What FEA can be used in: The whole tower analysis Detailed analysis of opening Detailed analysis of the connections Prof. Ch. Baniotopoulos I. Lavassas,

What FEA can be used in:What FEA can be used in:The whole tower analysisThe whole tower analysis

Detailed analysis of openingDetailed analysis of openingDetailed analysis of the connections Detailed analysis of the connections

Prof.Prof. Ch. BaniotopoulosCh. BaniotopoulosI. Lavassas, G. Nikolaidis, P.ZervasI. Lavassas, G. Nikolaidis, P.Zervas

Institute of Steel StructuresInstitute of Steel StructuresAristotle Univ. of Thessaloniki, GreeceAristotle Univ. of Thessaloniki, Greece

HISTWIN-High strength steel tower for wind turbines - RFSR-CT-2005-00031

Need for using a FE modelNeed for using a FE model

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A wind turbine tower is a simple cantilever.A wind turbine tower is a simple cantilever.

Assuming uniform wind pressure along its height, moment & Assuming uniform wind pressure along its height, moment & shear force at any point can be calculated directly regardless shear force at any point can be calculated directly regardless of the tower configurationof the tower configuration

Even when tower wind pressure is a function of height Even when tower wind pressure is a function of height

[ p=p(h) ] , moment & shear at the base can be calculated [ p=p(h) ] , moment & shear at the base can be calculated also by simple integrations of the load functionalso by simple integrations of the load function



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Meridional stress for local buckling check can also be Meridional stress for local buckling check can also be easily calculated by handeasily calculated by hand

Tower displacements & eigenmodes can’t be calculated Tower displacements & eigenmodes can’t be calculated so easily because of the change of the elastic so easily because of the change of the elastic characteristics of the cantilever along its height.characteristics of the cantilever along its height.

For this calculation a computational model is neededFor this calculation a computational model is needed



Computational model (Linear):Computational model (Linear):

All sections of the tower are simulated via linear All sections of the tower are simulated via linear beam elements.beam elements.

Rotor & blade system is simulated as a mass at Rotor & blade system is simulated as a mass at the top of the tower placed with eccentricitythe top of the tower placed with eccentricity

Soil-structure interaction can be simulated by the Soil-structure interaction can be simulated by the use of a rotational spring at tower baseuse of a rotational spring at tower base

By the use of a linear model we can calculate By the use of a linear model we can calculate tower displacements and perform an eigenvalue tower displacements and perform an eigenvalue analysis with accurate results. analysis with accurate results.

So what’s the need for a Finite Element model?So what’s the need for a Finite Element model?

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Need for Need for using using a FE modela FE model

Cross section of the tower is deformed due to Cross section of the tower is deformed due to the wind loadsthe wind loads

Stress concentration at the door position Stress concentration at the door position cannot be estimated by a linear modelcannot be estimated by a linear model

Bolt forces at flange positions cannot be Bolt forces at flange positions cannot be calculated from the linear model. A special calculated from the linear model. A special FE FE model is needed.model is needed.

Anchor forces and the stress state of the Anchor forces and the stress state of the

concrete on anchoring position need to be concrete on anchoring position need to be determined.determined.

Soil-structure interaction affects the tower Soil-structure interaction affects the tower dynamic characteristics, and its dynamic characteristics, and its displacements for wind loading.displacements for wind loading.


Need for Need for using using a FE modela FE model

Wind pressure distribution over the circumference Wind pressure distribution over the circumference of the tower causes ovalling of the circular tower of the tower causes ovalling of the circular tower sectionsection

But when it comes to the positions where the tower But when it comes to the positions where the tower section is much stiffer (flange & support positions) , section is much stiffer (flange & support positions) , the section shape is forced to be circular. the section shape is forced to be circular.

