Whipping and Springing Assessment
July 2015
Rule Note
NR 583 DT R01 E
Marine & Offshore Division
92571 Neuilly sur Seine Cedex – France
Tel: + 33 (0)1 55 24 70 00 – Fax: + 33 (0)1 55 24 70 25
Website: http://www.veristar.com
Email: [email protected]
 2015 Bureau Veritas - All rights reserved
MARINE & OFFSHORE DIVISION
GENERAL CONDITIONS
ARTICLE 1
1.1. - BUREAU VERITAS is a Society the purpose of whose Marine & Offshore Division (the "Society") is
the classification (" Classification ") of any ship or vessel or offshore unit or structure of any type or part of
it or system therein collectively hereinafter referred to as a "Unit" whether linked to shore, river bed or sea
bed or not, whether operated or located at sea or in inland waters or partly on land, including submarines,
hovercrafts, drilling rigs, offshore installations of any type and of any purpose, their related and ancillary
equipment, subsea or not, such as well head and pipelines, mooring legs and mooring points or otherwise
as decided by the Society.
The Society:
• "prepares and publishes Rules for classification, Guidance Notes and other documents (" Rules ");
• "issues Certificates, Attestations and Reports following its interventions (" Certificates ");
• "publishes Registers.
1.2. - The Society also participates in the application of National and International Regulations or Standards, in particular by delegation from different Governments. Those activities are hereafter collectively referred to as " Certification ".
1.3. - The Society can also provide services related to Classification and Certification such as ship and
company safety management certification; ship and port security certification, training activities; all activities and duties incidental thereto such as documentation on any supporting means, software, instrumentation, measurements, tests and trials on board.
1.4. - The interventions mentioned in 1.1., 1.2. and 1.3. are referred to as " Services ". The party and/or its
representative requesting the services is hereinafter referred to as the " Client ". The Services are prepared and carried out on the assumption that the Clients are aware of the International Maritime
and/or Offshore Industry (the "Industry") practices.
1.5. - The Society is neither and may not be considered as an Underwriter, Broker in ship's sale or chartering, Expert in Unit's valuation, Consulting Engineer, Controller, Naval Architect, Manufacturer, Shipbuilder, Repair yard, Charterer or Shipowner who are not relieved of any of their expressed or implied
obligations by the interventions of the Society.
ARTICLE 2
2.1. - Classification is the appraisement given by the Society for its Client, at a certain date, following surveys by its Surveyors along the lines specified in Articles 3 and 4 hereafter on the level of compliance of
a Unit to its Rules or part of them. This appraisement is represented by a class entered on the Certificates
and periodically transcribed in the Society's Register.
2.2. - Certification is carried out by the Society along the same lines as set out in Articles 3 and 4 hereafter
and with reference to the applicable National and International Regulations or Standards.
2.3. - It is incumbent upon the Client to maintain the condition of the Unit after surveys, to present
the Unit for surveys and to inform the Society without delay of circumstances which may affect the
given appraisement or cause to modify its scope.
2.4. - The Client is to give to the Society all access and information necessary for the safe and efficient
performance of the requested Services. The Client is the sole responsible for the conditions of presentation of the Unit for tests, trials and surveys and the conditions under which tests and trials are carried out.
ARTICLE 3
3.1. - The Rules, procedures and instructions of the Society take into account at the date of their
preparation the state of currently available and proven technical knowledge of the Industry. They
are a collection of minimum requirements but not a standard or a code of construction neither a
guide for maintenance, a safety handbook or a guide of professional practices, all of which are
assumed to be known in detail and carefully followed at all times by the Client.
Committees consisting of personalities from the Industry contribute to the development of those documents.
3.2. - The Society only is qualified to apply its Rules and to interpret them. Any reference to them
has no effect unless it involves the Society's intervention.
3.3. - The Services of the Society are carried out by professional Surveyors according to the applicable
Rules and to the Code of Ethics of the Society. Surveyors have authority to decide locally on matters related to classification and certification of the Units, unless the Rules provide otherwise.
3.4. - The operations of the Society in providing its Services are exclusively conducted by way of random inspections and do not in any circumstances involve monitoring or exhaustive verification.
ARTICLE 4
4.1. - The Society, acting by reference to its Rules:
• "reviews the construction arrangements of the Units as shown on the documents presented by the Client;
• "conducts surveys at the place of their construction;
• "classes Units and enters their class in its Register;
• "surveys periodically the Units in service to note that the requirements for the maintenance of class are
met.
The Client is to inform the Society without delay of circumstances which may cause the date or the
extent of the surveys to be changed.
ARTICLE 5
5.1. - The Society acts as a provider of services. This cannot be construed as an obligation bearing
on the Society to obtain a result or as a warranty.
5.2. - The certificates issued by the Society pursuant to 5.1. here above are a statement on the level
of compliance of the Unit to its Rules or to the documents of reference for the Services provided for.
In particular, the Society does not engage in any work relating to the design, building, production
or repair checks, neither in the operation of the Units or in their trade, neither in any advisory services, and cannot be held liable on those accounts. Its certificates cannot be construed as an implied or express warranty of safety, fitness for the purpose, seaworthiness of the Unit or of its value
for sale, insurance or chartering.
5.3. - The Society does not declare the acceptance or commissioning of a Unit, nor of its construction in conformity with its design, that being the exclusive responsibility of its owner or builder.
5.4. - The Services of the Society cannot create any obligation bearing on the Society or constitute any
warranty of proper operation, beyond any representation set forth in the Rules, of any Unit, equipment or
machinery, computer software of any sort or other comparable concepts that has been subject to any survey by the Society.
ARTICLE 6
6.1. - The Society accepts no responsibility for the use of information related to its Services which was not
provided for the purpose by the Society or with its assistance.
6.2. - If the Services of the Society or their omission cause to the Client a damage which is proved
to be the direct and reasonably foreseeable consequence of an error or omission of the Society,
its liability towards the Client is limited to ten times the amount of fee paid for the Service having
caused the damage, provided however that this limit shall be subject to a minimum of eight thousand (8,000) Euro, and to a maximum which is the greater of eight hundred thousand (800,000)
Euro and one and a half times the above mentioned fee. These limits apply regardless of fault including breach of contract, breach of warranty, tort, strict liability, breach of statute, etc.
The Society bears no liability for indirect or consequential loss whether arising naturally or not as
a consequence of the Services or their omission such as loss of revenue, loss of profit, loss of production, loss relative to other contracts and indemnities for termination of other agreements.
6.3. - All claims are to be presented to the Society in writing within three months of the date when the Services were supplied or (if later) the date when the events which are relied on of were first known to the Client,
and any claim which is not so presented shall be deemed waived and absolutely barred. Time is to be interrupted thereafter with the same periodicity.
ARTICLE 7
7.1. - Requests for Services are to be in writing.
7.2. - Either the Client or the Society can terminate as of right the requested Services after giving
the other party thirty days' written notice, for convenience, and without prejudice to the provisions
in Article 8 hereunder.
7.3. - The class granted to the concerned Units and the previously issued certificates remain valid until the
date of effect of the notice issued according to 7.2. here above subject to compliance with 2.3. here above
and Article 8 hereunder.
7.4. - The contract for classification and/or certification of a Unit cannot be transferred neither assigned.
ARTICLE 8
8.1. - The Services of the Society, whether completed or not, involve, for the part carried out, the payment
of fee upon receipt of the invoice and the reimbursement of the expenses incurred.
8.2. - Overdue amounts are increased as of right by interest in accordance with the applicable legislation.
8.3. - The class of a Unit may be suspended in the event of non-payment of fee after a first unfruitful
notification to pay.
