Lezione su applicazioni dell'ottimizzazione strutturale a casi reali di strutture per l'ingegneria civile tenuta nell'ambito del corso di dottorato sull'ottimizzazione strutturale, Roma, 21 maggio 2015.
Speeding up probabilistic inference of camera orientation by function ap...Nicolau Werneck
Slides from my presentation at the WSCG2011. Describes some modifications to existing techniques for camera orientation estimation in "Manhattan Worlds" aiming at faster calculation times.
PBWE - IN VENTO 2014 - Petrini StroNGER.comStroNGER2012
Building occupants’ comfort assessment in the PBWE framework.
by
Francesco Petrini, Pierluigi Olmati and Franco Bontempi.
This research deals with the problem of the comfort assessment of high-rise building occupants under wind action. Also if the problem has been studied by there searchers and by the civil engineering industry during last thirty years, appropriate methods to handling the design of high-rise buildings in order to avoid wind-induced
occupant discomfort has not been defined yet, mainly due to the high uncertainties involved in the determination of both the demand and the sensitivity of the building occupants to wind-induced vibrations. The main issues related with this problem are first summarized, then the growing, pioneering performance-based wind engineering (PBWE) approach is proposed as tool to handle the problem. The required analyses are presented and discussed on both the conceptual and operational point of view. A case-study is then presented in order to demonstrate the effectiveness of the proposed approach. In the PBWE view, the contribution of the work is focused on the procedural step identified as “damage analysis”, something that, in authors’ knowledge,has not been yet developed in the literature.
Speeding up probabilistic inference of camera orientation by function ap...Nicolau Werneck
Slides from my presentation at the WSCG2011. Describes some modifications to existing techniques for camera orientation estimation in "Manhattan Worlds" aiming at faster calculation times.
PBWE - IN VENTO 2014 - Petrini StroNGER.comStroNGER2012
Building occupants’ comfort assessment in the PBWE framework.
by
Francesco Petrini, Pierluigi Olmati and Franco Bontempi.
This research deals with the problem of the comfort assessment of high-rise building occupants under wind action. Also if the problem has been studied by there searchers and by the civil engineering industry during last thirty years, appropriate methods to handling the design of high-rise buildings in order to avoid wind-induced
occupant discomfort has not been defined yet, mainly due to the high uncertainties involved in the determination of both the demand and the sensitivity of the building occupants to wind-induced vibrations. The main issues related with this problem are first summarized, then the growing, pioneering performance-based wind engineering (PBWE) approach is proposed as tool to handle the problem. The required analyses are presented and discussed on both the conceptual and operational point of view. A case-study is then presented in order to demonstrate the effectiveness of the proposed approach. In the PBWE view, the contribution of the work is focused on the procedural step identified as “damage analysis”, something that, in authors’ knowledge,has not been yet developed in the literature.
Building occupants’ comfort assessment in the PBWE frameworkFranco Bontempi
This research deals with the problem of the comfort assessment of high-rise building occupants under wind
action. Also if the problem has been studied by the researchers and by the civil engineering industry during last thirty years, appropriate methods to handling the design of high-rise buildings in order to avoid wind-induced occupant discomfort has not been defined yet, mainly due to the high uncertainties involved in the determination of both the demand and the sensitivity of the building occupants to wind-induced vibrations. The main issues related with this problem are first summarized, then the growing, pioneering performance-based wind engineering (PBWE) approach is proposed as tool to handle the problem. The required analyses are presented and discussed on both the conceptual and operational point of view. A case-study is then presented in order to demonstrate the effectiveness of the proposed approach. In the PBWE view, the contribution of the work is focused on the procedural step identified as “damage analysis”, something that, in authors’ knowledge, has not been yet developed in the literature.
MSc thesis presentation - Aerospace Structures - July 2015Alessandro Rosati
MSc final thesis. Development of MATLAB tool and use of a Fortran-based software (Mul2) for understanding the evolution of stresses on typical aerospace structures subjected to increasing loads and damages: evaluation of ultimate loads.
Evaluation of the variation of natural frequencies/mode shapes of simple aerospace structures as a result of the introduction of damages.
new optimization algorithm for topology optimizationSeonho Park
authors devise new convex approximation called DQA which utilizes information of two consecutive points at iterates. Also, to guarantee global convergence, filter method is illustrated.
