress resultants, engineering elastic constants (E1, E2 , v12 , G12) and failure stresses (XT, XC, YT, YC, S) in the principal coordinate system of the UD ply were considered random variables (RV)
Element failure probabilityElement failure probability
i j
Laminate
i j
Assuming :•Laminate is a series system of layers•Each ply has one failure mode described by the specified failure criterion•Positive correlated failure modes among the layers
Brussels, 14-17 March 2011
z
Nz
Mz
Nx
xMx
NyMy
y
Element failure probabilityElement failure probability
i j
Laminate
i j
1
1
max , ,
max , ,
max ,
node i layer layer n
node j layer layer n
element node i node j
f f f
f f f
f f f
P P P
P P P
P P P
Brussels, 14-17 March 2011
z
Nz
Mz
Nx
xMx
NyMy
y
Failure criterionFailure criterion
i j
Laminate
i j
Limit state function for every ply formulated by Tsai-Hahn failure criterion
1
1
max ,
max , ,
max , ,
element node i node j
node i layer layer n
node j layer layer n
f f f
f f f
f f f
P P P
P P P
P P P
0 , 0g fail g safe 1g X R
Brussels, 14-17 March 2011
Reliability methods: Monte CarloReliability methods: Monte Carlo
Basic Variables (RVs)
E1, E2, v12, G12
XT, XC, YT, YC, SNx, Ny, Nz, Mx, My, Mz,
THIN analysis Output Variable (RV)
εx, εy, εs
Limit state function
g x R 1
• Random number generation for the basic variables•THIN analysis•Evaluation of limit state function• Layer failure probability
•Estimation of element failure probability• 2,000,000 simulations
• Random number generation for the basic variables•Stress-strain analysis through regression models•Evaluation of limit state function• Layer failure probability
•Estimation of element failure probability• 2,000,000 simulations
Design of Experiment10 input variables5 levels to be tested for every input variable (circumscribed CCD)6 output parameters (strains at the lower face of the bottom and the upper face of the top ply of the laminate).149 THIN analyses
Brussels, 14-17 March 2011
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0 10 20 30 40 50
Failu
re p
roba
bilit
y
# element
MC
RSM
EDW
Very good agreement between MC and RSM/MC.EDW is less accurate. (Correlation was not considered)
Failure Probability (IFF): Section 9.2mFailure Probability (IFF): Section 9.2m
[90][90]
[90]
[90][90]
[90]
[90]
[45] [45] [45]
[45]
[45]
[45]
[45]
[-45]
[-45][45]
[45][-45]
[-45]
[-45]
[90][90]
[90][90][90][90][90]
[90]
[90]
[90]
[90][90]
[90]
[90]
[90]
[45]
[-45]
[90]
[45]
Layer #
1
6
1220
26
32
40
41
44
45
48
Element #
Brussels, 14-17 March 2011
Failure Probability (IFF): Section 9.2mFailure Probability (IFF): Section 9.2m