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Tesi dottorato ingegneria navale UNIGE C.Rizzo
Tipologia: Tesi di laurea
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Prefazione
Sinossi:
Il presente lavoro parte dall’esperienza lavorativa dell’Autore come ispettore di una società di classificazione navale. I regolamenti per la costruzione sono il collegamento fra teoria e pratica, tra ricerca ed esperienza sul campo.
E’ facile intuire che questo ruolo riveste una particolare importanza: da un lato la teoria permette di sviluppare modelli matematici e metodologie di progettazione sempre più accurate, ma dall’altro è sempre necessaria una validazione sperimentale delle stesse.
Negli ultimi anni i regolamenti delle società di classificazione navale, ed in particolare quelli relativi alla progettazione strutturale, hanno subito profondi ed innovativi cambiamenti e probabilmente l’evoluzione non è del tutto completata.
Il primo capitolo di questo lavoro riassume l’origine storica dei regolamenti ed introduce le ragioni che hanno imposto un cambiamento che indubbiamente è per lo shipping una svolta importante.
Dopo una breve parentesi che introduce, anche dal punto di vista teorico, i nuovi concetti che stanno alla base dei moderni regolamenti, è sembrato opportuno un confronto tra alcuni dei regolamenti delle società di classifica sia sul piano teorico sia con esempi numerici.
L’obiettivo è quello di valutare l’impatto dei cambiamenti apportati e di fornire una panoramica sullo stato dell’arte. Tale scelta si è rivelata ancora più corretta considerando che le principali società di classifica hanno annunciato in questi mesi di voler redigere in breve tempo un regolamento comune per la costruzione delle navi, fatto impensabile anche pochi anni fa.
In particolare sono state esaminate e confrontate le formulazioni per il dimensionamento delle strutture di ABS, BV, DNV, GL, RINA e, per il caso delle verifiche a fatica, anche del CCS e del NKK.
Dopo l’analisi teorica sono presentati diversi esempi numerici analizzati in vario modo. Essi permettono di mettere in luce i diversi aspetti del cambiamento e di delineare quanto è suscettibile di ulteriori modifiche:
L’ultimo capitolo riguarda le possibili ulteriori ricerche e le conclusioni.
Nota:
Quanto riportato in questa tesi rappresenta il frutto di un’applicazione indipendente e di un’autonoma interpretazione non essendo stato ufficialmente riveduto e corretto da parte delle Società di Classificazione coinvolte. Tuttavia l’Autore desidera ringraziare tutti i colleghi delle Società di Classificane che hanno contribuito alla comprensione delle norme e dei regolamenti con le loro spiegazioni.
1.1 Classification Societies origin and their actual role in the shipping
To reduce the risks connected to a particular event, the Romans themselves usually asked for insurance companies, especially in the shipping transport subjected to human factors and environmental risks.
Who assumes the responsibility to insure the ship, of course, should evaluate if the ship’s features are suitable for the intended voyage, generally through the opinion of reliable experts.
Classification societies born as organizations among reliable engineers of insurance companies. These institutions were exactly created to issue appropriate documents certifying efficient conditions of the ships and their suitability to carry goods without damages.
Trades and business among Mediterranean people were always frequent but, after America discovery, ships dimensions and voyage length increased and more and more insurance companies’ risks. Ship’s features, owners and maintenance conditions notices became of crucial importance in shipping transports together with crew ability.
At the beginning, information were collected in registers prepared and published by insurers groups and owners groups whose opinion was necessarily on their respective side.
In London, the coffeehouses were popular centres for businessmen to meet in the last part of 17th Century and in the 18th^ Century. Marine insurers rendezvoused at Lloyd's in Lombard Street. Mr Edward Lloyd, the coffee house owner, was usual to gather information about ships and shipping world.