ARTICLE 9
9.1. - The documents and data provided to or prepared by the Society for its Services, and the information
available to the Society, are treated as confidential. However:
• "Clients have access to the data they have provided to the Society and, during the period of classification of the Unit for them, to the classification file consisting of survey reports and certificates which
have been prepared at any time by the Society for the classification of the Unit ;
• "copy of the documents made available for the classification of the Unit and of available survey reports
can be handed over to another Classification Society, where appropriate, in case of the Unit's transfer
of class;
• "the data relative to the evolution of the Register, to the class suspension and to the survey status of
the Units, as well as general technical information related to hull and equipment damages, may be
passed on to IACS (International Association of Classification Societies) according to the association
working rules;
• "the certificates, documents and information relative to the Units classed with the Society may be
reviewed during certificating bodies audits and are disclosed upon order of the concerned governmental or inter-governmental authorities or of a Court having jurisdiction.
The documents and data are subject to a file management plan.
ARTICLE 10
10.1. - Any delay or shortcoming in the performance of its Services by the Society arising from an event
not reasonably foreseeable by or beyond the control of the Society shall be deemed not to be a breach of
contract.
ARTICLE 11
11.1. - In case of diverging opinions during surveys between the Client and the Society's surveyor, the Society may designate another of its surveyors at the request of the Client.
11.2. - Disagreements of a technical nature between the Client and the Society can be submitted by the
Society to the advice of its Marine Advisory Committee.
ARTICLE 12
12.1. - Disputes over the Services carried out by delegation of Governments are assessed within the
framework of the applicable agreements with the States, international Conventions and national rules.
12.2. - Disputes arising out of the payment of the Society's invoices by the Client are submitted to the Court
of Nanterre, France, or to another Court as deemed fit by the Society.
12.3. - Other disputes over the present General Conditions or over the Services of the Society are
exclusively submitted to arbitration, by three arbitrators, in London according to the Arbitration
Act 1996 or any statutory modification or re-enactment thereof. The contract between the Society
and the Client shall be governed by English law.
ARTICLE 13
13.1. - These General Conditions constitute the sole contractual obligations binding together the
Society and the Client, to the exclusion of all other representation, statements, terms, conditions
whether express or implied. They may be varied in writing by mutual agreement. They are not varied by any purchase order or other document of the Client serving similar purpose.
13.2. - The invalidity of one or more stipulations of the present General Conditions does not affect the validity of the remaining provisions.
13.3. - The definitions herein take precedence over any definitions serving the same purpose which may
appear in other documents issued by the Society.
BV Mod. Ad. ME 545 L - 7 January 2013
RULE NOTE NR 583
NR 583
Whipping and Springing Assessment
SECTION 1
WHIPPING AND SPRINGING ASSESSMENT
APPENDIX 1
METHODOLOGY FOR LONG TERM DIRECT HYDRO-STRUCTURE
CALCULATIONS INCLUDING WHIPPING AND SPRINGING
RESPONSE
July 2015
Section 1
Whipping and Springing Assessment
1
Application
1.1
1.2
1.3
1.4
1.5
2
Container ships
Other types of ships
Additional loading conditions
6
General
Ship operational profile
Computation of extreme vertical bending moment
Criteria
Linear spectral fatigue assessment
4.1
4.2
4.3
4.4
5
6
Ultimate strength assessment
3.1
3.2
3.3
3.4
4
General
Additional service feature WhiSp
Additional class notation WhiSp
Scope
Documentation to be submitted
Loading conditions
2.1
2.2
2.3
3
5
8
General
Ship operational profile
Fatigue computation
Criteria
Non-linear fatigue assessment
5.1
5.2
5.3
5.4
9
General
Ship operational profile
Fatigue computation
Criteria
Appendix 1 Methodology for Long Term Direct Hydro-Structure Calculations
including Whipping and Springing Response
1
General
1.1
2
10
Wave environment
Ship hydro-structural model
3.1
3.2
3.3
3.4
3.5
3.6
3.7
2
Introduction
Operating conditions
2.1
3
10
12
General
Finite elements modeling
Hydrodynamic loads
Structural ship response
General modeling considerations
Type of simulations
Statistical analysis of ship response in an irregular sea state
Bureau Veritas
July 2015
4
Extreme response and Fatigue damage computation
4.1
4.2
5
July 2015
Extreme response
Fatigue damage
Long term analysis methods
5.1
5.2
5.3
5.4
25
28
General
Fully long-term analysis
Design Sea States Approach
Single Design Sea State
Bureau Veritas
3
4
Bureau Veritas
July 2015
NR 583, Sec 1
SECTION 1
1
WHIPPING AND SPRINGING ASSESSMENT
Application
1.1
General
1.1.1 The requirements of the present Rule Note apply to analysis criteria, structural modeling, load modeling and stress and
fatigue calculation of ships intended to be granted the additional service feature or additional class notation WhiSp, as defined
in NR467 Rules for Steel ships, Part A, Ch 1 Sec 2.
1.1.2 This Rule Note deals with the part of structural analysis which aims at performing ultimate strength and fatigue assessment based on direct hydro-structure calculations including Whipping and Springing response.
1.1.3 The additional class notation or additional service feature WhiSp is completed by 1, 2 or 3 depending on the level of
assessment, as defined in [1.4].
1.1.4 The additional class notations or additional service features WhiSp1, WhiSp2 and WhiSp3 are assigned at the design
stage.
1.2
Additional service feature WhiSp
1.2.1 An additional service feature WhiSp1, WhiSp2 or WhiSp3 may only be assigned to ships granted with the service notation container ship as defined in NR467 Rules for Steel Ships, Part A, Ch 1 Sec 2.
1.2.2 The additional service feature WhiSp1 is to be assigned to container ships of more than 300 m in length between perpendiculars and up to 350 m, for which the requirements of this Rule Note are to be applied. WhiSp2 or WhiSp3 may be assigned
instead of WhiSp1 upon request.
1.2.3 The additional service feature WhiSp2 is to be assigned to container ships of 350 m in length between perpendiculars and
above, for which the requirements of this Rule Note are to be applied. WhiSp3 may be assigned instead of WhiSp2 upon
request.
1.3
Additional class notation WhiSp
1.3.1 The additional class notations WhiSp1, WhiSp2 or WhiSp3 may be assigned to ships, other than those subject to [1.2],
complying with the requirements of this Rule Note.
1.4
Scope
1.4.1 Additional class notation or additional service feature WhiSp1
WhiSp1 notation covers the effect of linear springing in the fatigue damage assessment, but whipping is not considered neither
for fatigue nor for ultimate strength. This notation corresponds to the following calculation steps:
• Linear spectral fatigue assessment defined in [4].
1.4.2 Additional class notation or additional service feature WhiSp2
WhiSp2 notation corresponds to WhiSp1 notation with additional whipping computation for ultimate strength assessment. This
notation corresponds to the following calculation steps:
• Ultimate strength assessment defined in [3]
• Linear spectral fatigue assessment defined in [4].
1.4.3 Additional class notation or additional service feature WhiSp3
WhiSp3 notation corresponds to WhiSp2 notation with additional whipping computation for fatigue assessment. This notation
corresponds to the following calculation steps:
• Ultimate strength assessment defined in [3]
• Linear spectral fatigue assessment defined in [4]
• Non-linear fatigue assessment defined in [5].
July 2015
Bureau Veritas
5
NR 583, Sec 1
1.5
Documentation to be submitted
1.5.1 The following data is to be submitted by the Designer:
• The necessary loading conditions as required in [2]
• A provisional lightship distribution
• A list of structural details which will be considered for fatigue calculations. This list is to be agreed on by the Society
• A complete ship finite element model, as described in App 1, [3.2.1]
• Local very fine mesh models for all considered structural details, as described in App 1, [3.2.2].
