Applications of Structural Optimization: Corso di dottorato INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE / Petrini

Advanced specific case of structural
optimization
(service / ultimate / extreme scenarios)
Francesco Petrini
StroNGER s.r.l.
Corso di OTTIMIZZAZIONE
Facolta’ di Ingegneria Civile e Industriale
Sapienza Universita’ di Roma
Roma, 21 Giugno 2014

Object of the course
• Introduction of basic and advanced ideas and
aspects of structural design without to much
stress on the analytical apparatus but with
some insigth on the computational
techniques.
2
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.

Object of this lecture
• Examples of practical design cases where the
optimization has been conducted with respect
to specific performance requirements
– Offshore wind turbines (general)
– High rise buildings
• Regarding the behaviour under wind (service)
• Regarding the robustness under fire (ultimate)
3

INTRODUCTION
• Who I am
• Some basical concepts on optimization
4

Oct2004
Nov2008
PhD StudentPG
Assistant
Mar2009
Apr2009
Jul2009
Aug2009
MScdegree(laurea)
Jan2007
Jan2009
P.E.
Mar2005
Nov2005
Jan2005
Jan2006
Jan2008
(Sapienza University of Rome)
Jun2005
Mar2012
Mar2011
Associate Researcher
May2011
Jan2011
Apr2012
Jan2013
Jan2012
PhDdegree
Jan2010
Post-Doc Research Associate
Mar2010
Aug2010
Research Spin-off
Company. Co-founder and Director
Structures of the Next Generation:
Energy harvesting and Resilience
(Sapienza
University
of Rome)
Jan2014
Nov2012
Spin-off company
Mar2014
Aerodynamics and Aeroelasticity
PBD for Wind
PBD for Wind, Earthquake, Fire, Blast
Resilience
Energy Harvesting
Education and Milestones (2005-2014)

IABMAS’11
(Italy) – SS Chair
Oct2004
Oct2007
Mar2006
Nov2008
PhD StudentPG
Assistant
Mar2009
Apr2009
Jul2009
Aug2009
Design Consultant
(a long-span suspension
bridge)
Design Consultant
(precast connections)
Design Consultant
(offshore wind turbines)
Jan2007
Jan2009
Mar2005
Nov2005
Jan2005
Jan2006
Jun2007
Jan2008
Mar2012
Mar2011
Associate Researcher
May2011
ICASP’11
(Swizerland) – MS Chair
Jun2011
Jan2011
Ago2011
Apr2012
Jan2013
PMC’12 (USA) – SS Chair
Design Consultant
(critical infrastructure)
Jan2012 ASCE E&S ’10 (USA)
Jan2010
Post-Doc Research Associate
Mar2010
Aug2010
(Sapienza
University
of Rome)
Jun2013
Jan2014
ICOSSAR 2013
(USA) – MS Chair
Design Consultant
(tunnel construction)
People networking and design consulting (2005-2014)
Spin-off company

8
PAOLO E. SEBASTIANI (1985)
Ph.D. Student /Studente di
dottorato
PES

SOME BASICAL CONCEPTS ON
OPTIMIZATION
9

Optimization problem
formulation
10

Objective
Funcrion
Optimization problem formulation
Unconstrained Design space
Constrains
Constrained Design space
We must find the minimum of a certain Objective Function f, depending on certain Design
Variables (DV) x1,…,xn subjected to a number of constrains and by bounding the values of a certain
number of state variables (SV)
nn11
n
LSV,,LSV,RXx,0)x(g,0)x(hbeing)x(fmin ≤≤⊆∈≤= K
Constrains Design variables State variables
Objective Functions
Von Mises
stresses
11

First order Optimization method (FOOM)
One introduces the following unconstrained objective function:
( ) ( ) ( ) ( ) ( )





++++= ∑ ∑∑∑
= ===
2 31 m
1i
m
1i
iwih
m
1i
ig
n
1i
ix
0
wPhPgPqxPq,Q
f
f
x
( )
λ2
ii
i
ig
αg
g
gP 





+
=
λ is a large integer so that the function will be very large
when the constraint is violated and very small when it is not
Q is the dimensionless unconstrained objective function,
Px is the exterior penalty functions applied to the design variables,
Pg, Ph, and Pw are penalties applied to the constrained design and state variables,
f0 is the reference objective function value that is selected from the current group of design sets
q is the response surface parameter .
For each optimization iteration (j) a search direction vector d(j) is devised. The next iteration (j+1) is obtained from the
following equation:
( ) ( ) ( )j
j
j1j
s dxx +=+
( ) ( )
( ) ( )1j
1jk
jj
rq,Q −
−+−∇= dxd
( )
( ) ( )
( )[ ] ( )
( )
( )
( ) 21j
jT1jj
1j
q,Q
q,Qq,Qq,Q
r
−
−
−
∇
∇∇−∇
=
x
xxx
where sj is the line search parameter, and
The key to the solution of the global minimization of Q relies on the sequential generation of the search directions and on
internal adjustments of the response surface parameter (q).
ANSYS Inc. (2008). ANSYS Theory reference
12

Sub-problem approximation method (SAM)
13
• Generazione delle funzioni approssimate
(((( )))) (((( )))) errorexfxfˆ ++++==== ∑∑∑∑∑∑∑∑∑∑∑∑ ==== ========
++++++++====
n
1i
n
1j
jiij
n
1i
ii0 xxbxaafˆ i coefficienti ai e bij si determinano con
una interpolazione ai minimi quadrati
(((( )))) (((( )))) (((( ))))
(((( ))))
2n
1j
jjj2
d
fˆfΦE ∑∑∑∑====
−−−−==== i pesi Φ vengono associati ad ogni configurazione in base alla loro
ammissibilità o al valore della funzione obiettivo
• Minimizzazione del problema approssimato
Si introducono le funzioni barriera per eliminare i vincoli
(((( )))) (((( )))) (((( ))))





++++++++==== ∑∑∑∑∑∑∑∑ ========
m
1i
i
n
1i
ik0k gˆGxXpffˆp,xF
Si determina il minimo imponendo le condizioni di stazionarietà
• Convergenza
ττττ, ρρρρ sono, rispettivamente, le tolleranze delle
variabili di progetto e della funzione obiettivo
(((( )))) (((( ))))
(((( )))) (((( ))))
τff
τff
bj
1jj
≤≤≤≤−−−−
≤≤≤≤−−−− −−−− (((( )))) (((( ))))
(((( )))) (((( ))))
n1,2,3,...iρxx
n1,2,3,...iρxx
i
b
i
j
i
i
1j
i
j
i
====≤≤≤≤−−−−
====≤≤≤≤−−−− −−−−

14
Strumenti
Non determinano una
configurazione ottima; il
loro utilizzo consente di
evitare i minimi locali e
aumentare la
conoscenza dello spazio
di progetto
Analisi singola
I valori delle variabili sono introdotte
dall’utente
Generazione fattoriale
Si generano 2n configurazioni con n
numero delle variabili di progetto; ogni
configurazione assume i valori degli
estremi dell’intervallo
“Sweep”
Si generano da 2 a 10 configurazioni
per ogni variabile di progetto; si
suddivide l’intervallo rispetto ad una
configurazione di riferimento scelta
dall’utente
Generazione casuale
Si generano m configurazioni all’interno
dello spazio di progetto
Domain exploration

Optimization phases in the
structural design process
15

Structural design and structural optimization
Topological
Optimization
Design
Optimization
PBD
No
Structural check
Best design
config?
Refine
STOP
Pre sizing
Performance
requirements
Advanced
Model
Basic
Models
Conceptual
design
START
Refinement of the design
configuration with the goal of
obtaining satisfaction performances
in economical way
Shape optimization
(Options definition)
Parameters optimization
(Options refinement)
Feasible configuration selection
(Option selection)
Yes
Definition of the morphological
configuration of the object
Performance evaluations of the
candidate, feasible configurations
16

Performance-Based Design (PBD)
17

18
Fundamental requirements
(desired structural
attributes)
Non technical requirements,
expressing qualitatively a
fundamental goal
Set of criteria to assure that the
requirements are satisfied
Methods of evaluation to
measure the satisfaction of each
criterion
Commentary to explain the
rationale of each provision
- Safety
- Serviceability
- Integrity of subsystems
• mechanical
• electrical
• illumination
- Robustness
- Durability
e.g. building structures
remain stable under
extreme loads
e.g. design flexural strength
shall exceed the maximum
moment due to design loads
e.g. analysis and test
methods
Fundamental requirements
(desired structural
attributes)
Non technical requirements,
expressing qualitatively a
fundamental goal
Set of criteria to assure that the
requirements are satisfied
Methods of evaluation to
measure the satisfaction of each
criterion
Commentary to explain the
rationale of each provision
- Safety
- Serviceability
- Integrity of subsystems
• mechanical
• electrical
• illumination
- Robustness
- Durability
e.g. building structures
remain stable under
extreme loads
e.g. design flexural strength
shall exceed the maximum
moment due to design loads
e.g. analysis and test
methods
Il Performance-Based Engineering consiste in azioni quali la selezione dei siti, gli sviluppi concettuali,
predimensionamento e progetto, costruzione e manutenzione, dismissione e/o demolizione di una struttura, in modo
da assicurare che questa sia in grado di fornire prestazioni con un certo grado di affidabilità ed in maniera economica,
durante tutto il suo ciclo di vita.
Performance-Based Engineering (PBE)
Performance - Based Codes organization
Rosowski, D.V. and Ellingwood, B.R., (2002). “Performance-Based Engineering of wood frame housing: Fragility
Analysis methodology”, Journal of Structural Engineering, 128(1), 32-38.