Appunti del corso di dottorato:
INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE
Ia parte
Lezione del 28 maggio 2014
Lecture of the Ph.D. Course on STRUCTURAL OPTIMIZATION
May, 28, 2014
Corso di dottorato in Ottimizzazione Strutturale: applicazione mensola strall...Franco Bontempi
Appunti del corso di dottorato:
INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE
IIa parte
Lezione del 28 maggio 2014
Lecture of the Ph.D. Course on
STRUCTURAL OPTIMIZATION
2nd part
May, 28, 2014
Corso di dottorato in Ottimizzazione Strutturale: applicazione mensola strall...StroNGER2012
Appunti del corso di dottorato:
INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE
IIa parte
Lezione del 28 maggio 2014
Lecture of the Ph.D. Course on
STRUCTURAL OPTIMIZATION
2nd part
May, 28, 2014
Ph.D. Thesis project of Paolo E. Sebastiani PBEE - Mala Rijeka ViaductFranco Bontempi
The case study bridge "Mala Rijeka" is one of the most important bridges on the Belgrade - Bar International Line. The bridge was built in 1973 as the highest railway bridge in the World (Worlds Record Lists) and it is a continuous fivespan steel frame carried by six piers of which the middle ones have heights ranging from 50 to 137.5 m measured from the foundation interface. The main steel truss bridge structure consists in a continuous girder with a total length L=498.80 m. Static truss height is 12.50 m, and the main beams are not parallel, but are radially spread, in order to adjust to the route line.
Performance-based earthquake engineering (PBEE) consists of the evaluation, design and construction of structures to meet seismic performance objectives (expressed in terms of repair costs, downtime, and casualties) that are specified by stakeholders (owners, society, etc.).
It is based on the premise that performance can be predicted and evaluated with quantifiable confidence to make, together with the client, intelligent and informed trade-offs based on life-cycle considerations rather than
construction costs alone.
The Comprehensive Product Platform Planning (CP3) framework presents a flexible mathematical model of the platform planning process, which allows (i) the formation of sub-families of products, and (ii) the simultaneous identification and quantification of plat- form/scaling design variables. The CP3 model is founded on a generalized commonality matrix that represents the product platform plan, and yields a mixed binary-integer non- linear programming problem. In this paper, we develop a methodology to reduce the high dimensional binary integer problem to a more tractable integer problem, where the com- monality matrix is represented by a set of integer variables. Subsequently, we determine the feasible set of values for the integer variables in the case of families with 3 − 7 kinds of products. The cardinality of the feasible set is found to be orders of magnitude smaller than the total number of unique combinations of the commonality variables. In addition, we also present the development of a generalized approach to Mixed-Discrete Non-Linear Optimization (MDNLO) that can be implemented through standard non-gradient based op- timization algorithms. This MDNLO technique is expected to provide a robust and compu- tationally inexpensive optimization framework for the reduced CP3 model. The generalized approach to MDNLO uses continuous optimization as the primary search strategy, how- ever, evaluates the system model only at the feasible locations in the discrete variable space.
Corso di dottorato & Corso di formazione StroNGER2012
Basi di OTTIMIZZAZIONE STRUTTURALE, 6 luglio 2016 (totale di 8 ore)
&
LA PROGETTAZIONE STRUTTURALE ATTRAVERSO L’ANALISI DI CASI CRITICI, 7 e 8 luglio (totale di 16 ore)
I Restauri e la Città: l’esempio del Colosseo e della Casa di AugustoStroNGER2012
GLI ATTORI DEL DIVENIRE URBANO
Facoltà di Ingegneria
Sapienza Università di Roma
Sala del Chiostro 26 NOVEMBRE 2015
a cura di
Alessandro Cutini - Franco Bontempi
More Related Content
Similar to Applications of Structural Optimization: Corso di dottorato INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE / Petrini
Building occupants’ comfort assessment in the PBWE frameworkFranco Bontempi
This research deals with the problem of the comfort assessment of high-rise building occupants under wind
action. Also if the problem has been studied by the researchers and by the civil engineering industry during last thirty years, appropriate methods to handling the design of high-rise buildings in order to avoid wind-induced occupant discomfort has not been defined yet, mainly due to the high uncertainties involved in the determination of both the demand and the sensitivity of the building occupants to wind-induced vibrations. The main issues related with this problem are first summarized, then the growing, pioneering performance-based wind engineering (PBWE) approach is proposed as tool to handle the problem. The required analyses are presented and discussed on both the conceptual and operational point of view. A case-study is then presented in order to demonstrate the effectiveness of the proposed approach. In the PBWE view, the contribution of the work is focused on the procedural step identified as “damage analysis”, something that, in authors’ knowledge, has not been yet developed in the literature.