Looking forward we find Edward Lloyd distributing information in Lloyd's News which first appeared in
The IACS (International Association of Classification Societies) tells the origin of the classification societies hereunder reported:
“From the time of the Phoenecians, through the Romans, Venetians, Hanseatics and onward, marine insurers have been looking for some guarantee of the fitness of a ship for the voyage to be undertaken. It was therefore inevitable that the underwriters, gathered as a group at Lloyd's, should set up some system of inspection of hulls and equipment. In 1760 a Committee was formed for the purpose, the earliest existing result of their labours being Lloyd's Register Book for the years 1764-65-
66. This detailed vessel ownership, the master (early ISM?), characteristics and condition - but based on the unstated (and differing) standards of the earliest surveyors.
Nonetheless, an attempt was made to 'classify' the condition on an annual basis. The condition of the hull was classified A, E, I, O or U, according to the excellence of its construction and continuing soundness (or otherwise). Equipment was G, M, or B: simply, good, middling or bad. Any ship thus classed AG was considered as sound as could be, whilst one classed UB was obviously a bad risk. After a few years, G, M or B were replaced by 1, 2 or 3, which is the origin of the expression 'A1', meaning 'first or highest class'.
In 1769 the leading underwriters moved to their own premises off Cornhill and called themselves 'Members of the Society'. The many fallacies in the system of assigning class, not least the arbitrary limits to the number of years that a ship could remain in the highest class, which also depended on the place of build, led to a rival society of owners setting up their own register. In the 1820s, moves were made to clean up what had become a system in disrepute and combine the two registers. A telling point, made by one of the leading campaigners, was that the system of classification based on age created a glut of tonnage, because a ship, however well maintained, could never be restored to the highest class. Thus the reputable owner was forced to discard and replace her with new tonnage to acquire "the talismanic charm of A1" - presumably the discarded ship continued to trade, eventually to compete as 'sub-standard'.
It is easy to realize that a Classification Society is a very particular organization, satisfying at the same time the requirements of different customers and involved in a multiple tasks work. On a side, as recognized organization on behalf of the Flag Administration should assure that the minimum safety conditions for the ship, the crew and passengers, if any, and the environment; on the other side, it acts as third party at shipowner’s request to grant the ship is suitable for her mission profile. At the same time a Classification Society should, issuing its rules and guidelines, establish and codify design and maintenance methods of ships.
Considering the above, a Classification Society is a technical consultant not only to ship owners but for all designers involved in the shipping.
As a consequence of their history, Classification Societies can be neither considered as certifying authority only, neither as a world maritime police organization, taking into account they are paid by their customers, i.e. the ship owners. They are rules and certificate makers and, at the same time, quality assurance inspectors not only by appointment of the ship owner under a private contract but also so authorized to act on behalf of Flag State Administration.
Moreover, being ship owners no more a single businessman who manages his ships by his own but are usually banks, investment companies, etc. the technical management isn’t now carried out by the owner itself. Sometimes this technical lack is supported by Classification Societies acting as owners’ consultant.
1.2 The traditional Classification Societies Rules
Shipbuilding has a very long history: ships were built since the Biblical Noah's ark and a Biblical recommendation is still in force (the longitudinal deck camber / ship’s length ratio in the International Load Line Convention 1966).
The safety granted by the experience removed the need of the research of new solutions typical of other fields as nuclear engineering, airplane design, aerospace, etc.
The traditional rules for structures scantling were mainly based on parametric formulations deriving from experience considerations on the scantling of the classed fleet. A simple and typical example is the spacing of the stiffeners of a plate panel prescribed by several rules as follows:
supposed that a sufficiently strong scantling implies minimum stiffener spacing based on ship’s length only. The ship’s length, i.e. the parameter in the formula, should be calculated according to the rules definition and limits because of the statistical formulation origin.
This prescription is not directly related to any physical formulation involving strain or stresses or structures limit states, even if the hull girder length can be regarded as one of the influencing parameters.
The traditional rules generally give prescriptions on building measures of the structural elements like thickness, width, areas, inertia, modulus, etc. and its position. It is difficult to understand the physical meaning of the parameters used and, even more, to state the theoretical method on which the formula is based on. However the formulae are based on structural schemes and hypotheses and therefore their application should be in accordance with rules definition of parameters but theory is embedded and often calibration of coefficients hide it. We must also remember that automated computation facilities are available since few years and, being a task of the rules the easiness in application, formulations had to be simple.