19
Probabilistic approach to PBE
)θq( PDFs uncertain parameters
d
Rθ ∈ Uncertain parameters vector
Mathematical models: θ( )θh
Probability Integral
θ)dθ)q(θh()]θE[h(J ∫==
Expected value
( )θh
( )
θ)dθ)q(θ(Iθd)θq(P(F)J
d
R
F
θg
∫∫ ===
≤0
Failure
Probability
= Stochastic = Deterministic
Failure
Failure
threshold
Input Output
(response r)
)q(θ1
1θ
)q(θ2
2θ
P(M1)
P(M2)
P(Mk)
)q(r1
1r
b =
)q(r2
2r
nθ
),θq(θ mn
mθ
SYSTEM
Input Output
(response r)
)q(θ1
1θ
)q(θ2
2θ
P(M1)
P(M2)
P(Mk)
)q(r1
1r
b =
)q(r2
2r
)q(r2
2r
nθ
),θq(θ mn
mθ
nθ
),θq(θ mn
mθ
SYSTEM
( ) ( )
( )
( )


∈
∉
==
θgif θ
θgif θ
θIθh F
1
0
Failure domain( )θg
1)(
1
=∑=
k
i
iMP
Der Kiureghian, A., (2008). “Analysis of structural reliability under parameter uncertainties”, Probabilistic Engineering
Mechanics, 23, 351-358.

20
Fragility Curves and Intensity Measure (IM)
It is usual that inside the vector there is some parameter describing the Intensity Measure (IM) of the
stochastic loads acting on the structure (or system);
θ
∫
∞
⋅>=
0
1 dIM)IMY(P)LS( iiλ
It is desirable to express the LS by means of scalar threshold values (ri*) for opportune response
parameters (ri) and to describe the structural state by using of scalar demand-to-capacity ratios (e.g. for
the limit state LSi it is Yi= ri / ri* ).
Under these assumptions, the mean rate of failure for structure exposed to hazard can be expressed as
Where P(Yi>1|IM) is the conditional probability of failure given IM, which is know as the fragility
function.
The performance can be identified with an acceptable value of the occurrence l(LS) of exceeding a
certain Limit State (LS).

Performance-Based Earthquake Engineering (PBEE)
2007 2008

State of the art
dIMIMEDPEDPPLS ∫
+∞
⋅>=
0
)*()(λ)( IMEDPPfunctionfragility =
EDP
IM
Augusti,G.,Ciampoli,M.,(2008),“Performance-BasedDesigninrisk
assessmentandreduction”,ProbabilisticEngineeringMechanics,23,496-508
Jalayer,F.,Franchin,P.andPinto,P.E.(2007).“Ascalardamagemeasurefor
seismicreliabilityanalysisofRCframes”,EarthquakeEngng.andStruct.Dyn.,
36:2059-2079.

λ(DV) = ∫∫∫ P(DV|DM)·P(DM|EDP)·P(EDP|IM)·g(IM)·dDM·dEDP·dIM
P(x|y) conditional probability of x with respect to y
g(IM*) occurrence IM*
IM Environmental action magnitude (Intensity Measure)
EDP Engineering Demand Parameter describing the response
DM Damage Measure (components condition in terms of functionality requirements)
DV Decision Variable, it is representative of the structural performance
1. Hazard analysis g(IM)
2. Structural analysis P(EDP|IM)
3. Damage analysis P(DM|EDP)
4. Loss analysis P(DV|DM)
Risk
analysis
PEER approach for the PBEE (I)
Identifying the performance with an acceptable value of the occurrence l(DV) of exceeding a threshold
value DV.

O, D
g(IM|O,D)
g(IM)
p(EDP|IM)
P(EDP)
p(DM|EDP)
P(DM)
p(DV|DM)
P(DV)
Hazard analysis Struc’l analysis Damage analysis Loss analysis
IM: intensity
measure
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Facility
info
Decision-
making
λ(DV) = ∫∫∫ P(DV|DM)·P(DM|EDP)·P(EDP|IM)·g(IM)·dDM·dEDP·dIM
PEER approach for the PBEE (II)
Mitrani-Reiser, J. (2007). An ounce of prevention: probabilistic loss estimation for performance - based earthquake
engineering, Report EERL 2007-01, Pasadena, California, United States. Available on line at
http://peer.berkeley.edu/publications/peer_reports.html

Performance-Based Optimization
25

Topological
Optimization
Design
Optimization
PBD
No
Structural check
Best design
config?
Refine
STOP
Pre sizing
Performance
requirements
Advanced
Model
Basic
Models
Conceptual
design
START
(Option selection)
Yes
Performance evaluations of the
candidate, feasible configurations
26
By focusing on a specific performance
requirement
Investigation on what is the best
configuration
Volume, and weight are checked but not
optimized
Probabilistic Deterministic

OPTIMIZATION OF THE SUPPORT STRUCTURE OF OFFSHORE WIND TURBINES
• System design approach for complex structural systems optimization
• Substructure typology selection
• Parametric optimization
27

Motivations
1. Offshore wind farms are relatively new structural facilities located in challenging
environment, the preliminary design of the structural elements is usually very
conservative. A refinement is needed.
2. An offshore wind farm is formed by a number of wind turbines (50-200 elements)
and, consequently, a small individual reduction of structural material amount can
lead to significant saving of money if regarding the whole farm.
3. A new support structure is proposed here, and the correct sizing of its structural
parts is crucial in this phase.
28

Nominal power of a single turbine 3.0÷5.0 MW
Number of turbines 105
Hub height 100 ÷ a.s.l.
Nominal power of a the farm 315 ÷ 525 MW
Minimum distance from the shore 10 Km
Surface of the farm area 67.20 Km2
Water depth 20-35 m
Life span 29 years
An offshore wind farm in central Italy
Key facts
29
29

Offshore wind farm site location (1)
30
30

Offshore wind farm site location (2)
31
31

SYSTEM DESIGN APPROACH FOR
COMPLEX STRUCTURAL SYSTEMS
OPTIMIZATION
32

A “Complex System”
x,x’
z’
y’
Waves
Current
P
(t)vP
(t)w P
(t)u P
Turbulent
wind
P
Mean
wind
Vm(zP)
z
y
H
h
vw(z’)
Vcur(z’)
d
Terrain
33

NonLinearities
Uncertainty
Interactions
A “Complex System”
34

A System Engineering Approach
Since the structural behavior of offshore wind turbines is influenced by nonlinearities, uncertainties
or interactions, they can be defined as complex structural system
“a set of interrelated components which interact one with another in
an organized fashion toward a common purpose” (NASA, 1995)
Structure Structural system
“a device to channeling loads”
Decomposition
Structure
Actions
Performances
Structural
System
A fundamental task concerns the Structural System and Structural Performance decomposition
35

Structural decomposition
Macro - LevelDetail - Level
Structure
decomposition
Main
structure
(carrying loads)
Secondary
structure
Auxiliary
structure
Rotor-nacelle
assembly
Support structure
Energy
production
Energy transfer
Operation
Maintenance
Emergency
Substructure
Tower
Rotor
Nacelle
Blades
Foundations
Meso - Level
Junctions
Junctions
Micro - Level
37

Structural decomposition (II)
38
platform
tower
support
structure
rotor-nacelle
foundation
sea floor
water mean
level
sub-
structure
Meso - Level
Main
structure
(carrying loads)
Substructure
Tower
Rotor
Nacelle
Blades
Foundations
Rotor-nacelle
assembly
Support structure

( ) ( ) ( ) ( )( )nfexpnSnSnS jkuuuuuu kkjjkj
−⋅=
( )( ) 2
t0
0
u
2
u u1.75)log(zarctan1.16(n)dnSσ ⋅+⋅−== ∫
∞
5.0
0
uu2
x
u
200
300(x)dxR
u
1
L 





