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3 - Structural Integrity Evaluation of Offshore Wind Turbines - Giuliani

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Published on March 10, 2014

Author: StroNGER2012

Source: slideshare.net

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ASCE Earth & Space 2010 OWT Symposium

http://content.asce.org/files/pdf/EarthSpace2010Prelim-FINAL.pdf

http://ascelibrary.org/doi/book/10.1061/9780784410967
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Structural Integrity Evaluation of Offshore Wind Turbines Luisa Giuliani Franco Bontempi luisa.giuliani@uniroma1.it franco.bontempi@uniroma1.it Structural and Geotechnical Engineering Department University of Rome “La Sapienza”

Presentation outlineEARTH&SPACE 2010 STRUCTURAL INTEGRITY OF OFFSHORE WIND TURBINES What is it and why to care about it STRATEGIES AND MEASURE OF ACHIEVEMENT Robustness and vulnerability A CASE STUDY Investigation of an offshore turbine response to a ship collision CONCLUSIONS Conclusive evaluations on application and methodology L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 2/26 A CASE STUDY Investigation of an offshore turbine response to a ship collision STRATEGIES AND MEASURE OF ACHIEVEMENT Robustness and vulnerability CONCLUSIONS Conclusive evaluations on application and methodology STRUCTURAL INTEGRITY OF OFFSHORE WIND TURBINES What is it and why to care about it

Why care about structural integrity?EARTH&SPACE 2010 MIDDELGRUNDENS VINDMØLLELAUG Offshore wind farm in Øresund, outside Copenhagen harbor, 2000) Operator: Dong Energy Owner: 50% investor cooperative 50% municipality Official website: http://www.middelgrunden.dk L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 3/26

L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines Why care about structural integrity? 4/26 EARTH&SPACE 2010 RUNAWAY EVENT (Jutland, 2008) 1. High wind and breaking system failure 2. Blades spin out of control and fail 3. Blade debris collided with the tower4. Turbine tower collapses to the ground.

Why care about structural integrity?EARTH&SPACE 2010 RUNAWAY EVENT (Jutland, 2008) 1. High wind and breaking system failure 2. Blades spin out of control and fail 3. Blade debris collided with the tower4. Turbine tower collapses to the ground. DISPROPORTION BETWEEN CAUSE AND EFFECT L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 4/26

Disproportionate collapse in standardsEARTH&SPACE 2010 ASCE 7ASCE 7--02, 200202, 2002 The structural system shall be able to sustain local damage or failure with the overall structure remaining stable and not be damaged to an extend disproportionate to the original local damage GSA guidelines, 2003GSA guidelines, 2003 the building must withstand as a minimum, the loss of one primary vertical load-bearing member without causing progressive collapse Unified facilities criteriaUnified facilities criteria UFC 4UFC 4--023023--03, DoD 200503, DoD 2005 All new and existing buildings with three stories or more in height must be designed to avoid progressive collapse Model code 1990Model code 1990 Structures should withstand accidental circumstance without damage disproportionate to the original events (insensitivity requirement) ISO/FDIS 2394, 1998ISO/FDIS 2394, 1998 Structures and structural elements should satisfy, with proper levels of reliability: -exercise ultimate state requirements - load ultimate state requirements - structural integrity state requirements EN 1991EN 1991--11--7:20067:2006 Structures should be able to withstand accidental actions (fires, explosions, impacts) or consequences of human errors, without suffering damages disproportionate to the triggering causes CODESAMERICAN EUROPEAN L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 5/26

Structural integrityEARTH&SPACE 2010 STIFFNESS Service limit states (SLS) RESISTANCE STRUCTURALSAFETY Ultimate limit states (ULS) SECTIONSSECTIONS OR ELEMENTSOR ELEMENTS ? R > S f < ff < fadmadm RESISTANCE TO EXCEPTIONAL ACTION Structural integrity limit state (SILS) STRUCTURAL SYSTEM verification on FAILURE IS PREVENTED FAILURE IS PRESUMED L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 6/26