As far as the loads are concerned, traditional rules generally give pressure heads, internal and external. Their determination, especially for the dynamic part, was mainly empirical.
The modern rules continue the traditional assumption of the superimposition of two main structural models: the hull girder and the local structural elements such as plates and stiffeners, even if a direct calculation of complete model of a ship using the F.E.M. (finite element method) is more and more used and required. Generally the local structural element, e.g. as a plate panel, shall be in compliance
with local check, i.e. thickness check. Moreover, shall be such that hull girder strength is verified. If a stiffener is attached to the plate, the effective breadth thickness shall also be such to verify the section modulus check.
The combination of the various loads and the effects of the structural models superimposition was embedded in formulae coefficients.
1.3 New approaches of class rules
The new approach of Classification Societies Rules for steel ships is at present still under developing: all IACS members have not yet issued rules completely developed according to this new reliability approach but all members have already planned substantial rules upgrading.
The BV/RINA Rules 2000 edition and the DNV Rules are probably the most developed ones from this point of view. Also NKK released guidelines for direct strength analysis. It is worth to point out that LR, ABS and DNV are now planning to issue common Rules valid for typical ships (i.e. tankers, bulk carrier and container ships) classed with one of the three societies and IACS members are planning to have common rule bases shortly.
The innovations described in the following chapters modify completely the rules approach in respect to the previous rules editions mainly due to the following aspects:
In particular structures scantlings checks are based on the following approach, which is more similar to a design approach than to a rule check:
A more rational approach to the ship structure design is adopted introducing several new aspects, which constitute a significant step forward considering the more empirical formulae of traditional rules.
These approaches, allowed by modern computation systems, better investigate the load demand and structural capacity leading to a more efficient distribution of the steel in the hull.
In short a design approach, instead of a check approach, has been adopted in the modern rules editions: the structural analysis is divided in three main steps:
The previous rules edition provided only check formulae, obviously based on the above analysis, but in an implicit form. In the modern approach all the steps are explicitly presented.
The fatigue checks have been specially considered because they involve the definition of a very complete load set, they require the most advanced structural models for the stress definition and the structure resistance (limit state) is only known with large uncertainties. Therefore fatigue checks are probably the most representative test case for a comparison among Classification Societies rules.
By the way, the Author has carried out some experimental tests and data analyses achieving an appreciable knowledge of the phenomenon.
1.5 Structure of the thesis
The thesis follows the logical scheme hereunder reported:
A brief summary of the statistics and probability theory referring to well known basic principles is presented at the beginning and an introduction of structural reliability methods is briefly resumed mainly referring to ship’s structures applications.
On the basis of the above-mentioned introduction, the overall approaches of the main Classification Societies recent rules are presented.
The following arguments are then examined:
mainly from the theoretical point of view.
The midship sections in cargo area of typical ships (a double hull oil tanker, a bulk carrier and a container ship) are assessed according to the Rules, mainly using their software, if available.
Many numerical data can easily be obtained using software, but many others have also been obtained with the aim to have intermediate steps results (usually not provided by software) for some scantling procedures.
The following software have been briefly presented and then applied: ABS Safe Hull, BV Mars 2000, DNV Nauticus Hull, GL Poseidon, RINA Leonardo Hull, LR RuleCalc.
They have been used for hull girder, stiffeners and plating calculations, being the primary supporting members scantling in all examined rules assessed by large finite element models or, in simple cases, by isolate beam or three dimensional (grillage) structural models loaded by rules’ loads.
Truth to tell, some rules give parametric formulations for preliminary scantling of primary members, to be subsequently checked by direct calculations. In the light of the above, loads are carefully examined but comparison of primary supporting members is briefly outlined only.
