1. What FEA can be used in:. The whole tower analysis
What FEA can be used in: The whole tower analysis Detailed analysis of opening Detailed analysis of the connections Prof. Ch. Baniotopoulos I. Lavassas, G. Nikolaidis, P.Zervas Institute of Steel Structures Aristotle Univ. of Thessaloniki, Greece
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2. Need for using a FE model
A wind turbine tower is a simple cantilever.
Assuming uniform wind pressure along its height, moment & shear force at any point can be calculated directly regardless of the tower configuration
Even when tower wind pressure is a function of height
[ p=p(h) ] , moment & shear at the base can be calculated also by simple integrations of the load function
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3. Need for using a FE model
Meridional stress for local buckling check can also be easily calculated by hand
Tower displacements & eigenmodes can’t be calculated so easily because of the change of the elastic characteristics of the cantilever along its height.
For this calculation a computational model is needed
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4. Need for using a FE model
Computational model (Linear):
All sections of the tower are simulated via linear beam elements.
Rotor & blade system is simulated as a mass at the top of the tower placed with eccentricity
Soil-structure interaction can be simulated by the use of a rotational spring at tower base
By the use of a linear model we can calculate tower displacements and perform an eigenvalue analysis with accurate results.
So what’s the need for a Finite Element model?
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5. Need for using a FE model
Cross section of the tower is deformed due to the wind loads
Stress concentration at the door position cannot be estimated by a linear model
Bolt forces at flange positions cannot be calculated from the linear model. A special FE model is needed.
Anchor forces and the stress state of the
concrete on anchoring position need to be determined.
Soil-structure interaction affects the tower dynamic characteristics, and its displacements for wind loading.
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6. Need for using a FE model
Wind pressure distribution over the circumference of the tower causes ovalling of the circular tower section
But when it comes to the positions where the tower section is much stiffer (flange & support positions) , the section shape is forced to be circular.
This causes circumferencial stresses to the shell near flange positions
In buckling check (EC 3-1-6) not only meridional stress but circumferencial & shear stresses are used in combination as well
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7. Modern Finite Element Software
A few years ago, developing of a complex Finite Element model
was very difficult due to:
Need of expensive big computers (and expensive software) to run a non-linear analysis
Too much effort for developing the FE model geometry and loading
Toο much effort by hand to interpret the results (stress integrations etc).
Modern Finite Element software that can run on a simple PC offer:
Direct input of the geometry from CAD software
CAD capabilities inside the FEM software
Geometrical & material non-linear analysis capabilities
Unilateral contact with friction capabilities
Non-linear analysis now can run on a personal computer
Automatic procedures for results interpretation
Interfaces to join with design software
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8. Modelling Strategies can be described by the chart below:
Overall model
Linear
FE model
Foundation
Foundation included
Separate model for the Foundation
Foundation model
Linear (grid on elastic support)
FE model (including anchoring detail)
Details (Flanges, Door position etc) : Finite Elements
Separate models for the details
Included to the general model
Three different strategies will be presented
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9. Modelling strategies 1:Linear model
1: Linear model for the tower, and analytical detailed FE models to the door and flange positions
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10. Modelling strategies – 1:Linear model
FE model for the flanges and for the anchoring system
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11. Modelling strategies – 1:Linear model
Flanges are modelled using plate elements
Bolts are placed as linear elements connecting the
flanges active only in tension
All other nodes are connected thru unilateral
contact elements.
Moment & shear force is applied distributed
to the circumference.
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12. Modelling strategies – 1:Linear model
Advantages:
Easy developing of the general model and the part models
Fast calculation (on a simple PC: instant calculation for the overall model & minutes for the non-linear models of the flanges)
Easy change of the model configuration
Disadvantages:
Circumferencial variation of the tower loads cannot be introduced
Boundary conditions for the part models need to be estimated
Only meridional stress can be calculated
Circumferencial & shear stresses are neglected
EC requires the complete stress-state (meridional, circumferencial & shear) for the buckling check
Only Axial & Shear forces and Bending moment are available to be applied to the part models. In- plane deformation of the tower due to the wind load distribution is neglected
Soil-structure interaction is neglected or need to be estimated by introducing a rotational spring on tower support
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13. Modelling strategies – 1:Linear model
Modelling the foundation by linear elements
(grid of beams on unilateral elastic support)
to simulate soil-structure interaction
Simulates soil-structure interaction
Good for the design of the foundation
It doesn’t give an answer to the stress state of the anchoring system
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14. Modelling strategies 2:Simple FE model
Simple FE model for the tower, and corresponding analytical FE models to the door and flange positions
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15. Modelling strategies - 2:Simple FE model
Advantages:
Fast calculation in PC (about 1-2 minutes a run for the general model and about minutes for the non-linear analysis of the flange models)
Estimation of the full stress-state on any point
Disadvantages:
Boundary conditions for the part models need to be estimated
Much effort is needed for the transfer by hand the stress-state of a specific cross-section to the corresponding cross-section of the part model.