MSc thesis presentation - Aerospace Structures - July 2015Alessandro Rosati
MSc final thesis. Development of MATLAB tool and use of a Fortran-based software (Mul2) for understanding the evolution of stresses on typical aerospace structures subjected to increasing loads and damages: evaluation of ultimate loads.
Evaluation of the variation of natural frequencies/mode shapes of simple aerospace structures as a result of the introduction of damages.
new optimization algorithm for topology optimizationSeonho Park
authors devise new convex approximation called DQA which utilizes information of two consecutive points at iterates. Also, to guarantee global convergence, filter method is illustrated.
Appunti del corso di dottorato:
INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE
Ia parte
Lezione del 28 maggio 2014
Lecture of the Ph.D. Course on STRUCTURAL OPTIMIZATION
May, 28, 2014
Corso di dottorato in Ottimizzazione Strutturale: applicazione mensola strall...Franco Bontempi
Appunti del corso di dottorato:
INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE
IIa parte
Lezione del 28 maggio 2014
Lecture of the Ph.D. Course on
STRUCTURAL OPTIMIZATION
2nd part
May, 28, 2014
Corso di dottorato in Ottimizzazione Strutturale: applicazione mensola strall...StroNGER2012
Appunti del corso di dottorato:
INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE
IIa parte
Lezione del 28 maggio 2014
Lecture of the Ph.D. Course on
STRUCTURAL OPTIMIZATION
2nd part
May, 28, 2014
Ph.D. Thesis project of Paolo E. Sebastiani PBEE - Mala Rijeka ViaductFranco Bontempi
The case study bridge "Mala Rijeka" is one of the most important bridges on the Belgrade - Bar International Line. The bridge was built in 1973 as the highest railway bridge in the World (Worlds Record Lists) and it is a continuous fivespan steel frame carried by six piers of which the middle ones have heights ranging from 50 to 137.5 m measured from the foundation interface. The main steel truss bridge structure consists in a continuous girder with a total length L=498.80 m. Static truss height is 12.50 m, and the main beams are not parallel, but are radially spread, in order to adjust to the route line.
Performance-based earthquake engineering (PBEE) consists of the evaluation, design and construction of structures to meet seismic performance objectives (expressed in terms of repair costs, downtime, and casualties) that are specified by stakeholders (owners, society, etc.).
It is based on the premise that performance can be predicted and evaluated with quantifiable confidence to make, together with the client, intelligent and informed trade-offs based on life-cycle considerations rather than
construction costs alone.
The Comprehensive Product Platform Planning (CP3) framework presents a flexible mathematical model of the platform planning process, which allows (i) the formation of sub-families of products, and (ii) the simultaneous identification and quantification of plat- form/scaling design variables. The CP3 model is founded on a generalized commonality matrix that represents the product platform plan, and yields a mixed binary-integer non- linear programming problem. In this paper, we develop a methodology to reduce the high dimensional binary integer problem to a more tractable integer problem, where the com- monality matrix is represented by a set of integer variables. Subsequently, we determine the feasible set of values for the integer variables in the case of families with 3 − 7 kinds of products. The cardinality of the feasible set is found to be orders of magnitude smaller than the total number of unique combinations of the commonality variables. In addition, we also present the development of a generalized approach to Mixed-Discrete Non-Linear Optimization (MDNLO) that can be implemented through standard non-gradient based op- timization algorithms. This MDNLO technique is expected to provide a robust and compu- tationally inexpensive optimization framework for the reduced CP3 model. The generalized approach to MDNLO uses continuous optimization as the primary search strategy, how- ever, evaluates the system model only at the feasible locations in the discrete variable space.