2
2.1
Loading conditions
Container ships
2.1.1 Ultimate strength assessment
Extreme response analysis is to be carried out for a single loading condition, selected so as to maximise the still water bending
moment in hogging.
2.1.2 Fatigue assessment
Fatigue analysis is to be carried out for a single loading condition, selected so as to maximise the still water bending moment in
hogging.
2.2
Other types of ships
2.2.1 Ultimate strength assessment
Extreme response analysis is to be carried out for the following loading conditions:
• A full load condition, selected so as to maximise the still water bending moment in hogging or in sagging, as relevant
• A representative ballast condition.
2.2.2 Fatigue assessment
Fatigue analysis is to be carried out for the following loading conditions:
• A representative full load condition, selected in hogging or sagging, as relevant
• A representative ballast condition.
2.3
Additional loading conditions
2.3.1 Additional loading conditions may be considered for these calculations on a case-by-case basis, if deemed relevant by
the Society.
3
3.1
Ultimate strength assessment
General
3.1.1 Ultimate strength is checked as shown in Tab 1, using a fully non-linear dynamic structural response including whipping
and springing effects.
Table 1 : Ultimate strength assessment
Hydrodynamic loads
Structural response
Quasi-static
Linear
Weakly non-linear
X
(X)
Dynamic
Slamming
X
Note 1: Optional calculations steps are displayed within brackets.
3.2
Ship operational profile
3.2.1 Operating conditions
The vessels are designed for unrestricted navigation. The wave scatter diagram for North Atlantic from IACS Recommendation
No. 34 is to be used. This scatter diagram is given in App 1, Tab 1.
The sea states are to be modeled by a Pierson-Moskowitz spectrum and a “cos n” spreading function with n = 2, as defined in
App 1, [2.1.2].
6
Bureau Veritas
July 2015
NR 583, Sec 1
3.2.2
Loading conditions
The extreme response analysis is to be carried out for the loading conditions defined in [2], depending on the ship type and on
the way she is operated. Additional loading conditions may be contemplated on a case-by-case basis.
3.2.3
Wave heading
Wave headings are considered uniformly distributed from 0° to 360°.
A different distribution may be used if accurate information is available. The probability of each wave heading (relative angle
between the ship route and the wave direction) is then to be defined before runing the computations.
3.2.4
Speed profile
The ship speed is to be taken as 5 knots in all sea states.
Different speed profiles may be used if accurate information is available. They may be based on full-scale measurement data.
The speed dependance on the sea states is then to be defined before runing the computations.
3.3
Computation of extreme vertical bending moment
3.3.1
Linear extreme bending moment
A list of longitudinal locations where the vertical bending moment will be computed is to be defined. This list of cross-sections
is to include at least a calculation point in each hold, plus any additional locations deemed necessary.
The vertical bending moment RAO at each cross-section is to be computed using the linear hydrodynamic loads defined in App 1,
[3.3.1]. A linear long-term analysis is performed and the extreme value corresponding to a return period of 25 years is computed
with a probability of exceedance α = 0,63 (see App 1, [5.2.2]).
Note 1: Vertical bending moment means total vertical bending moment, i.e. it includes the still water bending moment and the wave bending
moment.
3.3.2
Weakly non-linear loads
This calculation step is optional but can be useful to separate the non-linear effects induced by wave non-linearities and those
induced by pure whipping.
The extreme vertical bending moment, corresponding to a return period of 25 years with a probability of exceedance α = 0,63,
is computed at each cross-section, using a Design Sea State approach (see App 1, [5.3]) together with a weakly non-linear time
domain hydro-structure model (see App 1, [3.3.2]). The Design Sea State is based on the most contributive sea state to the linear
extreme vertical bending moment amidships computed in [3.3.1].
3.3.3
Whipping simulations
The extreme vertical bending moment, corresponding to a return period of 25 years with a probability of exceedance α = 0,63,
is computed at each cross-section, using a Design Sea State approach (see App 1, [5.3]) together with a non-linear time domain
hydro-structure model including slamming forces (see App 1, [3.3.3]). The Design Sea State is based on the most contributive
sea state to the linear extreme vertical bending moment amidships computed in [3.3.1].
3.4
Criteria
3.4.1 It is to be checked that the hull girder ultimate bending capacity at any cross-section is in compliance with the following
formula:
MU
-------- ≥ M
γR
where:
MU
: Ultimate bending capacity of the hull transverse section defined in NR467, Pt B, Ch 6, Sec 3, with the difference
that strength characteristics of the cross-section are obtained considering half of the corrosion additions defined in
NR467, Pt B, Ch 4, Sec 2, [2]
M
: Extreme vertical bending moment computed in [3.3.3]
γR
: Partial safety factor taken equal to 1,1.
July 2015
Bureau Veritas
7
NR 583, Sec 1
4
Linear spectral fatigue assessment
4.1
General
4.1.1 The linear fatigue assessment is computed as shown in Tab 2, with and without springing. The difference between the two
computed fatigue damages represents the effect of linear springing on fatigue damage.
Table 2 : Linear fatigue assessment
Hydrodynamic loads
Linear
Structural response
4.2
4.2.1
Quasi-static
X
Dynamic
X
Weakly non-linear
Slamming
Ship operational profile
Operating conditions
The scatter diagram to be used is the worldwide scatter diagram, as defined in App 1, Tab 3. Other scatter diagrams could be
considered on a case-by-case basis, if a ship is designed for a specific area.
The sea states are to be modeled by a Pierson-Moskowitz spectrum and a “cos n” spreading function with n = 2, as defined in
App 1, [2.1.2].
4.2.2
Loading conditions
The fatigue analysis is to be carried out for the loading conditions defined in [2], depending on the ship type and on the way
she is operated. Additional loading conditions which could significantly contribute to the fatigue damage may be contemplated
on a case-by-case basis.
4.2.3
Wave heading
Wave headings are considered uniformly distributed from 0° to 360°.
A different distribution may be used if accurate information is available. The probability of each wave heading (relative angle
between the ship route and the wave direction) is then to be defined before runing the computations.
4.2.4
Speed profile
The ship speed is to be taken as 60% of the ship design speed in all sea states.
Different speed profiles may be used if accurate information is available. They may be based on full-scale measurement data.
The speed dependance on the sea states is then to be defined before runing the computations.
4.3
4.3.1
Fatigue computation
Linear quasi-static fatigue damage
The linear quasi-static stress RAO is computed for each structural detail (defined in [1.5]) according to App 1, [3.3.1] and App 1,
[3.4.1]. The linear fatigue damage and the corresponding fatigue life are then derived using sea state statistics from the considered scatter diagram and the appropriate S-N curve (see App 1, [4.2.2]). The damage shall be computed for a return period of
20 years, or xx years when the additional class notation VeriSTAR-HULL DFL xx years is assigned.
4.3.2
Linear dynamic fatigue damage
The linear stress RAO including dynamic structural response is computed for each structural detail (defined in [1.5]) according
to App 1, [3.3.1] App 1, [3.4.2]. The fatigue damage and the corresponding fatigue life are then derived using sea state statistics
from the considered scatter diagram and the appropriate S-N curve. The damage shall be computed for a return period of
20 years, or xx years when the additional class notation VeriSTAR-HULL DFL xx years is assigned.
8
Bureau Veritas
July 2015
NR 583, Sec 1
4.3.3 Impact of whipping on damage
For ships above 300m in length, the linear damage is to be corrected using the following partial safety factor:
L
α whip = ---------- – 0, 2
250
not to be taken more than 28/TFL where:
TFL
: Design fatigue life, in years, taken equal to:
• TFL = 20, when the additional class notation VeriSTAR-HULL DFL xx years is not assigned
• TFL = xx, when the additional class notation VeriSTAR-HULL DFL xx years is assigned. Special consideration is
to be given when xx is equal to or more than 30 years.