At the beginning, the input data of the various rules are discussed. Due to some minor differences in the basic principles adopted, some input data slightly differ, even if the ship is the same. However, the input data of each analyzed midship transverse section have been carefully checked in order to obtain the rule scantling of completely identical structures.
What reported in previous part of the thesis is herewith recalled in an attempt to explain similarities, differences, capabilities and peculiarities of each applied rule.
The structural software provided by the classification societies are able to give a large amount of results: the comparisons are therefore mainly given in a graphical format in order to highlight differences. Numerical data are reported in the Appendix and in references.
A resume of the work is reported. Suggestions for further research are also given in this chapter.
It seemed necessary to attach to the thesis the printing outputs, at least in electronic format, of the numerical calculation performed using the software or the prepared computer tools, even if they are intended to be interactive tools and therefore just a selection of the possible output is really reported.
As a conclusion of the thesis’ summary, in order to highlight, if necessary, the importance of a comparison among classification societies rules, it is hereunder reported a part of the speech of the Executive Vice President and Chief Technology Officer of ABS, Dr. Donald Liu at the 15th^ International Ship and Offshore Structures Congress held on 11-15 August 2003 at San Diego, California:
… ”One of the missions of a class society is to establish standards for the design, construction and operational maintenance of ships. In fact the work of ISSC has played some role in IACS’ rule making. The ISSC wave spectrum, for example, has been used by IACS, and the ISSC work in the areas of loads predictions and analysis has, for example, also been utilized. With the 10 IACS societies there are 10 different structural design standards that result in slightly different scantlings in a ship. The resulting differences in steel weight distinguish whether the ship is of robust design or of light scantling design. In the competitive world of shipbuilding, shipyards can and do play one class society against another to minimize scantlings so as to build the lowest cost ship. Shipowners have expressed their unhappiness with such a situation as they are asking for more robust and durable ships.
To eliminate this potential for competition between class societies and shipyards with regards to structural requirements and standards, IACS has recently embarked on a major effort to develop common classification rules for structural scantlings of a newbuilding from both global and local strength considerations, including hull girder strength, minimum scantling criteria, corrosion margins, and buckling and fatigue strength. The first ship types considered for the development of common rules are double hull tankers and double hull bulk carriers. The rules are scheduled to be completed in January 2005. This harmonization of classification rules is a big step forward for IACS and is supported by owners, shipyards and regulatory bodies.” …
1.6 References of Chapter 1
[1] SOLAS Safety of Life at Sea Convention Consolidated edition 2001, International Maritime Organization, London
[2] ISSC 2003, Proceedings of the 15th^ International Ship and Offshore Structures Congress, A. Mansour, C. Erteking ed.s, Elsevier 2003
[3] IACS, “What is IACS” web site www.iacs.org.uk,
[4] IACS, Unified Requirements UR, web site www.iacs.org.uk
[5] Rizzo C. DINAV Report 01CRI01 “Il ruolo delle società di classificazione delle navi”, Univ. di Genova, January 2001 (in italian)
2.1.2 Basics of probability theory
A qualitative definition of the words “probability”, “risk” and “chance” is widely known. The theory of probability aims to quantitatively assess this issue. As far as the meaning and interpretation of the probability theory results, everyone can have his own opinion, but the calculation methods remain still the same.
The classical definition of probability refers to the days that the probability calculus was founded by Pascal and Fermat. The inspiration for this theory was found in the games of cards and dices, [12].
The classical definition of the probability of the event A can be formulated as the ratio between the number of equally likely ways an experiment (trial) may lead to A and the total number of equally likely ways in the experiment. In the more used frequentistic definition the total number of experiment should became infinite:
tot
A
where N (^) A is the number of experiments where the event A occurred, N (^) tot is the total number of experiments. In principle we can carry out a large amount of experiments, at least infinite, aiming to obtain all the possible values of the outcome, i.e. covering the sample space.
Considering e.g. the strength of a standard steel specimen, this characteristic may be determined by performing N (^) A standardized tests. Tests results will, however, differ each other due to measurements errors and steel strength is assumed as random event. The set of all possible outcomes of the experiments is called the sample space Ω for the random quantity and A is the event of the measurements taken. The theory of sets can be resumed and applied to the probability theory.