Similar to Applications of Structural Optimization: Corso di dottorato INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE / Petrini (20)
Corso di dottorato & Corso di formazione StroNGER2012
Basi di OTTIMIZZAZIONE STRUTTURALE, 6 luglio 2016 (totale di 8 ore)
&
LA PROGETTAZIONE STRUTTURALE ATTRAVERSO L’ANALISI DI CASI CRITICI, 7 e 8 luglio (totale di 16 ore)
I Restauri e la Città: l’esempio del Colosseo e della Casa di AugustoStroNGER2012
GLI ATTORI DEL DIVENIRE URBANO
Facoltà di Ingegneria
Sapienza Università di Roma
Sala del Chiostro 26 NOVEMBRE 2015
a cura di
Alessandro Cutini - Franco Bontempi
SISTEMILA RETE STRADALE URBANA:UN’EMERGENZA DEL QUOTIDIANO O UN’OPPORTUNITA’ ...StroNGER2012
GLI ATTORI DEL DIVENIRE URBANO
Facoltà di Ingegneria
Sapienza Università di Roma
Sala del Chiostro 26 NOVEMBRE 2015
a cura di
Alessandro Cutini - Franco Bontempi
INFRASTRUTTURE IN AMBITO URBANO: COMPLESSITA’ DI PROGETTO E DURABILITA’StroNGER2012
GLI ATTORI DEL DIVENIRE URBANO
Facoltà di Ingegneria
Sapienza Università di Roma
Sala del Chiostro 26 NOVEMBRE 2015
a cura di
Alessandro Cutini - Franco Bontempi
61Resilienza dei centri urbani e rilievo delle costruzioni: un binomio indivi...StroNGER2012
GLI ATTORI DEL DIVENIRE URBANO
Facoltà di Ingegneria
Sapienza Università di Roma
Sala del Chiostro 26 NOVEMBRE 2015
a cura di
Alessandro Cutini - Franco Bontempi
Roma e le sue acque:il punto di vista della Protezione CivileStroNGER2012
GLI ATTORI DEL DIVENIRE URBANO
Facoltà di Ingegneria
Sapienza Università di Roma
Sala del Chiostro 26 NOVEMBRE 2015
a cura di
Alessandro Cutini - Franco Bontempi
Una visione ampia dei sistemi: robustezza e resilienza.StroNGER2012
GLI ATTORI DEL DIVENIRE URBANO
Facoltà di Ingegneria
Sapienza Università di Roma
Sala del Chiostro 26 NOVEMBRE 2015
a cura di
Alessandro Cutini - Franco Bontempi
L’investigazione antincendio sugli aspetti strutturali: una proposta di codificaStroNGER2012
I numerosi incendi che si innescano e danneggiano
le strutture hanno rivoluzionato, da una parte,
molte procedure sulla prevenzione definendo metodologie
gestionali più efficaci e stanno, dall’altra,
portando ad affinare procedure investigative
codificate atte a ridurre il rischio di errori/omissioni
durante le indagini.
Lo scopo di questo articolo è quello di esporre
una metodologia codificata di Structural Fire Investigation
(Investigazione sugli aspetti strutturali in
caso di incendio) atta ad individuare le cause scatenanti,
pregresse e latenti, che hanno determinato
l’evento accidentale.
L’iter investigativo, associato a determinate operazioni
strutturali e forensi che partono dalla raccolta
delle informazioni iniziali al repertamento e
controllo documentale per poi completarsi con le
verifiche computazionali, sicuramente aiuta a determinare,
in maniera rigorosa, le cause e l’origine
di un incendio. La modellazione degli incendi con
il software del NIST, Fire Dynamics Simulator
(FDS) e l’analisi strutturale con vari codici di calcolo,
permettono di verificare determinate ipotesi
maturate durante il repertamento e di avvalorare
scientificamente l’analisi semiotica rilevata sulla
scena, fornendo dati forensi utili in fase dibattimentale.
Quindi un’attività investigativa pianificata, permette
a qualsiasi utente, (VV.F., personale delle Forze
dell’Ordine, Consulente, Perito, CTU o Libero
Professionista), di svolgere indagini in maniera appropriata
secondo una linea guida che permette
di non tralasciare controlli a volte rilevanti per la
stesura della documentazione complessiva in forma
di report finale.