For ships to which the class notation WhiSp3 is assigned, αwhip is to be taken equal to 1.
4.4
Criteria
4.4.1 Linear quasi-static fatigue life
A minimum of 20 years fatigue life is to be achieved for each of the considered details.
When the additional class notation VeriSTAR-HULL DFL xx years is assigned, the fatigue life for each of the considered details
is to reach a minimum of xx years.
4.4.2 Linear dynamic fatigue life
A minimum of 20 years fatigue life is to be achieved for each of the considered details.
When the additional class notation VeriSTAR-HULL DFL xx years is assigned, the fatigue life for each of the considered details
is to reach a minimum of xx years.
5
Non-linear fatigue assessment
5.1
General
5.1.1 The non-linear fatigue assessment includes the whipping contribution to the fatigue damage, as shown in Tab 3.
Table 3 : Non-linear fatigue assessment
Hydrodynamic loads
Linear
Structural response
Quasi-static
(X)
Dynamic
(X)
Weakly non-linear
Slamming
X
Note 1: Intermediate calculations steps are displayed within brackets.
5.2
Ship operational profile
5.2.1 Operating conditions, loading conditions, wave headings and speed profile are to be the same as for a linear fatigue
assessment (refer to [4.2]).
5.3
Fatigue computation
5.3.1 Design Sea States and headings definition
A linear fatigue damage computation, including springing, is to be achieved as a first step (see [4.3]). Design Sea States and
headings are then chosen among those showing the highest contribution to the linear dynamic fatigue damage. A set of Design
Sea States is defined for each structural detail.
5.3.2 Whipping simulations
The fatigue damage and the corresponding fatigue life including whipping effects are derived for each structural detail using a
Design Sea States approach (see App 1, [5.3]) used in conjunction with a non-linear time domain hydro-structure model including slamming forces (see App 1, [3.3.3]).
5.4
Criteria
5.4.1 The fatigue life for each of the considered details is to reach a minimum of 20 years.
July 2015
Bureau Veritas
9
NR 583, App 1
APPENDIX 1
1
1.1
METHODOLOGY FOR LONG TERM DIRECT
HYDRO-STRUCTURE CALCULATIONS INCLUDING
WHIPPING AND SPRINGING RESPONSE
General
Introduction
1.1.1 The present Appendix describes the various methods and tools to be used for the direct calculation of the hydro-structural
response of ships, including whipping and springing response.
1.1.2 The following tools and methods are needed to determine the extreme stress or the total fatigue damage corresponding to
the ship life:
• A description of the operating conditions during all the ship life, including the wave environment and the ship operational
profile (see [2])
• A hydro-structure model of the ship, which is able to compute the ship response on any type of wave conditions, including
hydroelastic effects (see [3])
• Methods to derive extreme responses and the fatigue damage from the results of the previous computations (see [4])
• A long-term analysis methodology that is able to define the optimal number of computations to be run, in order to derive the
extreme response and the total fatigue damage. (see [5]).
1.1.3 There is not a single methodology to compute the extreme response and the total fatigue damage. This appendix presents
a list of methods and tools. Depending on what is to be simulated, a given long-term methodology is to be used in conjunction
with a specific hydro-structure model.
2
2.1
Operating conditions
Wave environment
2.1.1 Wave scatter diagram
A wave scatter diagram is a description of the joint probabilities of wave heights and wave periods. This description is made for
a given geographical area. Usually there is no information about the direction of the waves. The scatter diagrams are usually
based on visual observations and hindcast data, which are merged and extrapolated using some analytical functions. The Global Wave Statistics atlas gives some scatter diagrams for 104 areas in the world, including some seasonal and directional information (see Fig 1).
Figure 1 : Global Wave Statistics areas
10
Bureau Veritas
July 2015
NR 583, App 1
a) IACS scatter diagram
The IACS scatter diagram has been defined from the winter data of areas 8, 9, 15 and 16 (North Atlantic). This scatter diagram
is the basis of many standard long term analysis since the North Atlantic is the worst area in the World (considering wave
heights). The IACS scatter is given in Tab 1 and Tab 2, and defined according to the following probability density function:
β–1
H s – γ β
( ln ( T z – μ ) )
β H s – γ-
1 - -------------------exp  –  ------------exp  – ------------------------------p IACS ( H s ,T z ) = ---  ------------2






α α
α   T Z σ 2π
2σ
2
where:
α = 3,041
β = 1,484
γ = 0,660
μ = 0,7 + 1,27 Hs0,131
σ = 0,1334 + 0,0264 exp (− 0,1906 Hs)
Hs
Tz
: Significant wave height (m)
: Save up-crossing period (s).
b) Worldwide scatter diagram
The worldwide scatter diagram is representative of wave conditions around a worldwide trip. It is given in Tab 3 and Tab 4,
and defined according to the following probability density function:
β H s – γ
p W ( H s ,T z ) = ---  ------------α α 
β–1
H s – γ β
( ln ( T z – μ ) )
1
- --------------------- exp  – ------------------------------exp  –  ------------2


  α   T σ 2π
2σ
z
2
where:
α = 1,807
β = 1,217
γ = 0,83
μ = − 1,01 + 2,847 Hs0,075
σ = 0,161 + 0,146 exp (− 0,683 Hs).
2.1.2 Wave spectrum
A short term sea state is described by a wave spectrum, which is the power spectral density function of the vertical sea surface
displacement. Wave spectra are often given in the form of a parameterised analytical formula.
a) Pierson-Moskowitz spectrum
The Pierson-Moskowitz spectrum is frequently applied for wind seas. It was originally proposed for fully-developed sea. It
describes wind sea conditions that often occur for the most severe sea states. The Pierson-Moskowitz spectrum is given by:
4
2
ω 4
5ω p H s
- exp  – 1, 25  ------p 
S ( ω ) = ---------------5


ω 
16ω
where:
ω
: Wave angular frequency (rad/s)
ωp
: Peak angular frequency (rad/s)
2π
2π
ω p = ------- = ---------------------Tp
1, 408T z
Tp
Hs
: Peak period (s)
: Significant wave height (m).
b) The JONSWAP spectrum is formulated as a modification of the Pierson-Moskowitz spectrum for a developing sea state in a
fetch limited situation. It includes a peak-enhancement factor, the effect of which is to increase the peak of the PiersonMoskovitz spectrum. The JONSWAP spectrum is given by:
2
4
2
ω 4
5ω p H s
- exp  – 1, 25  ------p  γ
S ( ω ) = A ---------------5


ω 
16ω
 –( ω – ωp ) 
exp  ----------------------------
 2σ 2 ω 2p 
where:
γ
: Peak enhancement factor. For γ = 1 the JONSWAP spectrum reduces to a Pierson-Moskowitz spectrum
σ
: Relative measure of the width of the peak. In most cases, σ = 0,07 for ω < ωp and σ = 0,09 for ω > ωp
A
: Normalizing factor:
1
A = ------------------------------------------------------------------0, 803
5 ⋅ ( 0, 065 ⋅ γ
+ 0, 135 )
July 2015
Bureau Veritas
11
NR 583, App 1
c) Ochi-Hubble spectrum
Combined wind sea and swell may be described by a double peak frequency spectrum, i.e. where wind sea and swell are
assumed to be uncorrelated. The Ochi-Hubble spectrum is a general spectrum formulated to describe bimodal sea states.
The spectrum is a sum of two Gamma distributions, each with 3 parameters for each wave system.