OFFSHORE STANDARD, DNVOFFSHORE STANDARD, DNV--OSOS--J101, 2004J101, 2004 The structural system shall be able to resists accidental loads and maintain integrity and performance of the structure due to local damage or flooding. CONSIDERED LIMIT STATESCONSIDERED LIMIT STATES ACCIDENTAL ACTIONSACCIDENTAL ACTIONS Structural integrity for OWTEARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 7/26 ULS Ultimate Limit States ALS Accidental Limit States FLS Fatigue Limit States SLS Serviceability Limit States maximum load carrying resistance failure due to the effect of cyclic loading damage to components due to an accidental event tolerance criteria applicable to normal use

Presentation outlineEARTH&SPACE 2010 STRUCTURAL INTEGRITY OF WIND TURBINE What is it and why to care about it STRATEGIES AND MEASURE OF ACHIEVMENT Robustness and vulnerability A CASE STUDY Investigation of an offshore turbine response to a ship collision CONCLUSIONS Conclusive evaluations on application and methodology L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 8/26 STRUCTURAL INTEGRITY OF WIND TURBINE What is it and why to care about it STRATEGIES AND MEASURE OF ACHIEVMENT Robustness and vulnerability

Different factors affecting structural integrityEARTH&SPACE 2010 P(F) = P(D|H) P(F|DH)P(H) x x occurrence of collapse VULNERABILITY ROBUSTNESSEXPOSURE VULNERABILITY ROBUSTNESSEXPOSURE [Faber,2006] [Ellingwood,1983] STRUCTURALNON STRUCTURAL MEASURES avoid dispropor. collapselimit initial damageevent control 2) reduce the effects of the action 3) reduce the effects of a failure 1) reduce the action damage is caused in the structure critical event occurs near the structure damage spreads in the structure L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 9/26

EVENT CONTROL Non structural measuresEARTH&SPACE 2010 Malfunctioning and fire Natural actions Ship collision Malevolent attack System control Protective barriers Sacrificial structures Surveillance L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 10/26 a. Difficult to prevent every possible accidental event b. Difficult to protect WT (exposed to natural action) c. Difficult to surveille WT (wide and isolated area) reduce the occurrence of the action reduce the exposure of the structure 1)1) REDUCE THE ACTIONREDUCE THE ACTION

Structural measuresEARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 11/26 T O P D O W N Identification of failures at meso-level (intermediate components) Identification of failures at micro level (basic components) B O T T O M U P Deductive (top-down): critical event is modeled Inductive (bottom-up): critical event is irrelevant ROBUSTNESS 2) REDUCE THE EFFECTS2) REDUCE THE EFFECTS OF THE ACTIONOF THE ACTION 3) REDUCE THE EFFECTS3) REDUCE THE EFFECTS OF A FAILUREOF A FAILURE VULNERABILITY SHIP COLLISION DAMAGED COMPONENTS

d )d(R I ∆ ∆ = Structural robustnessEARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 12/26 structure B d P s STRUCTURE B: P s ROBUSTNESS CURVES P (performance) structure A STRUCTURE A damaged integer ∆P damaged more performant, less resistant integer (damage level) ∆P∆P more performant, less robust less performant, more robust PERFORMANCE ultimate resistance DAMAGE LEVEL # removed elements STRUCTURAL ROBUSTNESS: Insensitivity to local failure (ASCE/SEI-PCSGC, 2007 – Betonkalender, 2008) Proposed robustness measure: decrement of resistance that corresponds to an increment of damage in the structure

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 13/26 28 0 1 2 --- 8 d λ Exact maxima and minima curves EXHAUSTIVE INVESTIGATIONEXHAUSTIVE INVESTIGATION 1 Cd EX. 81 Exhaustive combinations Cd = E! d! × (E-d)! Ctot = Σd Cd = 2E 0 for D = E D a structure of 8 elements is considered as example Robustness curves