⋅== ∫
∞
z
x
z
The mean velocity magnitude varies with the
height.
MeancontributionStochasticcontribution
( )
( )[ ]5/3
ju
ju
2
V
uu
/z10,302fL1ω/2π
/zfL6,686σ
ωS jj
+
=
( )j
j
zV2π
ωz
f = ( )
( )
( ) ( )( )kj
2
kj
2
z
jk
zVzV2π
zzCω
ωf
+
−
=
Autospectrum
where:
α






=
hub
hub
z
z
UzU )(
0.14=α
For normal wind condition
( )
( )













 −
−−
−














−=
2
5.0exp4
5
4
2
4
5
exp
2
P
P
f
ff
Pf
f
f
g
fS
σ
γ
π
α
where f=2π/T is the frequency, fP=2π/TP is the peak
frequency, α is the equilibrium coefficient, g is gravity
acceleration, σ and γ parameters dependent from HS e
TP






−=
−
R
yearHTS
T
FH SR
1
1
1
1max,,,
Extreme events
analysis (Return
period TR).
7
1
,)( 




 +
⋅=
d
zd
UzU refc
x
z
d
water mean level
Wind Current and waves
JONSWAP spectrum
Design environment representation
Cross-
spectrum
40

ENVIRONMENT
Structure
Non
environmental
solicitations
STRUCTURE
Structural (non-
environmental)
system
Site-specific
environment
Wind site
basic
parameters
Other
environmental
agents
Waves site
basic
parameters
Wind, wave
and current
actions
Aerodynamic
and Aeroelastic
phenomena
Hydrodynamic
phenomena
1. Aleatoric
2. Epistemic
3. Model
Types of uncertainties
1. Aleatoric
2. Epistemic
3. Model
1. Aleatoric
2. Epistemic
3. Model
Propagation Propagation
Interaction
parameters
Structural parametersIntensity
Measure
( )IM ( )IP ( )SP
EXCHANGE ZONE
Interaction phenomena in the environment
Wind-wave-current interaction
Aeolian-hydrodynamic interactions
)10(01.0 1 mzVVcurr hourwind =⋅=
Wind speed- wave
height correlation
Wind generated
currents
)164.00291.0221.0(
2
1
10
2
10 +⋅−⋅= VVHs
Correlation data by Zaaijer, 2006, taking into account the
Italy Waves Atlas.
41

42
Environment action model: Waves and Current
( ) ( ) ( ) ( )( ) ( ) ( ) dztztztztzDctz
D
ctzd nnnndni 





+++= ,,,,
2
1
,
4
,
2
VvVvvF ρ
πρ
&
Inertia term Drag term
Morison equation for slender members (wave+current) since D/L<0.2
d
|z|
z
x
d+z
dF(z,t)
dz
A A Sect. A-A
D
tw
( ) ( )[ ]
( )
( )
( ) ( )[ ]
( )
( )tkx
kh
zhkH
tzxw
tkx
kh
zhkH
tzxu
ωω
ωω
−
+
=
−
+
=
sin
sinh
sinh
2
,,
cos
sinh
cosh
2
,,
( ) ( )[ ]
( )
( )
( ) ( )[ ]
( )
( )tkx
kh
zhkH
tzxw
tkx
kh
zhkH
tzxu
ωω
ωω
−
+
−=
−
+
=
cos
sinh
sinh
2
,,
sin
sinh
cosh
2
,,
2
2
&
&
Linear wave theory (Airy)
H

43
Wind force on moving member
( )
( ) RctUCtF
RctUCtF
arelariaDD
arelariaLL
)(
2
1
),(
)(
2
1
),(
2
2
ραα
ραα
=
=
2
2
1
UACF airaeroD ρ=
Wind force on the tower
φφ cossin LDx FFF +=
ac
R
Picture from:
Hau Erich, Wind Turbines: Fundamentals, technologies, Application,
Economics, 2nd edition. Springer-Verlag Berlin Heidelberg 2006.
xF
αc
Vortex Shedding displacements (across wind)
( )[ ]ct
across
SSD
r
⋅⋅⋅+
=





2
max 243.01
29.1
π
2
4
D
m
Sc
⋅
⋅⋅
=
ρ
υπ
Wind actions

44
Physics (I): Mean wind rotational sampling
( ) ( ) ( )12 ddd zFzFF iii S
X
S
X
S
X −=∆
z1
Ω
z2
Ω
Time t2Time t1
Vm(z1)
Vm(z2)
Tributary
area
S
Ω
dFX
S
Angular
rotational
velocity
hub
( ) ( ) ( )tFFtF ii
hub
i S
X
S
X
S
X ⋅⋅∆+= cosd
2
1
d
Additional peak in
the wind force
spectra
1.E-15
1.E-11
1.E-07
1.E-03
1.E+01
1.E+05
0.00001 0.001 0.1 10
Frequency [Hz]
ForceSpectraSFXFX
1

45
Physics (II): Turbulent wind rotational sampling
Variation of the turbulent force spectra with the blade position during its rotational
motion
Halfpenny A. (1988). Dynamic Analysis of Both On and Offshore Wind Turbines in the Frequency Domain. Ph.D. thesis.
University College London..
Connell J.R. (1988). “A PRIMER OF TURBULENCE AT THE WIND TURBINE ROTOR”, Solar Energy, 41 (3), 281-293
The wind forces acing on the Beam Element (BE) implies two different contributions:
i) the fluctuating component due to the variation of mean wind experimented by the BE at different height
during its rotational motion, and
ii) the so called “rotational sampled turbulent wind”, that is the stochastic contribution due to the incoming
wind turbulence experimented by the rotating BE

46
R
ΩΩΩΩ
Vm(r)
r
Vm(zhub)
u(r,t)
XY
Z
Aerodynamic actions by the BEM theory
Wind velocities and reference systems
- Evaluate the relative angle of attack and the relative speed of the wind with respect to specific
blade portions (BEs) at different locations
·r·(1+a’)
α
Y
X
D
L
β
φφφφ
VmR(r)=
Vm(r)·(1-a)
W
Rotor
plane
u(r,t)
v(r,t)
α’
FX= ½*ρ*Vm
2 (cL·cosϕ+cD·sinϕ)
aerodynamic force
reference system axis
windvelocity

Structural
system
modeling
Structure
Actions
Interactions
Modeling
levels
Systemic
Macro
Meso
Micro
Model
level
Scale Detail level Type of Finite Elements
Systemic
level
wind farm
approximate shape of the structural
components
BEAM elements
Macro
level
single turbine
approximate shape of the structural
components, correct geometrical
ratios between the components
BEAM elements
Meso
level
single turbine
detailed shape of the structural
components
SHELL, BRICK elements
micro
level
individual components
detailed shape of the connecting
parts
SHELL, BRICK elements
Differentiation of the modeling levels
Bontempi F., Li H., Petrini F., Manenti S., (2008). Numerical modeling for the analysis and design of offshore wind turbines, Proceedings of
ASEM'08, Jeju, Korea, 26-28 May 2008
48

1°1°
Macro
Global response
Meso Micro
Levels of modeling and results detail level
Jacket - Tower
connection
Detailed global response and
medium-detailed local
response
Detailed local response and
analysis of connections
49

SUBSTRUCTURE TYPOLOGY
SELECTION
50

Topological
Optimization
Design
Optimization
PBD
No
Structural check
Best design
config?
Refine
STOP
Pre sizing
Performance
requirements
Advanced
Model
Basic
Models
Conceptual
design
START
Shape optimization
(Option selection)
Yes
Definition of the morphological
configuration of the object
51

Classical and innovative support structure
Westgate, Z.J. and DeJong, J.T. (2005). Geotechnical considerations for offshore wind turbines.
Report for MTC OTC Project
Water depth (m) Foundation type
0-10 Gravity based
0-30 Mono-pile
>20 Tripod/Jacket
>50 Floating
Bontempi, F. (2010). Advanced topics
for offshore wind turbines. Earth&Space
2010 Conference
Strutted Quadruped
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 52
Others: Gravity-
based, Tension
leg

Monopile [m] Tripod [m] Jacket [m]
h a.s.l.=100
d=35
l found=40
D =5
tw=0,05
D found=6
h a.s.l. =100
d =35
l found =40
D =5
tw =0,05
D tripod =2,5
tw tripod =0,05
D found =2,5
h a.s.l. =100
d =35
l found =40
D =5
tw =0,05
Comparison of support structure typologies (Macro-Level models)
z
y x
Wind
Fluid-dynamic
Geotechnical
Foundation
Immersed
Emergent
d
l found
h a.s.l.
z
y x
z
y x
Wind
Fluid-dynamic
Geotechnical
Foundation
Immersed
Emergent
d
l found
h a.s.l.
D = tower diameter
D found =foundation piles diameters
tw= tower tubular thickness
h a.s.l.=100m
d=35m

Modal analysis
1° 3°
5°1° 3°
5°
3° 5°1° 3° 5°1°
0
0,5
1
1,5
2
2,5
1 3 5
Modes
Freq.[Hz]
monopile tripod jacket
3P
1P
Stiff-Stiff
Soft-Stiff
Soft-Soft