2
1
S ( ω ) = --4

i=1
4
λi
H si
1 ω p, i 
 ω4  λ + 1
---  ---------------------------- exp  –  λ i + ---  -------4λ i + 1
 p, i  i 4 
 ω  
 
4
Γ ( λ i )ω
2
where:
ωp,i
: Peak angular frequency (rad/s) of the component i
Hsi
: Significant wave height (m) of component i
λi
: Spectral shape parameter of the component i.
Directional short-crested wave spectra may be expressed in terms of the uni-directional wave spectra multiplied by a spreading
function:
S ( ω ,β ) = S ( ω )G ( β )
For a two-peak spectrum expressed as a sum of a swell component and a wind-sea component, each component may have its
own spreading function.
2.1.3
Spreading function
a) “Cos n” formulation
A common directional spreading function often used is:
Γ(n ⁄ 2 + 1)
π
n
G ( β ) = ------------------------------------------------ cos ( β – β 0 ) ………  β – β 0 ≤ ---

2
π ⋅ Γ(n ⁄ 2 + 1 ⁄ 2)
π
G ( β ) = 0………  β – β 0 > ---

2
where:
β
: Wave heading (deg)
β0
: Main wave heading (deg).
b) “Cos 2s” formulation
An alternative formulation is:
β – β 2s
Γ(s + 1)
G ( β ) = -------------------------------------------- cos  --------------0

2 
2 π ⋅ Γ(s + 1 ⁄ 2)
where:
β
: Wave heading (deg)
β0
: Main wave heading (deg).
3
3.1
Ship hydro-structural model
General
3.1.1 A good evaluation of the structural response of a ship in waves needs a proper coupling between a hydrodynamic model,
which describes the hydrodynamic interaction between the ship and the waves, and a structural model, which describes the
structural response to wave loads and inertia loads. Several levels of assumptions can be chosen for the hydrodynamic model
and the structural model, depending on which physical behavior is expected to be reproduced.
The ship structural response can be considered as:
• Quasi-static, which means that the structural response is strictly proportional to the applied loads. This model is described in
[3.4.1]
• Dynamic, if dynamic amplification occurs. This model is described in [3.4.2].
Three types of hydrodynamic loads may be considered to be applied to the ship:
• Linear loads (valid only for the smallest sea states), described in [3.3.1]
• Weakly non-linear loads (Froude-Krylov forces), described in [3.3.2]
• Slamming loads, described in [3.3.3].
12
Bureau Veritas
July 2015
July 2015
Bureau Veritas
Significant wave height (m)
0,000
0,000
0,000
0,000
0,000
0,000
0,001
0,032
1,303
8,5
7,5
6,5
5,5
4,5
3,5
2,5
1,5
0,5
1,336
0,000
9,5
TOTAL
0,000
0,000
14,5
10,5
0,000
15,5
0,000
0,000
16,5
11,5
0,000
17,5
0,000
0,000
18,5
0,000
0,000
19,5
12,5
0,000
20,5
13,5
0,000
21,5
3,5
2,156
0,174
0,015
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
165,422
133,765
29,310
4,5
5,953
0,999
0,167
0,028
0,005
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
2091,378
865,828
986,006
197,452
34,939
5,5
2,972
0,682
0,152
0,033
0,007
0,002
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
9280,164
1186,377
4975,934
2158,778
695,509
196,120
51,029
12,567
6,5
4,321
1,167
0,304
0,077
0,019
0,005
0,001
0,000
0,000
0,000
0,000
0,000
0,000
19921,761
634,434
7737,889
6229,957
3226,434
1354,283
498,354
167,023
52,127
15,367
7,5
3,271
0,959
0,270
0,073
0,019
0,005
0,001
0,000
0,000
0,000
0,000
24878,411
186,350
5569,612
7449,408
5674,915
3288,418
1602,922
690,240
270,144
97,874
33,245
10,684
8,5
Up-crossing period Tz
(continued in Tab 2)
4,432
1,407
0,428
0,125
0,035
0,010
0,003
0,001
0,000
0,000
20869,761
36,904
2375,647
4860,305
5099,065
3857,421
2372,647
1257,839
594,437
255,920
101,894
37,931
13,311
9,5
Table 1 : Wave scatter diagram for North Atlantic (IACS Recommendation 34)
12898,093
5,609
703,447
2065,929
2837,967
2685,481
2008,287
1268,549
703,177
350,546
159,849
67,504
26,648
9,906
3,488
1,169
0,374
0,115
0,034
0,010
0,003
0,001
0,000
10,5
6244,657
0,713
160,720
644,450
1114,071
1275,135
1126,030
825,936
524,871
296,856
152,221
71,730
31,381
12,849
4,955
1,809
0,628
0,208
0,066
0,020
0,006
0,002
0,000
11,5
2478,967
0,080
30,476
160,244
337,682
455,085
463,567
386,772
276,649
174,620
99,212
51,475
24,657
10,998
4,599
1,814
0,677
0,241
0,082
0,026
0,008
0,002
0,001
12,5
NR 583, App 1
13
14
Bureau Veritas
Significant wave height (m)
77,615
111,676
140,814
150,896
130,895
84,320
33,689
5,050
0,008
8,5
7,5
6,5
5,5
4,5
3,5
2,5
1,5
0,5
836,671
48,270
9,5
TOTAL
27,274
1,296
14,5
10,5
0,517
15,5
14,162
0,196
16,5
11,5
0,070
17,5
6,819
0,024
18,5
12,5
0,008
19,5
3,067
0,003
20,5
13,5
0,001
21,5
13,5
247,279
0,001
0,759
6,251
18,188
31,937
41,013
42,213
36,659
27,741
18,696
11,399
6,363
3,282
1,576
0,709
0,300
0,120
0,046
0,017
0,006
0,002
0,001
14,5
65,569
0,000
0,106
1,057
3,511
6,868
9,696
10,879
10,238
8,356
6,051
3,950
2,354
1,292
0,659
0,314
0,140
0,059
0,024
0,009
0,003
0,001
0,000
15,5
15,912
0,000
0,014
0,167
0,623
1,340
2,057
2,491
2,518
2,199
1,698
1,179
0,746
0,433
0,233
0,117
0,055
0,024
0,010
0,004
0,002
0,001
0,000
16,5
3,593
0,000
0,002
0,025
0,104
0,243
0,401
0,520
0,560
0,520
0,426
0,313
0,209
0,128
0,072
0,038
0,019
0,009
0,004
0,002
0,001
0,000
0,000
17,5
Up-crossing period Tz
(continued from Tab 1)
0,765
0,000
0,000
0,004
0,016
0,042
0,073
0,101
0,115
0,113
0,097
0,075
0,053
0,034
0,020
0,011
0,006
0,003
0,001
0,001
0,000
0,000
0,000
18,5
0,155
0,000
0,000
0,001
0,003
0,007
0,013
0,018
0,022
0,023
0,021
0,017
0,012
0,008
0,005
0,003
0,002
0,001
0,000
0,000
0,000
0,000
0,000
19,5
Table 2 : Wave scatter diagram for North Atlantic (IACS Recommendation 34)
0,030
0,000
0,000
0,000
0,000
0,001
0,002
0,003
0,004
0,004
0,004
0,004
0,003
0,002
0,001
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
20,5
0,006
0,000
0,000
0,000
0,000
0,000
0,000
0,001
0,001
0,001
0,001
0,001
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
21,5
100000,000
3051,421
22575,031
23809,869
19127,519
13289,246
8327,989
4806,133
2586,198
1308,440
626,158
284,736
123,482
51,221
20,373
7,786
2,865
1,016
0,348
0,115
0,037
0,011
0,003
TOTAL
NR 583, App 1
July 2015
July 2015
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,012
2,443
2,455
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
TOTAL
Significant wave height (m)
19
2,5
Bureau Veritas
0,311
0,007
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
330,660
310,529
19,813
3,5
4,269
0,383
0,042
0,005
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
3560,574
2734,624
764,174
57,076
4,5
4,242
0,771
0,146
0,029
0,006
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
11938,407
6403,577