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 13/26 0 1 2 --- 8 d Approximated maxima and minima curves HEURISTIC OPTIMIZATIONHEURISTIC OPTIMIZATION ERROR! (non cons.) 14 2 Reduced combinations = 1 d>1 Cd = = 2 ×[E-(d-1)] = E d=1 d=0 0 D Ctot = Σd Cd = E2 + 1 for D = E 1 28 Exhaustive combinations Cd = E! d! × (E-d)! Ctot = Σd Cd = 2E 0 for D = E D exponentialexponential polynomialpolynomial 8 Cd EX. Cd RED. a structure of 8 elements is considered as example Robustness curves

8/31 11/31 Stiffbeams(flex.behaviour)Stiffcolumns(shear-type) STRUCTURALBEHAVIOUR 16 17 18 13 14 15 9 10 121 1 5 6 87 1 2 43 19 20 21 λλλλλλλλgg 16 17 18 13 14 15 9 10 121 1 5 6 87 1 2 43 19 20 21 λλλλλλλλgg SHEAR-TYPE FRAME ROBUSTNESS 00,51 17 1 2 3 4 5 6 7 8 9 10 Damage Level PU[ad] MAX MIN FLEX-TYPE FRAME ROBUSTNESS 00,250,50,751 0 1 2 3 4 5 6 7 8 9 10 Damage Level PU[ad] MAX MIN λg 5 6 87 9 10 12 13 14 15 16 17 18 19 20 21 41 2 3 11 λg 14 17 1513 18 19 5 6 87 1211 41 2 3 9 10 16 20 21 1 2 43 5 6 87 9 10 1211 13 14 15 16 17 18 19 20 21 λg λg 14 17 20 1513 1816 2119 5 6 87 41 2 3 9 10 1211 EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 14/26 Comparison between different design solutions

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 15/26 Robustness applied to OWT OWT ROBUSTNESS COMPARISON between two jacket structures between two support types

Presentation outlineEARTH&SPACE 2010 STRUCTURAL INTEGRITY OF WIND TURBINE What is it and why to care about it STRATEGIES AND MEASURE OF ACHIEVMENT Robustness and vulnerability A CASE STUDY Investigation of an offshore turbine response to a ship collision CONCLUSIONS Conclusive evaluations on application and methodology L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 16/26 STRUCTURAL INTEGRITY OF WIND TURBINE What is it and why to care about it A CASE STUDY Investigation of an offshore turbine response to a ship collision STRATEGIES AND MEASURE OF ACHIEVMENT Robustness and vulnerability

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 17/26 OWT ship collision investigation

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 18/26 OWT ship collision investigation OWTSTRUCTURE MODELING Pointed mass for modeling rotor and nacelle. One-dimensional elements for leg and tower with elastic-plastic behavior (spread plasticity). Soil interaction accounted with 3D finite elements, which behave elastically. Zone extension calibrated in order to minimize boundary effects. Typical OWT: 5-6 MW power 36 m water depth. S355 steel monopile with hollow circular section; diameter and thickness vary along the tower. 4 diagonal legs connected to 4 45 m long foundation piles, 40 m deepened into the ground.

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 19/26 OWT ship collision investigation OWTLOAD SCENARIOS SHIP IMPACT MODELING Only self-weight is assumed to act on the turbine at the moment of impact. Three different scenarios are considered for ship collision point: A. Impact on one diagonal leg under the seabed (model node #17); 700 ton700 ton AA

700 ton700 ton AA EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 19/26 OWT ship collision investigation OWTLOAD SCENARIOS SHIP IMPACT MODELING Only self-weight is assumed to act on the turbine at the moment of impact. Three different scenarios are considered for ship collision point: A. Impact on one diagonal leg under the seabed (model node #17); B. Impact at the seabed (model node #38); 700 ton700 ton BB