This causes This causes circumferencialcircumferencial stresses to the shell stresses to the shell near flange positionsnear flange positions

In buckling check (EC 3-1-6) not only In buckling check (EC 3-1-6) not only meridional meridional stressstress but but circumferencial & shear stressescircumferencial & shear stresses are are used in combination as wellused in combination as well


Modern Finite Element SoftwareModern Finite Element Software

A few years ago, developing of a complex Finite Element model A few years ago, developing of a complex Finite Element model

was very difficult due to:was very difficult due to:

Need of expensive big computers (and expensive software) to run a non-linear analysisNeed of expensive big computers (and expensive software) to run a non-linear analysisToo much effort for developing the FE model geometry and loadingToo much effort for developing the FE model geometry and loadingToToοο much effort by hand to interpret the results (stress integrations etc). much effort by hand to interpret the results (stress integrations etc).

Modern Finite Element software that can run on a simple PC offer:Modern Finite Element software that can run on a simple PC offer:

Direct input of the geometry from CAD softwareDirect input of the geometry from CAD softwareCAD capabilities inside the FEM softwareCAD capabilities inside the FEM softwareGeometrical & material non-linear analysis capabilitiesGeometrical & material non-linear analysis capabilitiesUnilateral contact with friction capabilitiesUnilateral contact with friction capabilitiesNon-linear analysis now can run on a personal computer Non-linear analysis now can run on a personal computer Automatic procedures for results interpretationAutomatic procedures for results interpretationInterfaces to join with design softwareInterfaces to join with design software


Modelling strategiesModelling strategies

Modelling Strategies can be described by the chart below:Modelling Strategies can be described by the chart below:

Overall model

Linear FE model

Foundation included Separate model for the Foundation

Included to the general model Separate models for the details

Foundation

Details (Flanges, Door position etc) : Finite Elements

Foundation model

Linear (grid on elastic support) FE model (including anchoring detail)

Three different strategies will be presentedThree different strategies will be presented


Modelling strategiesModelling strategies 1:Linear model 1:Linear model

1: Linear model for the tower, and 1: Linear model for the tower, and analytical detailed FE models to the door analytical detailed FE models to the door and flange positionsand flange positions


Modelling strategiesModelling strategies – 1:Linear model – 1:Linear model

FE model for the flanges and for the FE model for the flanges and for the anchoring systemanchoring system


Flanges are modelled using plate elementsFlanges are modelled using plate elements

Bolts are placed as linear elements connecting the Bolts are placed as linear elements connecting the

flanges active only in tensionflanges active only in tension

All other nodes are connected thru unilateral All other nodes are connected thru unilateral

contact elements.contact elements.

Moment & shear force is applied distributed Moment & shear force is applied distributed

to the circumference. to the circumference.



Advantages:Advantages:

Easy developing of the general model and the part modelsEasy developing of the general model and the part modelsFast calculation (on a simple PC: instant calculation for the overall model & 10-15 minutes for the Fast calculation (on a simple PC: instant calculation for the overall model & 10-15 minutes for the

non-linear models of the flanges)non-linear models of the flanges)Easy change of the model configurationEasy change of the model configuration

Disadvantages:Disadvantages:

Circumferencial variation of the tower loads cannot be introducedBoundary conditions for the part models need to be estimatedOnly meridional stress can be calculatedOnly meridional stress can be calculatedCircumferencial & shear stresses are neglectedCircumferencial & shear stresses are neglectedEC 3-1-6 requires the complete stress-state (meridional, circumferencial & shear) for the EC 3-1-6 requires the complete stress-state (meridional, circumferencial & shear) for the buckling buckling checkcheckOnly Axial & Shear forces and Bending moment are available to be applied to the part models. In-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 plane deformation of the tower due to the wind load distribution is neglected SoilSoil--structure interaction is neglected or need to be estimated by introducing a rotational spring structure interaction is neglected or need to be estimated by introducing a rotational spring on on tower supporttower support



Modelling the foundation by linear elementsModelling the foundation by linear elements