Static extreme analysis
Wind on the
tower
Wind on the rotor-
nacelle assembly
Current and
wave
Design
Situation
D.L.C.
(GL, 2005)
Wind
Condition
(steady)
Marine
Condition
(regular)
Type of
Analysis
Load Factors γF
Environ. Grav. Inert.
Parked
(standstill or
idling)
6.1b Uhub=Ue100 H=Hred100
Ultimate
strength
1.35 1.1 1.25
6.1c Uhub=Ured100 H=Hmax100
Ultimate
strength
1.35 1.1 1.25
6.3b Uhub=Ue1 H=Hred100
Ultimate
strength
1.35 1.1 1.25
Vento su torre-Monopila
0
20
40
60
80
100
120
0 2000 4000 6000 8000
Azione [N/m]
quotas.l.m.[m]
Comb 6.1b Comb 6.1cLoad
Case 6.1b
Load
Case 6.1c
Heightabovemeansealevel[m]
Wind induced drag per unit
length [N/m]
Vento su torre-Monopila
0
20
40
60
80
100
120
0 2000 4000 6000 8000
Azione [N/m]
quotas.l.m.[m]
Case 6.1b
Load
Case 6.1c
Heightabovemeansealevel[m]
Wind induced drag per unit
length [N/m]
Drag e Inerzia (corrente+onde)-
Monopila
0
5
10
15
20
25
30
0 20000 40000 60000 80000
Azione [N/m]
quotasulfondale[m]
Case 6.1c
Heightabovebottom[m]
Wave-current induced force per
unit length [N/m]
Drag e Inerzia (corrente+onde)-
Monopila
0
5
10
15
20
25
30
0 20000 40000 60000 80000
Azione [N/m]
quotasulfondale[m]
Case 6.1c
Heightabovebottom[m]
Wave-current induced force per
unit length [N/m]

Static extreme analysis – Performances comparison
Reazione totale taglio a terra [ton]
0
100
200
300
400
500
600
700
Monopila Tripode Jacket
6.1b 6.1c 6.3b
Resultant shear stress at the bottom [N]
104
104 Momento ribaltante [ton*m]
0
5000
10000
15000
20000
25000
30000
35000
40000
6.1b 6.1c 6.3b
Spostamento navicella [m]
0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
5
6.1b 6.1c 6.3b
Resultant overturning moment at the bottom [N*m]
Horizontal hub displacement [m]
104
Monopile Tripod Jacket
Reazione totale taglio a terra [ton]
0
100
200
300
400
500
600
700
6.1b 6.1c 6.3b
Resultant shear stress at the bottom [N]
104
104 Momento ribaltante [ton*m]
0
5000
10000
15000
20000
25000
30000
35000
40000
6.1b 6.1c 6.3b
Spostamento navicella [m]
0
0,5
1
1,5
2
2,5
3
3,5
4
4,5
5
6.1b 6.1c 6.3b
Resultant overturning moment at the bottom [N*m]
Horizontal hub displacement [m]
104
Monopile Tripod Jacket
Combination 6.1b (GL 2005) Monopile Tripod Jacket
Action
Wind on rotor
[ton] 166,3 166,3 166,3
Wind on tower
[ton] 74 74 42,8
Wave and current
[ton] 337,2 337,2 350
Overturning
moment [ton*m] 35045,6 35045,6 33708,7
Reactions
at mud
line
Shear reaction at
mud line [ton] 577,5 577,5 559,1
Vertical reaction
at mud line (no
piles) [ton]
1071,4
1035,63
(max/pile=1501,8)
1376,8
(max/pile =992,9)
Structural
checks
Maximum stress
in the tower
[N/mm2]
286 230 151
Nacelle
displacement [m] 4,66 3,72 1,82

Comparison between classical support structures
Westgate, Z.J. and DeJong, J.T. (2005). Geotechnical considerations for offshore wind turbines.
Report for MTC OTC Project
Water depth (m) Foundation type
0-10 Gravity based
0-30 Mono-pile
>20 Tripod/Jacket
>50 Floating
peso monotubo 205.78 t
peso tripode 635.58 t
peso jacket 473.38 t
PESI SUPPORTO "E"
1057.8 t
735.58 t

Topological
Optimization
Design
Optimization
PBD
No
Structural check
Best design
config?
Refine
STOP
Pre sizing
Performance
requirements
Advanced
Model
Basic
Models
Conceptual
design
START
Refinement of the design
configuration with the goal of
obtaining satisfaction performances
in economical way
Shape optimization
(Option selection)
Yes
59

GEOMETRIA
Dimensioni in elevazione
Dimensioni in pianta
• Altezza totale: 180 m
• Altezza fuori terra: 140 m
• Altezza sopra il pelo libero: 105 m
61

MODELLAZIONE
2835 nodi
2910 elementi lineari
di 11 tipologie
44 elementi piani
62

Vincoli
Traslazione impedita
alla base dei pali
nelle tre direzioni
Traslazione
impedita nel
piano
orizzontale
a 10 m al di
sotto del fondale
marino
Azioni esterne
Totale carichi
orizzontali:
725,25 [t]
Peso proprio
della struttura:
1.165 [t] (navicella
inclusa)
Totale carichi
verticali:
1.515 [t]
Configurazioni
di carico
I CONFIGURAZIONE
II CONFIGURAZIONE
63
Configurazioni

● 105 Parametri
▶▶▶▶ 42 Potenziali variabili di progetto
■ 8 relative alla “forma” della struttura
■ 34 relative alle sezioni degli elementi
DESIGN OPTIMIZATION (D. O.)
64

• Variabili di progetto (Design variables DV’s): sono grandezze indipendenti e
cambiando il loro valore si persegue l’ottimizzazione del problema;
• Variabili di stato (State variables SV’s): sono “grandezze dipendenti” in quanto
funzioni delle variabili di progetto;
Elementi del problema
• Funzione obiettivo (Objective function OBJ) che si intende minimizzare. È unica e
anch’essa è una grandezza dipendente;
Funzione obiettivo (OBJ): minimizzare il peso
MINIMIZZARE
IL VOLUME (VO)
65

MOLTIPLICATORE
CARICO CRITICO
(BLF) ≥ 2,5
Variabili di stato (SV):
66

MASSIMA TENSIONE
DI TRAZIONE(LTS) ≥
FYS = 355*106/1,15 N/m2
MASSIMA TENSIONE DI
COMPRESSIONE (LTC) ≥
FYC = 355*106/1,7 N/m2
67
Variabili di stato (SV):

JORIZ
OD1
TW1
]]]]
SOSTEGNO[[[[
OD2
TW2
ORIZZ]]]]
OD3
TW3
TUBO-02]]]]
OD7
TW7
JVERT[[[[
OD5
TW5
JDIAG]]]]
OD6
TW6
DIAG]]]]
OD4
TW4
TUBO-1]]]]
OD10
TW10
TUBO-2]]]]
OD9
TW9
TUBO-0]]]]
OD8
TW8
Design variables

UndetectedbucklingAssemblageconstrains
Acceptable Unacceptable
Special checks on unconsidered aspects

In sintesi si ha:
• la necessariamente unica funzione obiettivo (OBJ ) MINIMIZZARE
IL VOLUME (VO)
• le 3 variabili di stato (SV ), vincoli dell’ottimizzazione:
[[[[
[[[[
MASSIMATENSIONE
DI TRAZIONE(LTS)
MASSIMATENSIONE DI
COMPRESSIONE (LTC)
MOLTIPLICATORE
CARICO CRITICO (BLF)
• le 20 variabili di progetto (DV ), grandezze su cui si opera:
DIAMETRI DEGLI
ELEMENTI (OD)
[[[[DIAMETRI DEGLI
ELEMENTI (OD)

Generazione casuale di configurazioni
(OPTYPE,RAND)
INDAGINI DEL DOMINIO
Scansione globale dello spazio di progetto
(OPTYPE,SWEEP)
Ad ogni ciclo genera valori casuali delle
variabili di progetto
Genera valori delle variabili di progetto
cambiando il valore di una variabile di
progetto per volta e mantenendo per le altre
il valore di riferimento scelto dall’utente

ANALISI
TIPOLOGIE DI ANALISI SAM FOOM SAMFOOM SAMEU FOOMEU SAMFOOMEU
GENERAZIONE CASUALE
SCANSIONE GLOBALE
SPAZIO DI PROGETTO
SELEZIONE SOLUZIONI
AMMISSIBILI
METODO DEL PROBLEMA
APPROSSIMATO
SELEZIONE DELLA
SOLUZIONE MIGLIORE
OTTIMIZZAZIONE AL
PRIMO ORDINE
0,8 * FYC
0,8 * FYC
1,2 * BLF
SAM= sub-problem approximation method
FOOM= First-order optimization method
SAMFOOM=SAM+FOOM
----EU= --- + Heuristic assumptions
0.8*LTCmax
0.8*LTSmax
1.2*BLF