29 May 2015 - Rome
Research Meeting with
University of Brasilia–Brazil
University of Nebraska-Lincoln (Omaha Campus)
University of Rome La Sapienza
StroNGER
29 May 2015 - Rome
Research Meeting with
University of Brasilia–Brazil
University of Nebraska-Lincoln (Omaha Campus)
University of Rome La Sapienza
StroNGER
29 May 2015 - Rome
Research Meeting with
University of Brasilia–Brazil
University of Nebraska-Lincoln (Omaha Campus)
University of Rome La Sapienza
StroNGER
29 May 2015 - Rome
Research Meeting with
University of Brasilia–Brazil
University of Nebraska-Lincoln (Omaha Campus)
University of Rome La Sapienza
StroNGER
Uso delle fibre di basalto nel risanamento degli edifici storiciStroNGER2012
Intervento di Stefania Arangio a:
Miglioramento e adeguamento sismico di strutture esistenti attraverso l'utilizzo di materiali compisiti in FRP
Ordine degli Ingegneri della Provincia di Roma
14 aprile 2015
IDENTIFICAZIONE STRUTTURALE DEL COMPORTAMENTO SPERIMENTALE DI CENTINE INNOVAT...StroNGER2012
Contributo a IF CRASC'15 di Alessandra Castelli e Francesco Petrini.
14-16 maggio 2015.
Universita' degli Studi di Roma La Sapienza
Facolta' di Ingegneria Civile e Industriale
ifcrasc15@stronger2012.com
Corso Ottimizzazione Strutturale Sapienza 2015StroNGER2012
Il corso vuole introdurre in maniera semplice i concetti, i metodi, gli strumenti necessari all’ottimizzazione di una struttura in termini di capacità prestazionali e sicurezza. L’attenzione è focalizzata sulle idee e sulle applicazioni, nella convinzione che gran parte dei dettagli algoritmici, seppure fondamentali nelle applicazioni più sofisticate, possano essere rimandati a successivi approfondimenti: questo anche alla luce degli strumenti computazionali moderni che permettono di concentrarsi sulla progettazione concettuale dei sistemi strutturali nelle forme più attuali. Gli studenti potranno quindi essere capaci di impostare e comprendere i processi ideativi alla base delle moderne forme strutturali che si presentano per le coperture, i ponti e gli edifici alti.
MIGLIORAMENTO ED ADEGUAMENTO SISMICO DI STRUTTURE ESISTENTI ATTRAVERSO L’UTIL...StroNGER2012
MIGLIORAMENTO ED ADEGUAMENTO SISMICO DI STRUTTURE ESISTENTI ATTRAVERSO L’UTILIZZO DI MATERIALI COMPOSITI IN FRP.
14 e 21 Aprile 2015.
https://www.ording.roma.it/seminario.aspx?id=14727
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Literature Review Basics and Understanding Reference Management.pptxDr Ramhari Poudyal
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
Using recycled concrete aggregates (RCA) for pavements is crucial to achieving sustainability. Implementing RCA for new pavement can minimize carbon footprint, conserve natural resources, reduce harmful emissions, and lower life cycle costs. Compared to natural aggregate (NA), RCA pavement has fewer comprehensive studies and sustainability assessments.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Online aptitude test management system project report.pdfKamal Acharya
The purpose of on-line aptitude test system is to take online test in an efficient manner and no time wasting for checking the paper. The main objective of on-line aptitude test system is to efficiently evaluate the candidate thoroughly through a fully automated system that not only saves lot of time but also gives fast results. For students they give papers according to their convenience and time and there is no need of using extra thing like paper, pen etc. This can be used in educational institutions as well as in corporate world. Can be used anywhere any time as it is a web based application (user Location doesn’t matter). No restriction that examiner has to be present when the candidate takes the test.
Every time when lecturers/professors need to conduct examinations they have to sit down think about the questions and then create a whole new set of questions for each and every exam. In some cases the professor may want to give an open book online exam that is the student can take the exam any time anywhere, but the student might have to answer the questions in a limited time period. The professor may want to change the sequence of questions for every student. The problem that a student has is whenever a date for the exam is declared the student has to take it and there is no way he can take it at some other time. This project will create an interface for the examiner to create and store questions in a repository. It will also create an interface for the student to take examinations at his convenience and the questions and/or exams may be timed. Thereby creating an application which can be used by examiners and examinee’s simultaneously.