4453,034
902,149
149,832
24,620
5,5
3,650
0,875
0,209
0,050
0,012
0,003
0,001
0,000
0,000
0,000
0,000
0,000
20796,550
7134,616
8840,681
3473,100
1007,271
257,824
63,057
15,201
6,5
6,982
1,944
0,532
0,144
0,038
0,010
0,003
0,001
0,000
0,000
0,000
23322,743
5072,812
9044,627
5547,994
2401,638
860,002
277,308
84,142
24,567
7,5
Up-crossing period Tz
(continued in Tab 4)
Table 3 : Worldwide scatter diagram
7,148
2,203
0,662
0,195
0,056
0,016
0,004
0,001
0,000
0,000
18764,858
2711,523
6019,232
4972,291
2882,476
1339,259
540,215
198,582
68,468
22,526
8,5
4,690
1,553
0,500
0,157
0,048
0,015
0,004
0,001
0,000
11611,104
1201,987
2999,974
3003,977
2156,785
1230,602
597,239
258,460
102,915
38,489
13,706
9,5
5828,231
470,151
1225,020
1376,350
1154,775
776,238
439,962
219,219
99,068
41,516
16,387
6,160
2,223
0,775
0,262
0,086
0,028
0,009
0,003
0,001
10,5
2478,873
169,019
435,063
517,480
485,360
372,218
240,687
135,663
68,612
31,846
13,794
5,646
2,203
0,826
0,299
0,105
0,036
0,012
0,004
0,001
11,5
NR 583, App 1
15
16
170,784
168,604
140,007
57,413
925,795
4
3
2
1
TOTAL
8,904
10
145,678
3,939
11
5
1,651
12
105,474
0,661
13
6
0,255
14
66,295
0,095
15
37,095
0,034
16
7
0,012
17
8
0,004
18
18,888
Significant wave height (m)
9
0,001
19
12,5
Bureau Veritas
312,524
18,786
42,023
49,485
52,673
48,965
39,093
27,078
16,604
9,200
4,688
2,227
0,997
0,425
0,173
0,068
0,068
0,009x
0,003
0,001
13,5
97,609
6,003
12,011
13,456
14,724
14,671
12,754
9,639
6,425
3,848
2,107
1,069
0,509
0,229
0,099
0,041
0,016
0,006
0,002
0,001
14,5
28,741
1,891
3,320
3,461
3,825
4,029
3,773
3,086
2,221
1,429
0,836
0,451
0,228
0,108
0,049
0,021
0,009
0,003
0,001
0,001
15,5
8,101
0,592
0,897
0,855
0,941
1,035
1,036
0,910
0,703
0,483
0,301
0,172
0,092
0,046
0,022
0,010
0,004
0,002
0,001
0,000
16,5
2,213
0,185
0,239
0,205
0,222
0,253
0,268
0,252
0,208
0,152
0,100
0,061
0,034
0,018
0,009
0,004
0,002
0,001
0,000
0,000
17,5
Up-crossing period Tz
(continued from Tab 3)
0,592
0,058
0,063
0,048
0,051
0,060
0,067
0,066
0,058
0,045
0,031
0,020
0,012
0,006
0,003
0,002
0,001
0,000
0,000
0,000
18,5
Table 4 : Worldwive scatter diagram
0,156
0,018
0,017
0,011
0,011
0,014
0,016
0,017
0,016
0,013
0,009
0,006
0,004
0,002
0,001
0,001
0,000
0,000
0,000
0,000
19,5
0,041
0,006
0,004
0,003
0,003
0,003
0,004
0,004
0,004
0,003
0,003
0,002
0,001
0,001
0,000
0,000
0,000
0,000
0,000
0,000
20,5
0,011
0,002
0,001
0,001
0,001
0,001
0,001
0,001
0,001
0,001
0,001
0,001
0,000
0,000
0,000
0,000
0,000
0,000
0,000
0,000
21,5
100010,000
26296,314
34000,219
20086,851
10485,649
5075,854
2325,236
1019,392
430,761
176,326
70,174
27,230
10,326
3,833
1,395
0,499
0,175
0,061
0,021
0,007
TOTAL
NR 583, App 1
July 2015
NR 583, App 1
3.2
3.2.1
Finite elements modeling
Complete ship model - Coarse mesh
The structural model is to represent the entire ship primary supporting members together with the attached plating. Fig 2 depicts
an example of a complete ship model. Ordinary stiffeners are also to be represented in the model in order to reproduce the stiffness and the inertia of the actual hull girder structure. All the elements are to be modeled with their net scantlings according to
the Rules for Steel Ships, Pt B, Ch 4, Sec 2. Therefore, the hull girder stiffness and inertia to be reproduced by the model are
those obtained by considering the net scantlings of the hull structure.
The complete ship is to be modeled so that the coupling between torsion, horizontal and vertical bending is properly taken into
account in the structural analysis.
The following requirements are to be satisfied:
• shell elements are to be used for the plating and web of primary supporting members (membrane elements are not to be
used)
• the plating between two primary supporting members may be modeled using only one element strip
• webs of primary supporting members may be modeled using only one plate element on their height
• face plates of primary supporting members are to be modeled using either shell elements or bar/beam elements with the
same cross-section
• ordinary stiffeners are to be modeled using bar/beam elements; they can be either modeled individually or grouped in
lumped stiffeners, depending on the model refinement
• openings and cut-outs for the passage of ordinary stiffeners or small pipes are to be disregarded
• manholes and similar openings in the web of primary supporting members may be disregarded; in such a case, the element
thickness is to be reduced by the ratio of the opening height by the web height.
Note 1: bar or beam elements are 2D elements including bending stiffness properties. Rod elements are not provided with any bending capacity and are therefore not to be used.
The finite element model is to include both the lightweight and the deadweight mass and inertia distributions.
The lightweight can be adjusted using one of the following techniques:
• modification of the density properties of plate and beam elements
• additional nodal masses fitted on the structural model.
An example of lightship adjustment using the first technique is shown in Fig 3.
Massive items (main engine, hatch covers) should preferably be excluded of the lightweight distribution and modeled similarly
to deadweight items.
Deadweight items (such as container stacks or liquids) are to be modeled as nodal masses linked to the model through additional elements designed in order to transfer loads without introducing artificial stiffness (interpolation elements). An example is
shown in Fig 4. Nodal masses are also to include the inertia properties of the items they represent.
Figure 2 : Example of a complete ship model
July 2015
Bureau Veritas
17
NR 583, App 1
Figure 3 : Example of lightship adjustment
Figure 4 : Example of deadweight modeling
3.2.2 Local detail models - Fine mesh and very fine mesh
When needed, fine mesh and very fine mesh models are to be built in accordance with the Rules for Steel Ships, Pt B, Ch 7, App 1
[3.4.3] (fine mesh) and [3.4.4] (very fine mesh). Typical locations for fatigue very fine mesh on a containership are shown in Fig 5,
and an example of very fine mesh is shown in Fig 6.
Fine meshes of primary supporting members are used for yielding check, very fine meshes of local details are used for fatigue
check.
In case of top-down modeling, prescribed displacements or prescribed loads, obtained from the global coarse mesh model, are
to be used at the boundaries of the local models.