700 ton700 ton BB EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 19/26 OWT ship collision investigation OWTLOAD SCENARIOS SHIP IMPACT MODELING Only self-weight is assumed to act on the turbine at the moment of impact. Three different scenarios are considered for ship collision point: A. Impact on one diagonal leg under the seabed (model node #17); B. Impact at the seabed (model node #38); C. Impact on the tower above the seabed (model node #548). t [s] F [MN] 0.5 1.5 2.00.0 7 Ship impact is modeled by means of an impulsive force acting on the collision point. The value of the force is 7 MN (ca. 700 ton) and the total length of the impulsive function is 2 s. Nonlinear dynamics analyses are carried on the structure. 700 ton700 ton CC

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 20/26 Nonlinear dynamic investigations SCENARIO A time: 0.025 s

time: 0.0 s EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 20/26 Nonlinear dynamic investigations SCENARIO A time: 0.3 s

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 20/26 Nonlinear dynamic investigations SCENARIO A time: 0.3 stime: 0.5 s

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 20/26 Nonlinear dynamic investigations SCENARIO A time: 0.5 stime: 0.8 s

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 20/26 Nonlinear dynamic investigations SCENARIO A time: 0.8 stime: 1.5 s

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 20/26 Nonlinear dynamic investigations SCENARIO A time: 1.5 stime: 3.0 s

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 21/26 Nonlinear dynamic investigations SCENARIO B time: 0.0 s

time: 0.0 s EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 21/26 Nonlinear dynamic investigations SCENARIO B time: 1.0 s

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 21/26 Nonlinear dynamic investigations SCENARIO B time: 1.0 stime: 3.0 s

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 22/26 Nonlinear dynamic investigations SCENARIO C time: 0.0 s

time: 0.0 s EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 22/26 Nonlinear dynamic investigations SCENARIO C time: 1.0 s

time: 1.0 s EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 22/26 Nonlinear dynamic investigations SCENARIO C time: 3.0 s

CONCLUSIONS Conclusive evaluations on application and methodology CONCLUSIONS Conclusive evaluations on application and methodology Presentation outlineEARTH&SPACE 2010 STRUCTURAL INTEGRITY OF WIND TURBINE What is it and why to care about it STRATEGIES AND MEASURE OF ACHIEVMENT Robustness and vulnerability A CASE STUDY Investigation of an offshore turbine response to a ship collision L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 23/26 STRUCTURAL INTEGRITY OF WIND TURBINE What is it and why to care about it A CASE STUDY Investigation of an offshore turbine response to a ship collision STRATEGIES AND MEASURE OF ACHIEVMENT Robustness and vulnerability

SCENARIO EFFECT OF ACTION EFFECT OF DAMAGE A Irreversible direct damage of impacted leg: VULNERABLE TO ACTION (not disproportionate, local resistance may be increased) Overloading of adjacent legs and part of monopile, but no damage propagation: ROBUST BEHAVIOR (other damages to be studied) B Elastic deformation: NOT VULNERABLE TO CONSIDERED ACTION --- C Elastic deformation: NOT VULNERABLE TO CONSIDERED ACTION --- EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 24/26 Nonlinear dynamic investigation results 700 ton700 ton 700 ton700 ton 700 ton700 ton 700 ton700 ton

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 25/26 FAILURECAUSES TYPES ACCIDENTAL ACTIONS HUMAN ERRORS § DESIGN § EXECUTION § MAINTENANCE § IMPACTS § COLLISIONS § FIRES UNFAVORABLE COMBINATIONS of usual load values or circumstances: SWISS CHEESE THEORY BLADES § OVER SPEED § FATIGUE FAILURE § LOCAL BUCKLING Handling exceptions of OWT