Soil-structure interaction is neglected or need to be estimated by introducing springs on tower support
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16. Modelling strategies - 3:Detailed FE model
1: Complete detailed model for the tower and the foundation
Shell skirts are modelled using shell elements
Flanges are modelled using brick elements
Foundation is modeled using brick elements
Unilateral contact to the ground
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17. Model details to the flange positions
Modelling Strategies – 3: Detailed FE model
Model details to the flange positions
Connection type for the flanges
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18. Modelling strategies – 3:Detailed FE model
Simulation of the eccentricity of mass at the top of the tower
Top-flange is undeformed in-plane (rigid links connection).
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19. Modelling strategies – 3: Detailed FE model
Modelling of the tower- foundation
anchoring
Embedded flange to the concrete
Partially prestressed anchors inside (but not connected to) the concrete
Unilateral contact between flanges & concrete
Collapse due to anchoring system failure
Nanamata, Japan
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20. Modelling strategies – 3:Detailed FE model
Foundation Modelling:
Concrete & shrink-mortar : Brick elements
Washer plates : Plate elements
Anchors : cable type elements active only in tension
Unilateral contact to the ground
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21. Modelling strategies – 3:Detailed Fe model
Cross-section to the foundation
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22. Modelling strategies – 3:Detailed Fe model
Anchoring Modelling detail
Each anchor is a single element connecting only the washer plates (active in tension)‏
Unilateral contact conditions between the base washer plate and the shrink mortar & between the embeded washer plate and the concrete
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23. Washer & base plates (von Mises stresses)‏
Modelling strategies – 3:Detailed Fe model
Design of the foundation-anchoring system
Washer & base plates (von Mises stresses)‏
Prestressed anchors (tensile forces)‏
Non-shrink mortar (compressive & shear stresses)‏
Concrete (compressive,shear & punching shear stresses)‏
Reinforcing bars
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24. Modelling strategies – 3:Detailed Fe model
Reinforcing bars check points
1,2 : Footing, bottom mesh
3,4 : Footing, top mesh
5 : Top of pedestal mesh
6 : Pedestal vertical rebars (transfer of tensile anchor forces)‏
7 : Circumferencial reinforecement (split-up forces)‏
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25. Modelling strategies - 3:Detailed FE model
Advantages:
Estimation of the full stress-state on any point
Best possible approximation to the real-world situation
No transfer of loads is needed from one model to another
No need to estimate any partial model boundary conditions
Disadvantages:
Big effort for developing the FE model
Changes to the model are difficult
Non-linear calculation needs time to run on a personal computer (can take 4-5 hours a run on a modern PC)
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26. Tower loads Vertical loads
Self mass & weight is estimated directly by the FE software
The rotor & nacelle mass is applied to the top of the tower distributed to the nodes of
the upper flange taking into account the eccentricity
(mass instead of loads, to be used in spectrum analysis as well)‏
Wind loads
At the top of the tower, rotor forces and moments are
applied
At tower stem wind pressure is calculated
acc. EC1-1-4 as a logarithmic function of z.
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27. Types of analysis for buckling check
EC 3-1-6, LS3 (Buckling limit state):
LA (Linear analysis)‏
MNA & LBA (Material non-linear analysis & Linear buckling analysis)‏
GMNIA (Geometric & material non-linear analysis with imperfections)‏
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28. Types of analysis Seismic loading:
Response spectrum analysis for the seismic loading must be performed
Additional time history harmonic response analysis for the seismic loading
(only in extreme cases)‏
Due to the distributed mass of the tower itself two eigenmodes are participating. Equivalent lateral load method cannot be used
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29. Comparison of results – Wind loading
Tower displacements for the linear model vs FE models
Linear model is accurate to the estimation of displacements for wind loading.
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30. Comparison of the results – Eigenvalue analysis
1st & 3rd mode shapes for the three models
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31. Comparison of the results for the three models
Comparison of results
Comparison of the results for the three models
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32. Conclusions:
Although the use of an overall complex Finite Element model needs more calculation effort, it is necesary in order to establish a better approach the stress state on the structure
With modern Finite Element software such a nonlinear analysis can be run on a simple personal computer
The cost of developing such a model is extremely small compared with the budget of a single aeolic park installation
Simplified models (linear model, even hand-calculation) are also necessary to develop in paralell, for initial design, and for checking the results of the FE model
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