(grid of beams on unilateral elastic support) (grid of beams on unilateral elastic support)

to simulate soil-structure interactionto simulate soil-structure interaction


Simulates soil-structure Simulates soil-structure interactioninteractionGood for the design of the Good for the design of the

foundationfoundationIt doesn’t give an answer to It doesn’t give an answer to

the stress state of the the stress state of the anchoring systemanchoring system


Modelling strategiesModelling strategies 2:Simple FE model 2:Simple FE model

Simple FE model for the tower, and Simple FE model for the tower, and corresponding analytical FE models to the corresponding analytical FE models to the door and flange positionsdoor and flange positions


Modelling strategiesModelling strategies - 2:Simple FE model - 2:Simple FE model


Fast calculationFast calculation in PC (about 1-2 minutes a run for the general model and about 10-15 minutes in PC (about 1-2 minutes a run for the general model and about 10-15 minutes for the non-linear analysis of the flange models)for the non-linear analysis of the flange models)

Estimation of the full stress-state on any pointEstimation of the full stress-state on any point


Boundary conditions for the part models need to be estimatedBoundary conditions for the part models need to be estimatedMuch effort is needed for the transfer by hand the stress-state of a specific cross-section to the 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.corresponding cross-section of the part model.Soil-structure interaction is neglected or need to be estimated by introducing springs on tower Soil-structure interaction is neglected or need to be estimated by introducing springs on tower supportsupport


Modelling strategiesModelling strategies - 3:Detailed FE model - 3:Detailed FE model

1: Complete detailed model for 1: Complete detailed model for the tower and the foundation the tower and the foundation

Shell skirts are modelled using Shell skirts are modelled using shell elementsshell elements

Flanges are modelled using Flanges are modelled using brick elementsbrick elements Foundation is modeled using Foundation is modeled using

brick elementsbrick elements Unilateral contact to the groundUnilateral contact to the ground


Model details to the flange positionsModel details to the flange positions

Modelling Strategies – 3: Detailed FE model

Connection type for the flanges


Simulation of the eccentricity of mass at the top of the towerSimulation of the eccentricity of mass at the top of the tower

Top-flange is undeformed in-plane (rigid links connection).Top-flange is undeformed in-plane (rigid links connection).

Modelling strategies – 3:Detailed FE model


Modelling of the tower- foundationModelling of the tower- foundation

anchoringanchoring

Embedded flange to the concreteEmbedded flange to the concretePartially prestressed anchors inside (but not Partially prestressed anchors inside (but not connected to) the concreteconnected to) the concreteUnilateral contact between flanges & concreteUnilateral contact between flanges & concrete

Collapse due to anchoring system failureCollapse due to anchoring system failure

Nanamata, JapanNanamata, Japan

Modelling strategies – 3: Detailed FE model


Foundation Modelling:Foundation Modelling:

Concrete & shrink-mortar : Brick elementsConcrete & shrink-mortar : Brick elements Washer plates : Plate elementsWasher plates : Plate elements Anchors : cable type elements active only in tensionAnchors : cable type elements active only in tension Unilateral contact to the groundUnilateral contact to the ground

Modelling strategies – 3:Detailed FE model


Cross-section to the foundationCross-section to the foundation

Modelling strategies – 3:Detailed Fe model


Anchoring Modelling detailAnchoring Modelling detail

Each anchor is a single Each anchor is a single element element connecting only the washer plates connecting only the washer plates (active in (active in

tension)tension)

Unilateral contact conditions Unilateral contact conditions between between the base washer plate and the shrink the base washer plate and the shrink mortar & between the embeded washer mortar & between the embeded washer

plate and the concreteplate and the concrete



Design of the foundation-anchoring systemDesign 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