RISULTATI
Controllo delle analisi
CONFIGURAZIONE I CONFIGURAZIONE II
ANALISI Gerarchia
torre
Diametri
(OD)
Spessori
(TW)
Gerarchia
(Torre)
Diametri
(OD)
Spessori
(TW)
SAM
FOOM
SAMFOOM
SAMEU
FOOMEU
SAMFOOMEU
Gerarchia
(Torre)

Andamento normalizzato degli elementi del problema
CARICO ORIZZONTALE ORTOGONALE ALLE BASI DEL JACKET
SAMEU SAMFOOMFOOMEU SAMFOOMEU SAMFOOM
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
START
LTC/LTC*
BLF/BLF*
LTS/LTS*
VO/VO*

CARICO ORIZZONTALE IN DIREZIONE DELLA DIAGONALE DELLA BASE DEL JACKET
SAMEU45 SAM45 FOOM45 FOOMEU45 SAMFOOMEU45SAMFOOM45
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
START
LTC/LTC*
BLF/BLF*
LTS/LTS*
VO/VO*
Andamento normalizzato degli elementi del problema

SAMFOOM 45
OD1 0,59 TW1 0,014
OD2 0,99 TW2 0,016
OD3 0,80 TW3 0,014
OD4 0,60 TW4 0,014
OD5 1,30 TW5 0,016
OD6 0,50 TW6 0,014
OD7 4,16 TW7 0,050
OD8 4,64 TW8 0,055
OD9 3,86 TW9 0,046
OD10 3,40 TW10 0,041
LTC [N/m2
] -3,470E+08 VO [m3
] 129,03
BLF 8,21 LTCE 1162
LTS [N/m2
] 2,809E+08 LTSE 950
Risultati per l’analisi SAMFOOM45
0
10
20
30
40
50
60
70
80
90
100
RAPPORTO[%]
JORIZZ SOSTEGNO ORIZZ DIAG JVERT JDIAG TUBO 2 TUBO 0 TUBO 1 TUBO 2
SEZIONI
ODn/ODn*
TWn/TWn*
0.00
0.01
0.02
0.03
0.04
0.05
0.06
TW[m]
SEZIONI
START
SAMFOOM 45
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
OD[m]
SEZIONI
START
SAMFOOM 45

16% DI RIDUZIONE
DEL VOLUME
TOTALE (VO)
24% DI RIDUZIONE
DEL VOLUME
DELLA TORRE
1% DI RIDUZIONE
DEL VOLUME
DEL JACKET
Results

Controllo della frequenza naturale della struttura
in relazione all’azione dinamica della turbina
(movimento del rotore): eventuale accoppiamento
della frequenza della struttura con quella del vento
e del moto ondoso.
Hz209636,0f optnat ====−−−−
Hz249565,0fnat ====
Controllo delle caratteristiche dinamiche
f1Pmin f1PMAX f3Pmin f3PMAX
Soft-
Soft
Soft-
Stiff
Stiff-
Stiff
Hz1150,0
60
9,6
f minP1 ========
Hz2017,0
60
1,12
f PMAX1 ========
Hz3450,0f3f minP1minP3 ====⋅⋅⋅⋅====
Hz6050,0f3f PMAX1PMAX3 ====⋅⋅⋅⋅====

Strutted innovative support
79

Summary
x1
x2
• Structure and piles 180 m
• Structure height: 140 m
• Immersed: 35 m
• Over water level: 105 m
Local constraints:
•maximum Von Mises ideal stress equals to
300MPa (strength criterion);
•maximum compression stress equals to
200MPa (local instability criterion);
•maximum ratio diameter/thickness equals to
100 (local instability criterion);
Global constraints:
•Eulerian buckling multiplier greater that 5;
•maximum horizontal displacement permitted
4 m.
• Objective Function: TOTAL VOLUME

Optimization problem algorithm

Macro-level model: Design variables trend
Diameters Thicknesses

Macro-level model: State variables trend
Compression stresses Von Mises stresses

Macro-level model: Configuration evolution

Macro-level model: Objective function

Meso-level model

Meso-level model: Effective buckling modes detection
Macro-level model Meso-level model
1° buckling mode load multipler = 9,08
1° buckling mode load
multipler = 10,12

Optimal configuration
•VOLUME=116 [m3]
Diamet ers[m] Thicknesses[m] d/t
D1 2.25 T1 3.1E-02 72.5
D2 3.14 T2 4.2E-02 75.5
D3 4.03 T3 4.2E-02 96.9
D4 4.56 T4 4.2E-02 109.5
D5 5.09 T5 5.2E-02 97.5
D6 2.37 T6 3.3E-02 71.8
D7 5.09 T7 5.2E-02 97.5
D8 5.30 T8 5.4E-02 98.3
D9 5.05 T9 5.4E-02 93.7
D10 4.80 T10 5.4E-02 89.1
D11 4.55 T11 5.4E-02 84.5
D12 4.31 T12 4.4E-02 97.9
D13 3.84 T13 4.4E-02 87.3
D14 3.37 T14 4.4E-02 76.7
D15 2.91 T15 4.4E-02 66.0
D16 2.44 T16 3.8E-02 64.8
D17 1.52 T17 1.6E-02 95.9
D18 2.32 T18 2.3E-02 99.4

Monopile-Quadruped comparison
Quadruped:
• VOLUME = 116 [m3]
• Weight = 904 [t]
• D max = 5 [m]
Monopile:
• VOLUME = 234 [m3]
• Weight = 1057 [t]
• D max = 9 [m]
peso monotubo 205.78 t
peso tripode 635.58 t
peso jacket 473.38 t
PESI SUPPORTO "E"
1057.8 t
735.58 t

Considerations on OWTs optimization
1. The Design Optimization of Owts is a fundamental step in the design of Offshore
Wind Farms.
2. The Design Optimization of such a complex structural systems has been carried out by
assuming simplified models for the actions.
3. Multi level detail models are needed in order to capture the main physical aspects.
4. A new support structure is proposed here, the optimization produced good results in
terms of weight if compared with another feasible solution (a monopile support
structure).

PERFORMANCE-BASED OPTIMIZATION OF AN HIGH-RISE BUILDING FOR WIND
• Performance-Based Wind Engineering (PBWE)
• Models for tall buildings and Occupant Comfort assessment
• Probabilistic Performance-Based analysis
• Probabilistic Performance-Based optimization by a TMD
91

Performance-Based Wind
Engineering (PBWE) procedure

The problem of risk assessment is disaggregated into the following elements:
- site and structure-specific hazard analyses, that is, the assessment of the probability density
functions f(IM), f(SP) and f(IP|IM, SP);
- structural analysis, aimed at assessing the probability density function of the structural response
f(EDP|IM,IP,SP) conditional on the parameters characterizing the environmental actions, the
wind-fluid-structure interaction and the structural properties;
- damage analysis, that gives the damage probability density function f(DM|EDP) conditional on
EDP;
- finally, loss analysis, that is the assessment of G(DV|DM), where G(·|·) is a conditional
complementary cumulative distribution function.
G(DV) = ∫…∫ G(DV|DM) · f(DM|EDP) · f(EDP|IM, IP, SP) · f(IP|IM,SP) ·
· f(IM) · f(SP) · dDM · dEDP · dIP · dIM · dSP
PBWE procedure
Interaction
Parameters
Structural
Parameters
Intensity
measure
IM IP SP
Engineering
Demand
Parameters
EDP
Damage
Measure
DM
Decision
Variable
DV

Petrini, F., Ciampoli M. (2011). “Performance-based wind design of tall buildings”, Structure & Infrastructure Engineering
- Maintenance, Management, Life-Cycle Design & Performance, i-first published 15 April 2011.
O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
Structuralanalysis Damageanalysis Loss analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O: location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
system parameters
Structural
system
info
Ciampoli M, Petrini, F., Augusti G., (2011). “Performance-Based Wind Engineering: toward a general procedure”,
Structural Safety, accepted for publication.
PBWE Flowchart

O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Aerodynamic
analysis
Struc’l analysis Damage analysis Loss analysis
IM: intensity measure
IP: interaction
parameters
EDP: engineering
demand parameters
DM: damage measures DV: decision variables
Select
O, D
O: location
D: design
Environment
info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural system
parameters
Structural
system info
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Aerodynamic
analysis
Struc’l analysis Damage analysis Loss analysis
IM: intensity measure
IP: interaction
parameters
EDP: engineering
demand parameters
DM: damage measures DV: decision variables
Select
O, D
O: location
D: design
Environment
info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP: structural system
parameters
Structural
system info
O, D
g(IM|O,D)
g(IM)
p(EDP|IM)
P(EDP)
p(DM|EDP)
P(DM)
p(DV|DM)
P(DV)
IM: intensity
measure
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Facility
info
Decision-
making
O, D
g(IM|O,D)
g(IM)
p(EDP|IM)
P(EDP)
p(DM|EDP)
P(DM)
p(DV|DM)
P(DV)
IM: intensity
measure
EDP: engineering
demand param.
DM: damage
measure
DV: decision
variable
Select
O, D
O: location
D: design
Facility
info
Decision-
making
PBWEPBEE