Figure 5 : Typical locations of fatigue very fine mesh
18
Bureau Veritas
July 2015
NR 583, App 1
Figure 6 : Very fine mesh of structural detail
3.3
Hydrodynamic loads
3.3.1 Linear
The linear part of the hydrodynamic loading is calculated by a validated numerical seakeeping code. The use of codes based on
the Boundary Element Method (BEM) is recommended. A typical hydrodynamic mesh for hydrodynamic calculation is shown in
Fig 7. In the case of linear calculations the mesh contains the mean underwater part only. The mesh size is to be chosen so that
the minimal wave length (defined on the basis of encounter frequency) is covered by at least 6 panels. Alternatively, a special
treatment of the high frequency calculations can be used in order to avoid the numerical inaccuracies inherent to the BEM
method. In any case, the problem of irregular frequencies is to be properly solved.
The hydrodynamic problem is solved for every degree of freedom: at least the 6 rigid body motions and the first natural elastic
modes if a dynamic structural response is considered. The equation of motion is then solved in the frequency domain for all the
generalized motions (rigid body modes and elastic modes).
The outputs of a linear hydro-structure computation are the Response Amplitude Operators (RAO). Ship motions RAOs and
internal hull girder loads RAOs are directly computed by the seakeeping software (the internal loads are calculated simply by
integration of the external intertia and pressure loads between the ship end and the considered section). Stress RAOs are computed from the structural analysis.
RAOs are to be computed for:
• at least 36 headings (10° step)
• frequencies in the range [0:2] rad/s
• a frequency step of 0,3(g/L)0,5
where:
g = 9,81 m/s2
L
: Length between perpendiculars.
Figure 7 : Typical hydrodynamic mesh for linear (yellow) and non-linear (yellow+green) seakeeping calculations
July 2015
Bureau Veritas
19
NR 583, App 1
3.3.2
Weakly non-linear
The minimum non-linearities that should be included are based on the so called Froude-Krylov approximation. The pressure of
the undisturbed incoming wave is applied to the hull on every wet panel, and not only under the mean waterline as it is done in
the linear computation. The mesh that is used to integrate the pressure loading has to include the part above the mean waterline. The non-linear hydrostatic restoring forces are also included by taking into account the real position of the ship in the integration of the hydrostatic pressure.
The motion equation is solved using a time domain seakeeping program. The radiation forces are included through the memory
functions, whereas the diffraction forces remain linear. All extra forces needed in the time domain simulation to ensure coursekeeping and to avoid low frequency motions should be properly included in the loading of the structural mesh. For each timestep a loading case is built and the corresponding structural response is calculated by 3D FEM analysis. If the dynamic structural
response is included, the stress response might be computed by modal summation if it is justified that the modal convergence is
achieved.
The outputs of a weakly non-linear hydro-structure computation are time traces. Ship motions and internal hull girder loads are
directly computed by the seakeeping software (the internal loads are calculated simply as the sum of the inertial and pressure
loads at each section). Time histories of stresses are computed by a structural analysis performed for each time step of the simulation.
3.3.3
Slamming
The slamming pressures are to be computed using either a CFD code or a Boundary Element Method provided that they are
properly validated and coupled with the seakeeping code. The slamming pressures are to be properly transferred to the FE
model at each time step of the time domain simulation.
The outputs of a non-linear hydro-structure computation are time traces. Ship motions and internal hull girder loads are directly
computed by the seakeeping software (the internal loads are calculated simply as the sum of the inertial and pressure loads at
each section).
Time histories of stresses are computed by a structural analysis performed for each time step of the simulation. If duly justified a
modal approach can be used to reconstruct the stress history without performing a FE calculation at each time step.
3.4
Structural ship response
3.4.1
Quasi-static ship response
Once the hydrodynamic seakeeping problem is solved, the different loading cases for FE model analysis need to be constructed.
Each loading case is composed of the hydrodynamic pressure loading on the wet panels, the inertial and the gravity loading on
each finite element and the additional damping loading. The perfect equilibrium of the overall loading needs to be ensured. In
case of important differences between the hydrodynamic and the structural meshes, special care is to be given to the pressure
transfer. Both pressure and nodal forces approaches for pressure transfer are acceptable.
The structural problem is solved using a FEA software for each loading case. The structural response is supposed to be static and
linear. In case of top-down modeling, once the problem is solved for the coarse mesh, the corresponding problem is solved for
every fine mesh. The stresses obtained from this analysis are then used for fatigue, yielding or buckling computation. This computational scheme is depicted in Fig 8.
3.4.2
Dynamic ship response
The first step of the dynamic analysis is the modal FE model analysis in dry (vacuum) condition, which is to be done with care.
Local structural modes are to be removed. The first 10 dry distortion modes are normally considered enough. An illustration of
the first mode shape of a container ship is given in Fig 10. Once the dry modes are obtained, the modal displacements are to be
transfered from the structural model to the hydrodynamic model and the corresponding hydrodynamic problems are to be
defined. An example of transfer mesh is given in Fig 11. Once the hydrodynamic problem is solved, a fully coupled dynamic
equation is solved, giving the modal amplitudes.
Special care is to be given to the separation of the quasi-static and dynamic parts (as illustrated in Fig 12) of the response to
ensure a proper convergence of the results. The quasi-static part of the response is calculated using the quasi-static method
explained in [3.4.1]. The dynamic part of the response is calculated by summing up the dynamic contribution of each mode.
Special attention is to be given to the fine mesh analysis for the dynamic part. The total response is obtained by summing the
quasi-static part and the dynamic part as shown in Fig 9.
20
Bureau Veritas
July 2015
NR 583, App 1
Figure 8 : Computational scheme for Quasi-static analysis
FE Model
Mass
properties
Motions
Hydrodynamic
loads
Motion
equation solver
HG loads
Accelerations
Pressure
Stresses
FE Analysis
Figure 9 : Computational scheme for Dynamic analysis
FE Model
Mass
properties
FE Modal
Analysis
Motions
Hydrodynamic
loads
Motion
equation solver
HG loads
Accelerations
Pressure
FE Analysis
Stresses
by modal
summation
Stresses
Figure 10 : Typical first structural natural mode shape of a container ship
July 2015
Bureau Veritas
21
NR 583, App 1
Figure 11 : Transfer of the modal displacements from structural to hydrodynamic model
Figure 12 : Typical springing response and its decomposition into quasi static and dynamic part.
3.5
3.5.1
General modeling considerations
Mass properties
For each loading condition the following mass properties computed from the FE model should be verified according to the values
from the trim and stability booklet:
• Mass
• Radii of giration
• Longitudinal distribution
• Location of the center of gravity.
3.5.2
Hydrostatic balance
For each loading condition, the computed values of displacement, trim, and vertical still water bending moment are to be
checked and compared to the values of the trim and stability booklet. The following tolerances are considered acceptable:
• 2% of the displacement
• 0,1° of the trim angle
• 10% of the still water bending moment.
It is also worth checking the following hydrostatic properties:
• Draft at aft perpendicular and forward perpendicular
• Location of the center of buoyancy (LCB)
• Tranverse and longitudinal metacentric height (GMt and GMl).
22
Bureau Veritas
July 2015
NR 583, App 1
3.5.3 Roll damping
Additional damping forces are to be added to the motion equation in order to take into account the viscous damping and damping due to rudders, bilge keels, and other existing appendages. This additional damping is to be added to the wave damping
computed by the hydrodynamic program. This damping could be based on experimental data or empirical methods. This damping is essentially non-linear and may be modeled by a linear and a quadratic damping coefficient. An equivalent linearised
damping coefficient may be used when the problem is solved in linear frequency domain. If no information is available a linear
damping of 5% of the critical damping is to be applied using the following formula:
Δ ⋅ g ⋅ GM t ⋅ T 44
B 44 = 0, 05 ⋅ -------------------------------------π
where:
B44
: Roll damping
Δ
: Mass of the ship, in kg
g
: 9,81 m/s²
GMt
: Transverse metacentric height, in m
T44
: Roll natural period, in s.