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 25/26 FAILURECAUSES TYPES ACCIDENTAL ACTIONS HUMAN ERRORS § DESIGN § EXECUTION § MAINTENANCE § IMPACTS § COLLISIONS § FIRES UNFAVORABLE COMBINATIONS of usual load values or circumstances: SWISS CHEESE THEORY BLADES § OVER SPEED § FATIGUE FAILURE § LOCAL BUCKLING TOWER § SHAFT CRACKS § WELDING FAILURE (FATIGUE OR FAULTY DESIGN) Handling exceptions of OWT

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 25/26 FAILURECAUSES TYPES ACCIDENTAL ACTIONS HUMAN ERRORS § DESIGN § EXECUTION § MAINTENANCE § IMPACTS § COLLISIONS § FIRES UNFAVORABLE COMBINATIONS of usual load values or circumstances: SWISS CHEESE THEORY BLADES § OVER SPEED § FATIGUE FAILURE § LOCAL BUCKLING TOWER § SHAFT CRACKS § WELDING FAILURE (FATIGUE OR FAULTY DESIGN) FOUNDATION § MOSTLY FOR OWT IN CONSTRUCTION Handling exceptions of OWT

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 26/26 PreventionPrevention Indirect design Direct design Top-down methods Bottom-up methods Collapse resistance Structural robustness PresumptionPresumption Event control SpecificSpecific analysesanalyses StructuralStructural measuresmeasures performedavoided CriticalCritical eventevent modeled no yes Invulnerability Unaccounted may happen! No hazards can occur Hazards don’t cause failure Progressive collapse susceptibility ? Effects areEffects are uncertainuncertain ? Behavior followingBehavior following other hazardsother hazards remains unknown!remains unknown! irrelevant FAULTFAULTFAILUREFAILURE SECURITYSECURITY INVULNERABILITYINVULNERABILITY Handling exceptions of OWT

Structural Integrity Evaluation of Offshore Wind Turbines Luisa Giuliani Franco Bontempi luisa.giuliani@uniroma1.it franco.bontempi@uniroma1.it Structural and Geotechnical Engineering Department University of Rome “La Sapienza”

10/31 1 2 S14 32 4 S1 S124 3 4 S2 3 S124 4 S3 2 1 3 4 1 2 3 4 1 4 1 3 1 2 42 3 2 4 3 42 3 2 1 1 1 4 3 42 3 d=0 d=2 d=1 d=3 2 1 3 4d=4 3 4 S123 S1234 4 S134 S13 4 S134 S23 4 S134 S12 4 S4 S0 Computational tree of a non-deterministic Turing machine: all possible configurations are computed in polynomial time (# computational steps s = # system elements E). State of acceptance: damaged configuration Initial state: nominal configuration Damaged configurationsEARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 13/26

DI1Di1, D/d r1 maxI a i i a <<→<<∀       − = EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides 0 1 2 3 4 5 6 d λ 0 1 2 3 4 5 6 d λa. Maximum inclination of all the secant lines that connect the first point of the curves with the points pertaining to greater damage levels.

DI1Di1, D/d r1 maxI a i i a <<→<<∀       − = EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides 0 1 2 3 4 5 6 d λ 0 1 2 3 4 5 6 d λa. Maximum inclination of all the secant lines that connect the first point of the curves with the points pertaining to greater damage levels b. Highest variation of secant lines between two subsequent points (critical elements are most relevant) ( ) ( ) Di 2 rrrr maxI 1iii1i b <∀       −−− = +− )isostatic(5.0I0)linear( b ≤≤←

DI1Di1, D/d r1 maxI a i i a <<→<<∀       − = EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides c. Area subtended by the curve of minima weighted by the difference between that area and the area subtended from the curve of maxima (representing the scattering) a. Maximum inclination of all the secant lines that connect the first point of the curves with the points pertaining to greater damage levels b. Highest variation of secant lines between two subsequent points (critical elements are most relevant) [ ] [ ]       −⋅+= ∑∑ == D 0d LOWUP D 0d LOW c )d(r)d(rk)d(rDI ( ) 1k0for,1D2I5.0 c <<−⋅<≤→ 0 1 2 3 4 5 6 d λ 0 1 2 3 4 5 6 d λ ( ) ( ) Di 2 rrrr maxI 1iii1i b <∀       −−− = +− )isostatic(5.0I0)linear( b ≤≤←