Models for tall buildings and
Occupant Comfort assessment

Loss of serviceability
Lossofintegrityof
non-structural
elements
Motionperception
bybuilding
occupants
Tamura,Y.(2009).Windandtallbuildings,ProceedingsoftheFifthEuropean&
AfricanConferenceonWindEngineering(EACWE5),Florence,Italy,
July19-23,2009..
w(t;z2)Vm(z2)
Vm (z1)
Vm (z3)
V(t;z2)
v(t;z2)u(t;z2)
X
Z
Y
θ
B1
B2
H
Displacements
Accelerations
Serviceability under Wind (I)
Discomfort level in terms of
perception thresholds
1
Vibration frequency
Accelerationthresholds
formotionperception

Loss of serviceability
Lossofintegrityof
non-structural
elements
Motionperception
bybuilding
occupants
Bashor,R.andKareem,A.(2007)."ProbabilisticPerformanceEvaluationofBuildings:An
OccupantComfortPerspective",Proc.12thInternationalConferenceonWind
Engineering,1-6July,Cairns,Australia.Availableonlineathttp://www.nd.edu/~nathaz/
[Accessed15June2010].
w(t;z2)Vm(z2)
Vm (z1)
Vm (z3)
V(t;z2)
v(t;z2)u(t;z2)
X
Z
Y
θ
B1
B2
H
Displacements
Accelerations
Discomfort level in terms of
perception thresholds
Usually Across wind vibration is
critical for comfort
The reference period for comfort
evaluation is 1 year
1
2
3 1st natural frequency is dominant4
1
10
100
0,1 1
a[cm/s2]
f [Hz]
Office Apartment
Italian Guidelines
f1
Scalarthreshold
Serviceability under Wind (II)

Case study structure
Structure and FE model
Structure
Height H= 305 m
Lengths B1=B2= 50 m (square)
No of floors = 74
3dframeontheexternalperimeter
centralcore
bracing system
A steel structure
Finite Element model
B1
B2
H
FE Model
About 10,000 Elements
About 4,000 Nodes
About 24,000 DOFs

Experimental model of Actions
SpenceS.M.J.,GioffrèM.,GusellaV.(2008a).Influenceofhighermodesonthedynamic
re-sponseofirregularandregulartallbuildings,Proc.6thInternational
ColloquiumonBluffBodiesAerodynamicsandApplications(BBAAVI),Milano,
Italy,July20-24,2008.
Boundary Layer Wind Tunnel of
the CRIACIV in Prato, Italy
-60
-40
-20
0
20
40
60
80
100
120
140
3000 3200 3400 3600 3800
F [KN]
t [s]
Along Across
1:500Scalemodel
Response time
history
Time domain structural analyses
(Experimental actions)
Time domain
analyses
Experimental
forces
Time domain analyses
-30
-20
-10
0
10
20
30
3500 3600 3700 3800 3900 4000
aL, aD
[cm/s2]
t [s]Along Across

( )
( )
( ) )(),(
),,(exp
1
),(),(
22
212
2
ωχωρ
ωξξ
ωρω
⋅⋅⋅⋅=
=⋅⋅−⋅
⋅⋅⋅⋅=
∫∫
hSVc
dAdAf
A
hSVchS
uumxD
A A
uumxDDD tt
( )
)(),h(S
)(HVc
),h(S)(H),h(S
2
uu
22
mxD
DD
2
rr tttt
ωχω
ωρ
ωωω
⋅⋅
⋅⋅⋅⋅
=⋅=














⋅+







−
⋅
⋅
⋅
=
2
0
2
2
2
0
2
2
0
2
2
41
1
1
)(
ω
ω
ν
ω
ω
ω
ω
m
H
rrm
p
grr σ⋅+= rg
Wind action spectra
(analytical)
Response spectra
Peak response
Frequency domain response
Frequency domain analyses
Response Peak Factor
Analytical model of the buffeting forces
( ) ( ) ( ) ( )( )ωfexpωSωSωS jkuuuuuu kkjjkj
−=
( )
( )
( ) ( )( )kj
2
kj
2
z
jk
zVzV2π
zzCω
ωf
+
−
=
Cross-spectrum
5.0
0
uu2
x
u
200
300(x)dxR
u
1
L 





⋅== ∫
∞
z
were:
( )
( ) [ ]5/3
ju
ju
x2
u
uu
/zLf10.3021ω/2π
/zLfσ6.686
ωS jj
⋅⋅+⋅
⋅⋅⋅
=
( )( ) 2
fri0
0
u
2
u
u1.75)log(zarctan1.16
(n)dnSσ
⋅+⋅−=
== ∫
∞
)z(V2π
zω
f
jm
j
⋅
⋅
=
Autospectrum
( ) 3ew(t)2ev(t)1eu(t))j(zmV)jz(t;jV
rrrr
⋅+⋅+⋅+=
α
10m
10
z
V(z)V








⋅=
Solari,G.Piccardo,G.(2001).Probabilistic3-Dturbulencemodelingforgustbuffetingof
structures,ProbabilisticEngineeringMechanics,(16),73–86.
Turbulentwindvelocityspectra(analytical)
Model of the Vortex shedding forces
(Varying with the angle of attack)
1.E+01
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
0.000 0.001 0.010 0.100 1.000
PSD
n [Hz]
Total Force spectrum
Turbulenceforce spectrum
Vortexsheddingforcespectrum

Experimentalwind
forcespectra
Extrapolationofananalytical
Vortexsheddingforcespectra
Model of the Vortex shedding forces
n
Compatibilityofanalytical
andexperimentalspectra
1.E+01
1.E+03
1.E+05
1.E+07
1.E+09
1.E+11
0.000 0.001 0.010 0.100 1.000
PSD
n [Hz]
TotalForce spectrum
Turbulent component
Vortexsheddingcomponent
Global forcespectrum
Analytical wind spectra
n

1
10
100
0.1 1
aL,D
p[cm/s2]
n [Hz]
Office Apartment aL
p aD
p
f1
aL,D
p[cm/s2]
n [Hz]
-30
-20
-10
0
10
20
30
3500 3600 3700 3800 3900 4000
aL, aD
[cm/s2]
t [s]Along Across
Structural response- max accelerations
Time domain: results
Structural response – accelerations
Comfort evaluation
Across
Along
Reference mean
wind velocity:
Vm(H) = 35 m/s
(annual mean
recurrence)
Along
w(t;z2)Vm(z2)
Vm (z1)
Vm (z3)
V(t;z2)
v(t;z2)u(t;z2)
X
Z
Y
θ
B1
B2
H
Across
0
5
10
15
20
25
30
-20 0 20 40 60
aL
p
[cm/s2]
θ [deg]
aL
p
aD
p
Due to
vortex
shedding
effect

Probabilistic Performance-Based
analysis

Hazard analysis
Aeolian risk assessment
O
f(IM|O)
f(IM) f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
Structuralanalysis Damage analysis Loss analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O:location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
systemparameters
Structural
system
info
( ) ( ) 













θ
−⋅





θ
⋅
θ
θ
=θ
θ−θ
θ
)(
10
1)(
10
10, exp
)(
)(
),(f 10
kk
V
c
V
c
V
c
k
V
The roughness length z0 is characterized by a lognormal
PDF. The mean value μz0 and the standard deviation σz0
of z0 are expressed as function of θ (assuming a slight
difference between four sectors, i.e. a mean value of z0
varying between 0.08 m and 0.12 m and a COVz0 equal
to 0.30).
V10 and θ are described by their joint probability
distribution function
IM =
θ
V10
z0
Parameters c(θ) and k(θ) are derived from NIST® wind
speed database.
(Annual occurrence)

Interaction analysis IP =
gr
CD
CL
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O:location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
systemparameters
Structural
system
info

gr
CD
CL
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O:location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
systemparameters
Structural
system
info
rrm
p
grr σ⋅+= )T(log
.
)T(log
winde
windegr
⋅η
+⋅η=µ
2
5770
2 Davenport (1983)
Reliable results for
broad band processes

gr
CD
CL
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O:location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
systemparameters
Structural
system
info
- In the Davenport formulation the peak factor does not depend on the bandwidth of the stochastic process.
- Alternative formulations consider this dependence
rrm
p
grr σ⋅+= )T(log
.
)T(log
winde
windegr
⋅η
+⋅η=µ
2
5770
2 Davenport (1983)
( )