Examination System is very useful for Teachers/Professors. As in the teaching profession, you are responsible for writing question papers. In the conventional method, you write the question paper on paper, keep question papers separate from answers and all this information you have to keep in a locker to avoid unauthorized access. Using the Examination System you can create a question paper and everything will be written to a single exam file in encrypted format. You can set the General and Administrator password to avoid unauthorized access to your question paper. Every time you start the examination, the program shuffles all the questions and selects them randomly from the database, which reduces the chances of memorizing the questions.
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
An Approach to Detecting Writing Styles Based on Clustering Techniquesambekarshweta25
An Approach to Detecting Writing Styles Based on Clustering Techniques
Authors:
-Devkinandan Jagtap
-Shweta Ambekar
-Harshit Singh
-Nakul Sharma (Assistant Professor)
Institution:
VIIT Pune, India
Abstract:
This paper proposes a system to differentiate between human-generated and AI-generated texts using stylometric analysis. The system analyzes text files and classifies writing styles by employing various clustering algorithms, such as k-means, k-means++, hierarchical, and DBSCAN. The effectiveness of these algorithms is measured using silhouette scores. The system successfully identifies distinct writing styles within documents, demonstrating its potential for plagiarism detection.
Introduction:
Stylometry, the study of linguistic and structural features in texts, is used for tasks like plagiarism detection, genre separation, and author verification. This paper leverages stylometric analysis to identify different writing styles and improve plagiarism detection methods.
Methodology:
The system includes data collection, preprocessing, feature extraction, dimensional reduction, machine learning models for clustering, and performance comparison using silhouette scores. Feature extraction focuses on lexical features, vocabulary richness, and readability scores. The study uses a small dataset of texts from various authors and employs algorithms like k-means, k-means++, hierarchical clustering, and DBSCAN for clustering.
Results:
Experiments show that the system effectively identifies writing styles, with silhouette scores indicating reasonable to strong clustering when k=2. As the number of clusters increases, the silhouette scores decrease, indicating a drop in accuracy. K-means and k-means++ perform similarly, while hierarchical clustering is less optimized.
Conclusion and Future Work:
The system works well for distinguishing writing styles with two clusters but becomes less accurate as the number of clusters increases. Future research could focus on adding more parameters and optimizing the methodology to improve accuracy with higher cluster values. This system can enhance existing plagiarism detection tools, especially in academic settings.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Harnessing WebAssembly for Real-time Stateless Streaming PipelinesChristina Lin
Traditionally, dealing with real-time data pipelines has involved significant overhead, even for straightforward tasks like data transformation or masking. However, in this talk, we’ll venture into the dynamic realm of WebAssembly (WASM) and discover how it can revolutionize the creation of stateless streaming pipelines within a Kafka (Redpanda) broker. These pipelines are adept at managing low-latency, high-data-volume scenarios.
Applications of Structural Optimization: Corso di dottorato INTRODUZIONE ALL'OTTIMIZZAZIONE STRUTTURALE / Petrini
1. 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
2. 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.
3. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
6. 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
(Sapienza University of Rome)
Spin-off company
Mar2014
Aerodynamics and Aeroelasticity
PBD for Wind
PBD for Wind, Earthquake, Fire, Blast
Resilience
Energy Harvesting
Education and Milestones (2005-2014)
7. 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
(Sapienza University of Rome)
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)
(Sapienza University of Rome)
Spin-off company
11. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
12. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
13. Sub-problem approximation method (SAM)
13
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
• 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. 14
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
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
16. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
18. 18
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
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. 19
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
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. 20
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
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).
21. Performance-Based Earthquake Engineering (PBEE)
2007 2008
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
22. 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.
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
23. 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.