( ) ( ) Di 2 rrrr maxI 1iii1i b <∀       −−− = +− )isostatic(5.0I0)linear( b ≤≤← DI1Di1, D/d r1 maxI a i i a <<→<<∀       − = EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides 0 1 2 3 4 5 6 d λ 0 1 2 3 4 5 6 d λ c. Area subtended by the curve of minima weighted by the difference between that area and the area subtended from the curve of maxima (representing the scattering) a. Maximum inclination of all the secant lines that connect the first point of the curves with the points pertaining to greater damage levels b. Highest variation of secant lines between two subsequent points (critical elements are most relevant) d. Scattering from linear trend, calculated as the area subtended between the curves and the straight line that connect the point of the integer structure with that one of the null one. [ ] [ ] 2 D )1k()d(rk)d(rI D 0d UP D 0d LOW d ∑∑ == +−+= EDand1k0for,1I1 d =<<<≤−→ ( ) 1k0for,1D2I5.0 c <<−⋅<≤→[ ] [ ]      −⋅+= ∑∑ == D 0d LOWUP D 0d LOW c )d(r)d(rk)d(rDI

( ) ( ) Di 2 rrrr maxI 1iii1i b <∀       −−− = +− )isostatic(5.0I0)linear( b ≤≤← [ ] [ ]       −⋅+= ∑∑ == D 0d LOWUP D 0d LOW c )d(r)d(rk)d(rDI ( ) 1k0for,1D2I5.0 c <<−⋅<≤→ [ ] [ ] 2 D )1k()d(rk)d(rI D 0d UP D 0d LOW d ∑∑ == +−+= EDand1k0for,1I1 d =<<<≤−→ DI1Di1, D/d r1 maxI a i i a <<→<<∀       − = EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides c. Area subtended by the curve of minima weighted by the difference between that area and the area subtended from the curve of maxima (representing the scattering) a. Maximum inclination of all the secant lines that connect the first point of the curves with the points pertaining to greater damage levels b. Highest variation of secant lines between two subsequent points (critical elements are most relevant) e. Upper and lower bound for maximal damage that makes the structure unstable UPLOW e DkDI ⋅+= E2I0and1k0andDDD1 c UPLOW ≤≤<<≤≤≤← d. Scattering from linear trend, calculated as the area subtended between the curves and the straight line that connect the point of the integer structure with that one of the null one. 0 1 2 3 4 5 6 d λ 0 1 2 3 4 5 6 d λ DLOW DUP

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides START d := 0 for e =1 to E d := 1 NL static analysis λu 0 λu,e 1 Remove element e Pushover analysis Restore element e for d = 2 to D λu 1 MAX, e1 MAX λu 1 MIN, e1 MIN Remove element e(d-1) MIN for e =1 to E λu,e d Remove element e Pushover analysis Restore element e CALLCALL ““CURVE MAXCURVE MAX”” CALLCALL ““CURVE MINCURVE MIN”” Robustness quantification if e <> ed MIN λu d MIN, ed MIN ““CURVE MINCURVE MIN““ MACROMACRO Curve of minima END Restore integer structure Calculate area or derivativesExtrapolate equations Calculate corresponding ∆RFix an admitted ∆d Identify critical elementsSpot abrupt decrement ROBUSTNESS QUANTIFICATIONROBUSTNESS QUANTIFICATION ALGORITHM FOR HEURISTIC OPTIMIZATIONALGORITHM FOR HEURISTIC OPTIMIZATION