The probability theory is mathematically build up by the following (only) three axioms:
where P is the probability measure;
where Ω is the sample space;
given that E 1 , E 2 , E 3 , …., En are mutually exclusive events (i.e. without common elements), then:
P (∪ (^) i E )= ∑ i P ( Ei ) Eq. 2.
easily noticed.
2.1.3 Conditional probability
The concept of conditional probability is of special interest in risk and reliability analysis being the basis for updating the prior probability estimates based of new information, knowledge and evidence. Practically it defines the probability that an event occurs when another event of the same sample space has occurred, so reducing the sample space.
The conditional probability of the event E 1 , given that the event E 2 has occurred, is defined as:
2
1 2 1 2
It is seen that the conditional probability is not defined if the conditioning event is the empty set.
As an example, let’s consider two black boxes, one containing 70% of white marbles and 30% of black marbles, the other containing 30% of white marbles and 70% of black marbles. We can consider the probability to extract a black marble (event E 1 ) conditioned to the probability to extract from the second box (event E 2 ).
The event E 1 is said to be statistically independent from the event E 2 if:
implying that the occurrence of the event E 2 does not affect the probability of E 1. The definitions of mutually exclusive and statistically independent events have different meanings. It is noted that, if two events are statistically independent, they are not mutually exclusive (because E 1 and E 2 occur independently each from the other) and that if two events are mutually exclusive they are not statistically independent (if E 1 occurs, E 2 can’t occur and this is a relationship between the events).
Therefore, remembering the definition of conditional probability, it can be written:
and it follows immediately that, if the events E 1 and E 2 are independent,
The above equation defines the joint probability in case of independent events, i.e. the probability that the two events occur at the same time. Based on the above findings, the important rule of Bayes may now be derived.
Consider the sample space Ω divided into n mutually exclusive events, moreover let the event A be an event in the sample space Ω. Then we can write the probability of the event A , i.e. P(A) as:
= ∑ ⋅
i i i
n n
n
1 1 2 2
1 2 Eq. 2.
This is known as the total probability theorem. The Bayes interpretation of probability gets out from the application of the above-mentioned axioms and theorem. Using the conditional probability concept it can be simply drawn out:
∑ ⋅
j j j
i i i
knowledge about the event A. As mentioned previously, the rule due to Bayes is extremely important, it allows dealing with uncertainties in a quantitative way. It can also be shown that Bayesian interpretation of probability is mathematically equivalent to the frequentistic one.
Let’s consider again the two black boxes, one containing 70% of white marbles and 30% of black marbles, the other containing 30% of white marbles and 70% of black marbles. If we extract from one of the boxes one marble, without knowing which is the box containing the 70% of white marbles, the probability to extract a white ball is obviously 0.5.
But after five extractions let’s we define e.g. the event E=[w, w, w, w, b], i.e. four white balls and one black ball. Assuming to restore the starting situation, we can evaluate the probability to extract a white ball conditioned to the knowledge of the above event.
In a similar way the sample coefficient of kurtosis κ is defined as:
4
σ
κ
∑ −
i
tot
Eq. 2.
which is a measure of the peakedness of the histogram. Typically one would compare the sample coefficient of kurtosis to that of a normal distribution, which is 3.0.
The above parameters summarize the features of a single data set.
When observations of physical phenomena are done, generally two or more characteristic quantities are monitored and illustrated in scatter diagrams. As a characteristic indicating the tendency toward high-high pairings and low-low pairings, i.e. a measure of the correlation between the observed data sets, the sample covariance σXY is useful, which is defined as:
= (^) ∑ (^) i i − i − tot
σ Eq. 2.
The sample covariance has the property that if there is a tendency in the data set that the values of x (^) i
positive and the sample covariance will be positive. The other way around will result in a negative sample covariance. The sample covariance may be normalized in respect to the sample standard deviations of the individual data sets σ X and σ Y and the result is called the sample correlation coefficient r (^) XY defined as:
X Y
i i i tot
XY
σ σ
∑ − −
Eq. 2.