ReinfReinforcing barsorcing bars check points check points

1,2 : 1,2 : Footing, bottom meshFooting, bottom mesh

3,4 : 3,4 : Footing, top meshFooting, top mesh

5 5 :: Top of pedestal mesh Top of pedestal mesh

6 6 :: Pedestal vertical rebars (transfer of tensile anchor forces)Pedestal vertical rebars (transfer of tensile anchor forces)

7 7 :: Circumferencial reinforecement (split-up forces)Circumferencial reinforecement (split-up forces)



Modelling strategiesModelling strategies - 3:Detailed FE model - 3:Detailed FE model


Estimation of the full stress-state on any pointEstimation of the full stress-state on any pointBest possible approximation to the real-world situationBest possible approximation to the real-world situationNo transfer of loads is needed from one model to anotherNo transfer of loads is needed from one model to anotherNo need to estimate any partial model boundary conditionsNo need to estimate any partial model boundary conditions


Big effort for developing the FE modelBig effort for developing the FE modelChanges to the model are difficultChanges to the model are difficultNon-linear calculation needs time to run on a personal Non-linear calculation needs time to run on a personal computer (can take 4-5 hours a run on a modern PC)computer (can take 4-5 hours a run on a modern PC)


Tower loads

Vertical loadsVertical loads

Self mass & weight is estimated directly by the FE softwareSelf mass & weight is estimated directly by the FE software

The rotor & nacelle mass is applied to the top of the tower The rotor & nacelle mass is applied to the top of the tower distributed to the nodes ofdistributed to the nodes of

tthe upper flange taking into account he upper flange taking into account the eccentricitythe eccentricity(mass instead of loads, to be used in spectrum analysis as well)(mass instead of loads, to be used in spectrum analysis as well)

Wind loadsWind loads

At the top of the towerAt the top of the tower, rotor forces and moments are , rotor forces and moments are

appliedapplied

At tower stem wind pressure is calculated At tower stem wind pressure is calculated

acc. EC1-1-4 as a logarithmic function of z.acc. EC1-1-4 as a logarithmic function of z.


Types of analysis

Types of analysis Types of analysis for buckling check for buckling check

EC 3-1-6EC 3-1-6, LS3 (Buckling limit state), LS3 (Buckling limit state)::

LA (Linear analysis)LA (Linear analysis)MNA & MNA & LBALBA ( (Material non-linear analysis & Material non-linear analysis & Linear buckling analysis)Linear buckling analysis)GMNIA (Geometric & material non-linear analysis with imperfections)GMNIA (Geometric & material non-linear analysis with imperfections)


Types of analysis

SSeismic loading:eismic 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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Comparison of results – Wind loading

Tower displacements for the linear Tower displacements for the linear model vs FE models model vs FE models

Linear model is accurate Linear model is accurate toto the the estimation of displacements for estimation of displacements for wind loading.wind loading.


Comparison of the results – Eigenvalue analysis

11stst & 3 & 3rdrd mode mode sshapes for the hapes for the three three modelsmodels


Comparison of results

Comparison of the results for the three models


ConclusionConclusionss::

Although the use of an overall complex Finite Element model needs Although the use of an overall complex Finite Element model needs more calculation effort, it is necesary in order to establish a better more calculation effort, it is necesary in order to establish a better approach the stress state on the structureapproach the stress state on the structure

With modern Finite Element software such a nonlinear analysis can be With modern Finite Element software such a nonlinear analysis can be run on a simple personal computerrun on a simple personal computer

The cost of developing such a model is extremely small compared with The cost of developing such a model is extremely small compared with the budget of a single aeolic park installation the budget of a single aeolic park installation

Simplified models (linear model, even hand-calculation) are also Simplified models (linear model, even hand-calculation) are also necessary to develop in paralell,necessary to develop in paralell, for initial design, and for for initial design, and for checking the checking the results of the FE modelresults of the FE model


What FEA can be used in: The whole tower analysis Detailed analysis of opening Detailed analysis of the connections Prof. Ch. Baniotopoulos I. Lavassas,

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