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides Pushover on integer structure Resulting robustness histogram Plastic strain development Axial stress development Meshed elements Plastic moment development Response curve Max and min robustness histogramsPlasticization development ALGORITHM FOR REDUCED ANALYSESALGORITHM FOR REDUCED ANALYSESMax resistance

STAR STRUCTURE ROBUSTNESS 00,51 0 1 2 3 4 5 6 7 8 Damage Level PU[ad] MAX MIN t d R R Dd cos25.0max ,...,1 ←=       ∂ ∂ =′ = EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides # of elements: E = 8 static indetermin. level: i = 21 lower max. damage: Dmin = 8 upper max. damage: Dmax = 8 fixed max. damage: D = 8 reduced combination: Cred = 65 exhaust. combination: Cex= 256 λλgg 1 2 4 3 5 8 6 7 STATIC INDETERMINANCY: high restrain grade Damage d El. ID Pumin El. ID Pumax 0 0 1 0 1 1 1 0,831745 3 0,896185 2 5 0,648331 7 0,832096 3 4 0,523591 2 0,684849 4 8 0,376882 8 0,580928 5 2 0,269581 6 0,429733 6 6 0,16434 4 0,320632 7 7 0,042504 1 0,261956 8 3 0 5 0 MIN CFG MAX CFG Ib ≈ 0 Ia ≈ 1 ROBUSTNESS INDICATOR: ( ) ( ) Di 2 rrrr maxI 1iii1i b <∀       −−− = +− )isostatic(5.0I0)linear( b ≤≤→ Ed0 Ed )d(r maxIa ≤≤∀       = )isostatic(EI1 b ≤≤→ Ib maximum slope pt. tangent (measure the abrupt decrement due to the removal of critical element) Ia maximum secant starting from the 1st pt. (account for the lateness of an abrupt decrement)

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides # of elements: E = 21 static indetermin. level: i = 4 lower max. damage: Dmin = 2 upper max. damage: Dmax = 9 fixed max. damage: D = 9 reduced combination: Cred = 286 exhaust. combination: Cex= 695860 λ 15 16 1417 11 9 1210 18 20 1921 13 7 5 3 1 2 4 6 8

TRUSS STRUCTURE ROBUSTNESS 00.250.50.751 0 1 2 3 4 5 6 7 8 9 Damage Level PU [ad] MAX MIN EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides # of elements: E = 21 static indetermin. level: i = 4 lower max. damage: Dmin = 2 upper max. damage: Dmax = 9 fixed max. damage: D = 9 reduced combination: Cred = 286 exhaust. combination: Cex= 695860 Damage d El. ID Pumin El. ID Pumax 0 0 1 0 1 1 9 0,471351 1 0,888941 2 3 0 2 0,888941 3 10 0 11 0,628625 4 17 0 12 0,628625 5 16 0 5 0,628625 6 1 0 6 0,628625 7 5 0 13 0,628625 8 11 0 14 0,628625 9 6 0 17 0 MIN CFG MAX CFG 12 1 2 11 5 6 13 14 17 9 3 λ 15 16 1417 11 9 1210 18 20 1921 13 7 5 3 1 2 4 6 8 MAX 1 15 16 14 11 9 1210 18 20 1921 13 7 5 3 2 6 84 17 0,26 > Ib > 0,13 MIN 15 16 1417 11 9 1210 18 20 1921 13 7 5 3 1 2 4 6 8 4,76 > Ia > 1,11

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides # of elements: E = 13 static indetermin. level: i = 12 lower max. damage: Dmin = 2 upper max. damage: Dmax = 10 fixed max. damage: D = 10 reduced combination: Cred = 158 exhaust. combination: Cex= 8100 5 8 6 97 12 10 1311 4 2 31 λ