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
24. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
26. 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
Feasible configuration selection
(Option selection)
Yes
Performance evaluations of the
candidate, feasible configurations
26
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
By focusing on a specific performance
requirement
Investigation on what is the best
configuration
Volume, and weight are checked but not
optimized
Probabilistic Deterministic
27. OPTIMIZATION OF THE SUPPORT STRUCTURE OF OFFSHORE WIND TURBINES
• System design approach for complex structural systems optimization
• Substructure typology selection
• Parametric optimization
27
28. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
29. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
30. Offshore wind farm site location (1)
30
30
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
31. Offshore wind farm site location (2)
31
31
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
33. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
35. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
37. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
38. Structural decomposition (II)
38
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
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
40. ( ) ( ) ( ) ( )( )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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
41. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
42. 42
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
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. 43
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
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. 44
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
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. 45
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
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. 46
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
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
48. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
49. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
51. 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
Shape optimization
(Options definition)
Parameters optimization
(Options refinement)
Feasible configuration selection
(Option selection)
Yes
Definition of the morphological
configuration of the object
51
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
52. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 52
Others: Gravity-
based, Tension
leg
53. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 53
54. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 54
55. 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]
Comb 6.1b Comb 6.1cLoad
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]
Comb 6.1b Comb 6.1cLoad
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]
Comb 6.1b Comb 6.1cLoad
Case 6.1c
Heightabovebottom[m]
Wave-current induced force per
unit length [N/m]
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 55
56. 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
Monopila Tripode Jacket
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
Monopila Tripode Jacket
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
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
Monopila Tripode Jacket
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
Monopila Tripode Jacket
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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 56
57. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 57
peso monotubo 205.78 t
peso tripode 635.58 t
peso jacket 473.38 t
PESI SUPPORTO "E"
1057.8 t
735.58 t
59. 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
59
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
61. GEOMETRIA
Dimensioni in elevazione
Dimensioni in pianta
• Altezza totale: 180 m
• Altezza fuori terra: 140 m
• Altezza sopra il pelo libero: 105 m
61
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
62. MODELLAZIONE
2835 nodi
2910 elementi lineari
di 11 tipologie
44 elementi piani
62
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
63. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
Configurazioni
64. ● 105 Parametri
▶▶▶▶ 42 Potenziali variabili di progetto
■ 8 relative alla “forma” della struttura
■ 34 relative alle sezioni degli elementi
DESIGN OPTIMIZATION (D. O.)
64
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
65. • 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
66. MOLTIPLICATORE
CARICO CRITICO
(BLF) ≥ 2,5
Variabili di stato (SV):
66
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
67. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
Variabili di stato (SV):
70. 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)
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 70
71. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 71
72. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 72
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
73. 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)
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 73
74. 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*
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 74
75. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 75
77. 16% DI RIDUZIONE
DEL VOLUME
TOTALE (VO)
24% DI RIDUZIONE
DEL VOLUME
DELLA TORRE
1% DI RIDUZIONE
DEL VOLUME
DEL JACKET
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 77
Results
78. 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 ====⋅⋅⋅⋅====
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80. 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
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81. Optimization problem algorithm
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 81
82. Macro-level model: Design variables trend
Diameters Thicknesses
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 82
83. Macro-level model: State variables trend
Compression stresses Von Mises stresses
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 83
84. Macro-level model: Configuration evolution
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 84
85. Macro-level model: Objective function
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 85
86. Meso-level model
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 86
87. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 87
89. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 89
90. 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).
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D.
91. 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
93. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 93
94. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 94
95. 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)
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
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
PBWEPBEE
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 95
99. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 99
100. 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
101. ( )
( )
( ) )(),(
),,(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
102. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 102
103. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 103
105. 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)
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 105
106. 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
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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 106
Aeolian risk assessment
107. 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
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
rrm
p
grr σ⋅+= )T(log
.
)T(log
winde
windegr
⋅η
+⋅η=µ
2
5770
2 Davenport (1983)
Reliable results for
broad band processes
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 107
Aeolian risk assessment
108. 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
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
- 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
+
+
Reliable results for
broad band processes
Vanmarcke (1975)
Aeolian risk assessment
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 108
109. 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
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
- 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)
Reliable results for
broad band processes
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
+
+
Aeolian risk assessment
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 109
110. 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
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
(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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 110
Aeolian risk assessment
111. Interaction analysis IP =
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
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
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
Aeolian risk assessment
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 111
112. 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
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
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
Aeolian risk assessment
113. 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
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
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
Aeolian risk assessment
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 113
114. 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.