≤⋅η
>⋅η
⋅η+
−
⋅η
=σ
+
+
+
+
122if650
122if
46
213
45
2
21
.T.
.T
.
)Tln(
.
)Tln(
.
windr,e
windr,e
windr,e
windr,e
gr
)ln(2
577.0
)ln(2
,
,
windre
windreg
T
Tr
⋅η
+⋅η=µ
+
+
Vanmarcke (1975)

gr
CD
CL
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O:location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
systemparameters
Structural
system
info
- In the Davenport formulation the peak factor does not depend on the bandwidth of the stochastic process.
- Alternative formulations consider this dependence
rrm
p
grr σ⋅+= )T(log
.
)T(log
winde
windegr
⋅η
+⋅η=µ
2
5770
2 Davenport (1983)
rR1
2
rB
2
rR2
2
n*Srr
n (Hz)
rR1
2
rB
2
rR2
2
n*Srr
n (Hz)
Background
(broad band process)
Resonant
(narrow band
process)
Lightly damped
buildings
Highly damped
buildings
( )











≤⋅η
>⋅η
⋅η+
−
⋅η
=σ
+
+
+
+
122if650
122if
46
213
45
2
21
.T.
.T
.
)Tln(
.
)Tln(
.
windr,e
windr,e
windr,e
windr,e
gr
Vanmarcke (1975)
)ln(2
577.0
)ln(2
,
,
windre
windreg
T
Tr
⋅η
+⋅η=µ
+
+

gr
CD
CL
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O:location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
systemparameters
Structural
system
info
(Vanmarcke 1975)
Therefore, the bandwidth
parameter, and also the response
peak factor must depend on the
structural damping
rR1
2
rB
2
rR2
2
n*Srr
n (Hz)
rR1
2
rB
2
rR2
2
n*Srr
n (Hz)
Background
(broad band process)
Resonant
(narrow band
process)
Lightly damped
buildings
Highly damped
buildings

gr
CD
CL
462.2507.1265.0 2
+ξ+ξ−=µ
rg
( )











≤⋅η
>⋅η
⋅η+
−
⋅η
=σ
+
+
+
+
122if650
122if
46
213
45
2
21
.T.
.T
.
)Tln(
.
)Tln(
.
windr,e
windr,e
windr,e
windr,e
gr
( )







<≤
η
<≤
η−
=η +
+
+
1690if
690100if
380631 450
r
r
r
r
.
r
r,e
q.
.q.
.q.
r
r
r σ
σ
=+η &
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O:location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
systemparameters
Structural
system
info
Vanmarcke
(1975)
(Obtained from time-domain analyses)
The peak response factor gr is described by a Gaussian distribution function
g*r = -0.256ξ2 + 1.507ξ + 2.462
3.00
3.40
3.80
4.20
4.60
0.5 1 1.5 2 2.5
g*r
ξ [%]
rgµ
rgµ

Interaction analysis
The aerodynamic coefficients CD ,CL are described by Gaussian
distributions. Mean values are expressed as a function of θ, varying from
those corresponding to a square shape (for θ = 0°) to those corresponding
to a rhomboidal shape (for θ = 45°); the coefficient of variations of CL and
CD are taken equal to 0.07 and 0.05.
IP =
gr
CD
CL
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O:location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
systemparameters
Structural
system
info
0
0.2
0.4
0.6
0.8
1
1.2
-90 -60 -30 0 30 60 90Meanaerodynamiccoefficients
µ µ
DCµ
60 90
θ [deg]
LCµ
462.2507.1265.0 2
+ξ+ξ−=µ
rg
( )











≤⋅η
>⋅η
⋅η+
−
⋅η
=σ
+
+
+
+
122if650
122if
46
213
45
2
21
.T.
.T
.
)Tln(
.
)Tln(
.
windr,e
windr,e
windr,e
windr,e
gr
( )







<≤
η
<≤
η−
=η +
+
+
1690if
690100if
380631 450
r
r
r
r
.
r
r,e
q.
.q.
.q.
r
r
r σ
σ
=+η & Vanmarcke
(1975)
(Obtained from time-domain analyses)
The peak response factor gr is described by a Gaussian distribution function
g*r = -0.256ξ2 + 1.507ξ + 2.462
3.00
3.40
3.80
4.20
4.60
0.5 1 1.5 2 2.5
g*r
ξ [%]
rgµ
rgµ

Structural analysis EDP = aL
p
O
f(IM|O)
f(IM)
f(IP|IM,SP)
f(IP)
f(EDP|IM,IP,SP)
G(EDP)
f(DM|EDP)
G(DM)
f(DV|DM)
G(DV)
Hazard analysis
Interaction
analysis
IM: intensity
measure
IP: interaction
parameters
EDP:engineering
demand param.
DM:damage
measure
DV:decision
variable
Select
O, D
O:location
D:design
Environme
nt info
Decision-
making
D
f(SP|D)
f(SP)
Structural
characterization
SP:structural
systemparameters
Structural
system
info
G(EDP) = ∫…∫ G(EDP|IM, IP, SP) · f(IP|IM,SP) · f(IM) · f(SP) · dIP · dIM · dSP
Monte Carlo sim
(5000 runs)
w(t;z2)Vm(z2)
Vm (z1)
Vm (z3)
V(t;z2)
v(t;z2)u(t;z2)
X
Z
Y
θ
B1
B2
H
aL
p
Reduced
formulation

Risk Curve. EDP= aL
p = peak acceleration in across wind direction
The annual probabilities of exceeding the human perception thresholds for
apartment and office building vibrations are 0.0576 and 0.0148 respectively.
w(t;z2)Vm(z2)
Vm (z1)
Vm (z3)
V(t;z2)
v(t;z2)u(t;z2)
X
Z
Y
θ
B1
B2
H
aL
p
Ciampoli M, Petrini F. (2011). “Performance-Based Aeolian Risk assessment and reduction for tall buildings”,
Probabilistic Engineering Mechanics, accepted for publication.

Probabilistic Performance-Based
optimization by a TMD

TUNED MASS DAMPER (TMD)
C1
K1 CTMD
KTMD
M1
MTMD

C1
K1 CTMD
KTMD
M1
MTMD
Sistema Principale
(struttura)
‫ܯ‬1 = massa
‫ܭ‬1 = ߱1
2
∙ ‫ܯ‬1 = rigidezza
‫ܥ‬1 = 2 ∙ ‫ܯ‬1 ∙ ߱1 ∙ ߦ1 =
= smorzamento

C1
K1 CTMD
KTMD
M1
MTMD
Sistema Principale
(struttura)
Sistema Secondario
(TMD)
ߛ =
‫ܯ‬ܶ‫ܦܯ‬
‫ܯ‬1
= rapporto tra le masse
ߚ =
߱ܶ‫ܦܯ‬
߱1
= rapporto tra le pulsazioni
‫ܥ‬ܶ‫ܦܯ‬ = 2 ∙ ‫ܯ‬ܶ‫ܦܯ‬ ∙ ߱ܶ‫ܦܯ‬ ∙ ߦܶ‫ܦܯ‬ =
= smorzamento TMD
T M D T L D
‫ܯ‬1 = massa
‫ܭ‬1 = ߱1
2
‫ܥ‬1 = 2 ∙ ‫ܯ‬1 ∙ ߱1 ∙ ߦ1 =
= smorzamento

C1
K1 CTMD
KTMD
M1
MTMD
Sistema Principale
(struttura)
ߛ =
‫ܯ‬ܶ‫ܦܯ‬
‫ܯ‬1
= rapporto tra le masse
ߚ =
߱ܶ‫ܦܯ‬
߱1
= rapporto tra le pulsazioni
‫ܥ‬ܶ‫ܦܯ‬ = 2 ∙ ‫ܯ‬ܶ‫ܦܯ‬ ∙ ߱ܶ‫ܦܯ‬ ∙ ߦܶ‫ܦܯ‬ =
= smorzamento TMD
In cui:
߱݅ = ට
‫ܭ‬݅
‫ܯ‬݅
= pulsazione naturale
ߦ݅ =
‫ܥ‬݅
‫ܥ‬ܿ‫ݎ‬
=
‫ܥ‬݅
2∙‫ܯ‬݅∙߱݅
= smorzamento percentuale
con i = 1, TMD
T M D T L D
‫ܯ‬1 = massa
‫ܭ‬1 = ߱1
2
‫ܥ‬1 = 2 ∙ ‫ܯ‬1 ∙ ߱1 ∙ ߦ1 =
= smorzamento
Sistema Secondario
(TMD)