VIERENDEEL STRUCTUREROBUSTNESS 00,250,50,751 0 1 2 3 4 5 6 7 8 9 10 Damage Level PU [ad] MAX MIN EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides # of elements: E = 13 static indetermin. level: i = 12 lower max. damage: Dmin = 2 upper max. damage: Dmax = 10 fixed max. damage: D = 10 reduced combination: Cred = 158 exhaust. combination: Cex= 8100 Damage d El. ID Pumin El. ID Pumax 0 0 1 0 1 1 6 0,187621 1 0,938097 2 10 0 2 0,625317 3 1 0 3 0,375242 4 2 0 6 0,187621 5 3 0 7 0,187621 6 4 0 8 0,187621 7 5 0 9 0,187621 8 7 0 4 0,187621 9 8 0 5 0,187621 10 9 0 10 0 MIN CFG MAX CFG 6 1 2 3 7 8 9 4 5 10 6 10 5 8 6 97 12 10 1311 4 2 31 λ MIN 5 8 6 97 12 1311 4 2 31 10 0,31 > Icr > 0,09 MAX λ 5 8 6 97 12 1311 4 2 31 10 8,12 > Ia > 2,03

TRUSS STRUCTURE ROBUSTNESS 00,250,50,751 0 1 2 3 4 5 6 7 8 9 Damage Level PU [ad] MAX MIN EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides 5 8 6 97 12 10 1311 4 2 31 λ VIERENDEEL STRUCTURE ROBUSTNESS 00,51 0 1 2 3 4 5 6 7 8 9 10 Damage Level PU [ad] MAX MIN 6 6 1 2 3 7 8 9 4 5 1010 High element connectionHigh element number 14 5 3 1 2 4 6 8 λ 7 5 3 1 2 4 6 8 14 11 9 1210 18 20 1921 13 15 1617 λ STATIC INDETERMINANCY i = 4 i = 12 0,26 > Ib > 0,13 0,31 > Ib > 0,09 9 3 12 1 2 11 5 6 13 14 17 8,12 > Ia > 2,034,76 > Ia > 1,11

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides 3 1 4 2 5 λλgg STATICINDETERMINANCY restraint I3V STRUCTURE ROBUSTNESS 00,51 0 1 2 3 4 5 Damage Level PU[kN] MAX MIN I3C STRUCTURE ROBUSTNESS 00,250,50,751 0 1 2 3 4 Damage LevelPU[kN] MAX MIN 3 1 2 4 λλgg connection 14 13 15 16 10 12 11 9 6 5 1 2 7 8 4 3 λλgg I3E STRUCTURE ROBUSTNESS 00,250,50,751 0 1 2 3 4 5 Damage Level PU[kN] MAX MIN element

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 27/21 Additional slides HIGH CONNECTION Continuity Compartmentalization Isolation Element number Element connection LOCAL REDUCTION OF CONTINUITY LOCAL MECHANISM DEVELOPMENT Redundancy Fragility LOW CONNECTION LOCAL REDUCTION OF DUCTILITY (inhomogeneous stiffening of predetermined sections) EARLY RUPTURE AND DETACHMENT Element ductility Ductility External (restraints) STRESS IS NOT TRANSMITTED COLLAPSE STANDSTILL STRESS REDISTRIBUTION HIGH STRESS TRANSMISSION on adjoining elements after a localized failure TRIGGERING OF CHAIN RUPTURE PROGRESSIVE COLLAPSE DISPROPORTIONATE COLLAPSE SUSCEPTIBILITY SUDDEN/EARLY COLLAPSE Internal (constraints) * Starossek & Wolff, 2005* FEASIBLE ALTERNATE LOAD PATH ROBUSTNESS

EARTH&SPACE 2010 L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines 14/26

L. Giuliani, F. Bontempi - Structural Integrity Evaluation of Offshore Wind Turbines Why caring for structural integrity? 2 EARTH&SPACE 2010 LILLEGRUND offshore wind farm (Øresund between Malmö and København, Siemens, June 2008)

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