Aeolian risk assessment
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 114
116. TUNED MASS DAMPER (TMD)
C1
K1 CTMD
KTMD
M1
MTMD
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 116
117. C1
K1 CTMD
KTMD
M1
MTMD
Sistema Principale
(struttura)
ܯ1 = massa
ܭ1 = ߱1
2
∙ ܯ1 = rigidezza
ܥ1 = 2 ∙ ܯ1 ∙ ߱1 ∙ ߦ1 =
= smorzamento
TUNED MASS DAMPER (TMD)
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 117
118. 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
∙ ܯ1 = rigidezza
ܥ1 = 2 ∙ ܯ1 ∙ ߱1 ∙ ߦ1 =
= smorzamento
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 118
TUNED MASS DAMPER (TMD)
119. 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
∙ ܯ1 = rigidezza
ܥ1 = 2 ∙ ܯ1 ∙ ߱1 ∙ ߦ1 =
= smorzamento
Sistema Secondario
(TMD)
TUNED MASS DAMPER (TMD)
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 119
120. ݈ܽ = 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 120
EFFETTO DEL TMD SULLA RISPOSTA STRUTTURALE
121. ݈ܽ = 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
1.E-04
1.E-03
1.E-02
1.E-01
1.00E-01
RPSD
Frequenza (Hz)
Non controllata
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 121
EFFETTO DEL TMD SULLA RISPOSTA STRUTTURALE
122. ݈ܽ = 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
1.E-04
1.E-03
1.E-02
1.E-01
1.00E-01
RPSD
Frequenza (Hz)
Controllata
Non controllata
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 122
EFFETTO DEL TMD SULLA RISPOSTA STRUTTURALE
123. Optimization parameters
Design Parameters
γ = mTMD/mtot
β = ωTMD/ ω1
ξ* = damping of TMD
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 123
124. C1
K1 CTMD
KTMD
M1
MTMD
EFFETTO DEL TMD SULLA RISPOSTA STRUTTURALE
305 m
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 124
125. ANALISI PARAMETRICA CON TMD
ߛ =
݉ܶܦܯ
݉1
; ߚ =
߱ܶܦܯ
߱1
; ߦ = smorzamento;
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 125
127. 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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 127
128. 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
Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 128
129. 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
131. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 131
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)
132. Case study
40 floors, 160 m heigth, 35 m x 35 m floor, office building
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 132
RENDERING STRUCTURAL SYSTEM FEM MODEL
133. Case study
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 133
Outrigger
Bracing
System
Frame BFrame A
Frame B
Frame A
134. The role of the outrigger and of
the lateral bracing
135. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 135
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
136. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 136
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
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 137
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
138. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 138
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
139. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 139
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
140. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 140
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
Progressive Collapse
141. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 141
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
142. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 142
Frame BFrame A
SWAY COLLAPSE NO-SWAY COLLAPSE
Progressive Collapse
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 144
Lateral Force: Dir. +Z
SCENARIO
Without Wind Wind Γ=0.5 Wind Γ=1.0 Wind Γ=1.5
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 145
SCENARIO
Without Wind Wind Γ=0.5 Wind Γ=1.0 Wind Γ=1.5
Lateral Force: Dir. -Z
146. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 146
Lateral Force: Dir. +Z
DEFORMED SHAPE
Without Wind Wind Γ=0.5 Wind Γ=1.0 Wind Γ=1.5
After 180 min After 140 min After 152 min After 82 min
88 min
Vertical
69 min
Outwards
16 min
Outwards
<10 min
Outwards
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 148
Configurations: position of the outrigger
CONFIGURATIONS
G A B C
STEEL MASS [TON]
877 857 877 877
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Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 149
Configurations: vertical brace system
CONFIGURATIONS
G D E F
STEEL MASS [TON]
877 817 994 939
150. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 150
Multi-hazard analyses – 3 heated columns
151. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 151
Multi-hazard analyses – 3 heated columns
Initial
152. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 152
Multi-hazard analyses – 3 heated columns
Initial
153. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 153
Multi-hazard analyses – 3 heated columns
Initial
155. Corso di Dottorato: Introduzione all'oƫmizzazione strutturale Roma, 21 Giugno 2014
Prof.-Ing. Franco Bontempi, Ing. Francesco Petrini, Ph.D. 155
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.