݈ܽ = ൞
ܽ0
݊0
0.56 ‫ݎ݁݌‬ ݊0 < 1‫ݖܪ‬
ܽ0 ‫ݎ݁݌‬ 1‫ݖܪ‬ ≤ ݊0 ≤ 2‫ݖܪ‬
0.5 ∙ ܽ0 ∙ ݊0 ‫ݎ݁݌‬ ݊0 ≥ 2‫ݖܪ‬
ܽ0 = 6 ܿ݉/‫ݏ‬2
= per i piani adibiti ad uffici; (a)
ܽ0 = 4 ܿ݉/‫ݏ‬2
= per i piani adibiti ad abitazioni; (b)
݊0 = frequenza fondamentale dell’edificio.
Uffici
Abitazioni
EFFETTO DEL TMD SULLA RISPOSTA STRUTTURALE

݈ܽ = ൞
ܽ0
݊0
0.56 ‫ݎ݁݌‬ ݊0 < 1‫ݖܪ‬
ܽ0 ‫ݎ݁݌‬ 1‫ݖܪ‬ ≤ ݊0 ≤ 2‫ݖܪ‬
0.5 ∙ ܽ0 ∙ ݊0 ‫ݎ݁݌‬ ݊0 ≥ 2‫ݖܪ‬
ܽ0 = 6 ܿ݉/‫ݏ‬2
ܽ0 = 4 ܿ݉/‫ݏ‬2
Uffici
Abitazioni
1.E-04
1.E-03
1.E-02
1.E-01
1.00E-01
RPSD
Frequenza (Hz)
Non controllata

݈ܽ = ൞
ܽ0
݊0
0.56 ‫ݎ݁݌‬ ݊0 < 1‫ݖܪ‬
ܽ0 ‫ݎ݁݌‬ 1‫ݖܪ‬ ≤ ݊0 ≤ 2‫ݖܪ‬
0.5 ∙ ܽ0 ∙ ݊0 ‫ݎ݁݌‬ ݊0 ≥ 2‫ݖܪ‬
ܽ0 = 6 ܿ݉/‫ݏ‬2
ܽ0 = 4 ܿ݉/‫ݏ‬2
Uffici
Abitazioni
1.E-04
1.E-03
1.E-02
1.E-01
1.00E-01
RPSD
Frequenza (Hz)
Controllata
Non controllata

Optimization parameters
Design Parameters
γ = mTMD/mtot
β = ωTMD/ ω1
ξ* = damping of TMD

C1
K1 CTMD
KTMD
M1
MTMD
305 m

ANALISI PARAMETRICA CON TMD
ߛ =
݉ܶ‫ܦܯ‬
݉1
; ߚ =
߱ܶ‫ܦܯ‬
߱1
; ߦ = smorzamento;

TMD
Design Parameters
γ = mTMD/mtot
β = ωTMD/ ω1
ξ* = damping of TMD
Aeolian Risk reduction by TMD
90
0.125 0.145 0.165 0.185
β = 0.70 ; ξ* = 1% - 10% β = 0.80 ; ξ* = 1% - 10%
β = 0.90 ; ξ* = 1% - 10% β = 1.02 ; ξ* = 1% - 10%
β = 1.10 ; ξ* = 1% - 10% β = 1.20 ; ξ* = 1% - 10%
β = 1.30 ; ξ* = 1% - 10% Uncontrolled
Apartment Office
aL
p[mm/s2]
n [Hz]
β = ξ* =
β = ξ* =
β = ξ* =
β = ξ* =
β = ξ* =
β = ξ* =
β = ξ* =
Parametric analysis Effects on risk
γ = 1/150

CONFIGURAZIONE OTTIMALE DEL TMD
ߛ =
݉ܶ‫ܦܯ‬
݉1
=
1
150
⇒ ݉ܶ‫ܦܯ‬ ≅ 568 ‫݊݋ݐ‬
Realizzata con una sfera di acciaio
di raggio pari a circa 2.60 m
ߦ = 8%, per limitare gli spostamenti
sulla massa del TMD
ߚ =
߱ܶ‫ܦܯ‬
߱1
=1, il che consente di
ottenere un risultato migliore

INTRODUZIONE DI UN SECONDO TMD
Accelerazione di picco
Non controllata 15.6 cm/s2
TMD 1 10.6 cm/s2
TMD 2 9.63 cm/s2
γ β ξ Piano
TMD 1 1/300 1 0.05 74
TMD 2 1/300 1 0.05 38
305 m
160 m
3
30
0.1 1
a (m/s2)
n0 (Hz)
Uffici
Residenze
Non controllata
1 TMD
2 TMD

PERFORMANCE-BASED OPTIMIZATION OF AN HIGH-RISE BUILDING STRUCTURAL
SYSTEM FOR RELIABILITY AGAINST PROGRESSIVE COLLAPSE
• Robustness of high-rise buildings in case of fire
• The role of the outrigger and of the lateral bracing
• Multi-hazard considerations
• Structural system optimization
129

Robustness of high-rise buildings
in case of fire

time
Temperature PREVENTION PROTECTION
Passive
Measures
Ignition
Flashover
Active
Measures
ROBUSTNESS
Ineffectiveness
of measures
Robustness role in case of fire
Joelma Building,
Sao Paulo (1974)
Mandarin Oriental
Hotel, Beijing (2009)
Windsor Tower,
Madrid (2005)

Case study
40 floors, 160 m heigth, 35 m x 35 m floor, office building
RENDERING STRUCTURAL SYSTEM FEM MODEL

Case study
Outrigger
Bracing
System
Frame BFrame A
Frame B
Frame A

The role of the outrigger and of
the lateral bracing

Frame A Assumptions
- Collapse for displacement of 1 meter on the top
- Exposure to 180 minutes of ISO Curve
- 30 cases of fire changing initial fire location and number of
involved columns
Frame B
FIRE LOCATION 6th floor
t
T
Nominal
ISO 8344
0
200
400
600
800
1000
0 10 20 30 40 50 60
ISO 834
θ ipe 270
θ ipe 300
θ hem 260
θ hea 240
θ hem280
Progressive collapse assessment

Progressive collapse assessment
Frame A Assumptions
- Collapse for displacement of 1 meter on the top
- Exposure to 180 minutes of ISO Curve
- 30 cases of fire changing initial fire location and number of
involved columns
Frame B

1 Heated
Column
2 Heated
Columns
3 Heated
Columns
4 Heated
Columns
5 Heated
Columns
30 min - 696°C 30 min - 696°C 30 min - 696°C 30 min - 696°C 30 min - 696°C
Frame B - Worst case scenarios

Progressive Collapse
1 Heated
Column
2 Heated
Columns
3 Heated
Columns
4 Heated
Columns
5 Heated
Columns
After 180 min After 107 min After 93 min After 102 min After 87 min

Frame A - Worst case scenarios
1 Heated
Column
2 Heated
Columns
3 Heated
Columns
4 Heated
Columns
5 Heated
Columns
26 min - 640°C 28 min - 680°C 29 min - 690°C 30 min - 696°C 31 min - 705°C

1 Heated
Column
2 Heated
Columns
3 Heated
Columns
4 Heated
Columns
5 Heated
Columns
After 180 min After 180 min After 126 min After 144 min After 100 min

Outrigger role
VMises Deformation
Without Fire
1 Heated
Column
2 Heated
Columns
3 Heated
Columns
4 Heated
Columns
5 Heated
Columns
195235 156 117 78 39 0 plastic elastic

Frame BFrame A
SWAY COLLAPSE NO-SWAY COLLAPSE

Lateral Force: Dir. +Z
SCENARIO
Without Wind Wind Γ=0.5 Wind Γ=1.0 Wind Γ=1.5

SCENARIO
Lateral Force: Dir. -Z

Lateral Force: Dir. +Z
DEFORMED SHAPE
After 180 min After 140 min After 152 min After 82 min
88 min
Vertical
69 min
Outwards
16 min
Outwards
<10 min
Outwards

Structural system optimization

Configurations: position of the outrigger
CONFIGURATIONS
G A B C
STEEL MASS [TON]
877 857 877 877

Configurations: vertical brace system
CONFIGURATIONS
G D E F
STEEL MASS [TON]
877 817 994 939

Multi-hazard analyses – 3 heated columns

Initial

1. Due to their nature complex, real structures requires advanced models, both for
actions and structural parts.
2. A suitable way to deal with the above is the adoption of a systemic approach, that is
the switching from the vision of a structure as an isolated entity to the vision of a
structure as “a set of interrelated components which interact one with another in an
organized fashion toward a common purpose”.
3. The systemic vision is particularly useful in presence of non-linear interactions (i.e.
between the structure and the environment), cascading effects, high level of
uncertainty.
4. Classical optimization algorithms are in general, not exhaustive for conducting the
optimization of such a structural systems, if not coupled with rational, heuristic
considerations from the designer.
5. One of the most rational way to deal with the design of complex structures is the
Performance-Based Design approach, that can be conducted both in deterministic
or in probabilistic terms.
6. The Performance-Based Optimization is an appropriate way to optimize complex
structural systems.

Applications of Structural Optimization: Corso di dottorato INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE / Petrini

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