It is limited in the interval [–1 ; +1] and the extreme values of the interval are only achieved in case the data pairs are perfectly correlated, implying that the points on the scatter diagram lie on a straight line.
A negative correlation coefficient between two variables implies that if the outcome of one variable is large compared to its mean value the outcome of the other variable is likely to be small compared to its mean value. A positive correlation coefficient between two variables implies that if the outcome of one variable is large compared to its mean value the outcome of the other variable is also likely to be large compared to its mean value.
In short the correlation coefficient indicates if there is a linear relationship between the two data sets (events). However, the linear relationship of the two events implies a physical relationship between the phenomena. The statistical dependency or independency should not be confused with the correlation: in the first case any type of relationship relates the events, in the latter linear dependency is required.
2.1.5 Probability distribution of random variables
Mathematical formulations and empirical relations can generally model an engineering system. In other words physical relations are modeled by mathematics: e.g. the acceleration is proportional to the force applied to a mass. But if we assume that the force is a random variable, it is defined as an event (i.e. a set of data) and in the same way the acceleration and the mass.
In case we assume to model random phenomena, the evolution of the system can be studied on the basis of the model as a function of basic random variables, which should be able to represent also all types of uncertainties, physical, statistical and modeling ones, that are included in the analysis.
Although many complex methods have been proposed to represent these uncertainties, in most cases it is sufficient to model the quantities by random variables with given standardized distribution functions and distribution parameters estimated on the basis of statistical and/or subjective information.
Quantitatively explaining the above sentence, we can define the probability that a random variable X is
We can also define, if the variable is continuous, the density function:
This is equivalent to say that for each data set, we are able to define the probability of occurrence of each possible sample point (i.e. the outcome of a trial) in the sample space.
According to the previously given definitions, the mean, the standard deviation, and the other indexes can be defined also for a stochastic continuous variable as the first, second, third order moments:
∫ ∫
+∞
−∞
The same theory is applied to random variables defined by an n-dimensional random vector, whose components are random variables. In addition it can be defined the covariance between two
∫ ∫ ∫
+∞
−∞
+∞
−∞
On the basis of the covariance, the sample correlation coefficient is defined:
i j
XiXj XiXj
σ σ
ρ = Eq. 2.
If two random variables are independent, their correlation coefficient is zero and the joint density function is the product of the 1-dimensional density functions. In many cases it is possible to obtain a sufficiently accurate approximation to the n-dimensional distribution function from the 1-dimensional distribution functions of the n variables and their parameters, and the correlation coefficients.
Commonly standard probability model are used in reliability calculations (uniform, beta, normal, extreme values distribution as exponential, Gumbel, Rayleigh, Weibull), defined on the basis of parameters such as mean, variance, etc. Each statistical model is suitable for certain physical variables, e.g. non-negative values, maximum or minimum values, symmetrically distributed values, etc. and it is used to approximate the real outcomes.
2.1.6 Model fitting and estimation
According to the Galileo’s lesson, the experience data are the basis of any calculation model. It should, however, be emphasized that the model should aim for simplicity and at the same time should be close enough to reality to allow for including important data information collected during the lifetime of the considered technical system.
The most commonly used standardized probability models are the uniform distribution, beta distribution, normal distribution, lognormal distribution, and extreme value distributions. Their mathematical details and several examples can be found in many books, e.g. ref. [8], [9], [11], [13], [16].
The beta and uniform distributions are defined for a finite interval of non-zero probability. The normal distribution is used if the stochastic variable is the sum of great number of individual contributions. A lognormal distribution follows if log(X) is normally distributed. As a result a log-normally distributed variable is always non-negative, which makes it appropriate for the modeling of non-negative uncertain variables. The extreme distributions form a complete family for cases when a variable is the maximum or minimum of e.g. a stochastic process over a given time interval or a large number of