These damping forces should be applied to the FE model as nodal forces to ensure a perfect equilibrium between the forces
applied to the FE model and the acceleration solution of the motion equation.
3.5.4 Structural damping
Extra damping taking into account structural damping and cargo damping is to be added to the wave damping computed by the
hydrodynamic program for the flexible modes. The structural damping may varied between 1% and 3% of the critical damping
and tends to increase for the higher vibration modes.
K ii ⋅ T ii
B ii = η ii ⋅ --------------π
where:
Bii
: Additional damping of flexible mode i
Kii
: Total stiffness (hydrostatic + structural) of the flexible mode i
Tii
: Natural period of mode i
ηii
: Fraction of the critical damping for the flexible mode i.
These damping forces should be applied to the FE model as nodal forces to ensure a perfect equilibrium between the forces
applied to the FE model and the acceleration solution of the motion equation.
3.6
Type of simulations
3.6.1 General
The type of hydro-structural simulations depends on which hydrodynamic loads and which structural model are used. Possible
simulations are shown in Tab 5.
Table 5 : Types of hydro-structural simulations loads
Hydrodynamic loads
Linear
Structural
response
Weakly non-linear
Slamming
Quasi-static
Linear seakeeping
Non-linear seakeeping
Local slamming effect
Dynamic
Linear springing
Non-linear springing and wave
induced whipping
Non-linear springing and slamming
induced whipping
3.6.2 Linear seakeeping
Rigid body linear seakeeping response can be simulated using the quasi-static structural model with linear hydrodynamic loads.
This model is used for linear fatigue assessment without springing effects in Sec 1, [4].
3.6.3 Linear springing
Linear springing response can be simulated using the dynamic structural model with the linear seakeeping loads. This model is
used for linear fatigue assessment including springing effects in Sec 1, [4].
3.6.4 Non-linear seakeeping
Non-linear hull girder loads, such as hogging and sagging bending moment, can be evaluated using this model.This model can
be used for intermediate results of the ultimate strength assessment in Sec 1, [3].
July 2015
Bureau Veritas
23
NR 583, App 1
3.6.5
Local slamming effect
Local structural deformations due to slamming pressures can be computed using this model.
3.6.6
Non-linear springing and wave induced whipping
Because this model is taking into account non-linear wave loads and a structural dynamic response, it can simulate linear and
non-linear springing as well as wave-induced whipping. It is to be noted that it is not possible to separate the whipping response
from the springing response.
3.6.7
Non-linear springing and slamming induced whipping
This model is the most complex as it includes all non-linear loads, including slamming loads, coupled with a structural dynamic
response. It can simulate linear and non-linear springing as well as slamming-induced whipping. It is to be noted that it is not
possible to separate the whipping response from the springing response. This model is used for ultimate strength assessment Sec
1, [3] and non-linear fatigue assessment Sec 1, [5].
3.7
Statistical analysis of ship response in an irregular sea state
3.7.1
Linear frequency domain simulations
In case of linear hydrodynamic loads ( [3.3.1]) and linear structure response, the ship behaviour is defined by its RAOs. On a
given irregular sea state, the ship response is characterised by the response spectrum defined as:
360
 RAO ( ω, μ )S
2
SR ( ω ) =
ω
( ω , μ ) dμ
0
The spectral moments of the response are defined as:
∞ 360
mn =
  ω RAO ( ω, μ )S
n
e
2
ω
( ω, μ ) d μ d ω
0 0
Where the encounter frequency ωe is defined as:
2
ω U
ω e = ω – ----------- cos μ
g
The mean up-crossing period is defined as:
m
Tz = 2π -------0
m2
The probability density of response range follows the Rayleigh distribution. Its cumulative distribution function is:
2
–x
P Range ( x ) = 1 – exp  ----------
 8m 0
The cumulative distribution function of the cycles amplitudes (maxima or minima) is:
2
–x
P Amp ( x ) = 1 – exp  ----------
 2m 0
3.7.2
Non-linear time domain simulations
In case of non-linear hydrodynamic loads ( [3.3.2] and [3.3.3]), the simulation of the ship response is done in time domain.
From a statistical point of view, this time domain signal can be analysed with two different counting methods.
The up-crossing counting method consists in dividing the response into cycles (one cycle being defined between two consecutive mean level up-crossing), and to keep the maximum and the minimum of each cycle. The mean up-crossing period is
defined as the mean period of all the cycles. The maxima and minima are sorted and used to define an empirical cumulative
distribution function of the response. This distribution may be different from a Rayleigh distribution, because of the non-linearity
of the simulation. The up-crossing counting method is used to define the extreme response on a sea state, or a set of sea states.
An analytical function (Weibull distribution for instance) can be fitted to the empirical cumulative distribution function, in order
to be able to extrapolate the results to a lower probability level. Special care should be taken to the fitting procedure, and to the
possible error introduced by an extrapolation.
24
Bureau Veritas
July 2015
NR 583, App 1
If a linear result if available, it might be useful to compare the empirical distribution of the non-linear response with the empirical distribution of the linear response (which should converge to a Rayleigh distribution), and to fit a relationship between the
non-linear response and the linear response having the same probability. Hence the cumulative distribution function of the nonlinear response can be defined from the linear cumulative distribution function of the equivalent linear response.
The rainflow counting method consists in dividing the responses into cycles, taking into account all the local maxima and
minima. The mean period of all the cycles may be different from the up-crossing period. This counting method is used to compute fatigue damage.
4
Extreme response and Fatigue damage computation
4.1
Extreme response
4.1.1 Definition
The extreme response associated to a return period Tr is the maximum response the ship will see while sailing during a period Tr
with given environmental conditions. The extreme reponse is associated to a given exceedence probability or risk.
It can be an extreme load response (bending moment, torsion, acceleration...) or an extreme stress response.
4.1.2 Short term extreme
For a given short term condition (sea state and heading), the maximum short term response, corresponding to a duration T,
exceeded with a risk α is defined by:
α = 1 – P(x)
N
T
N = ----Tz
where:
N
: Number of response cycles in the duration of the sea state
Tz
: Zero up-crossing period of the response in seconds
T
: Duration of the sea state in seconds
P(x)
: Cumulative distribution function of the response.
Note 1: Usually the extreme short term response is defined as the response where the cumulative distribution function is equal to 1-1/N:
1
P ( x ) = 1 – ---N
For N larger than 100, the risk α corresponding to this extreme response is 63%.
If the response is computed from a frequency domain linear computation, the cumulative distribution function is to be based on
a Rayleigh distribution ( [3.7.1]). Hence the extreme short term response is perfectly known, whatever the duration of the sea
state and the associated risk are.
On the other hand, the use of the cumulative distribution function based on the results of a time domain simulation of finite
duration ( [3.7.2]) is more complex. The empirical distribution is only known up to the value of the maximum response
achieved during the time domain simulation, and the tail of this distribution does not statistically converge. Hence it is not possible to compute a short term extreme corresponding to a longer duration T and/or a lower risk α. For a good statistical convergence of the short term maxima, it is advised to run a time domain simulation at least (10/α) longer than the desired reference
duration T of the short term maxima.
If an analytical fitting function is used, the short term extreme can be computed for any duration and risk, but special care
should be given to the results, depending on the extrapolation procedure.
Another solution can be to increase the significant wave height of the short term condition, in order to increase the probability
of exceedence of a given response. From a linear simulation, the cumulative distribution functions in two short term conditions
of wave height Hs and λ Hs are linked by the following relation:
P ( x ) = 1 – ( 1 – P' ( x ) )
λ
2
where:
P(x)
: Cumulative distribution function of the response in a significant wave height Hs
P’(x)
: Cumulative distribution function of the response in a significant wave height λ Hs.
The same relationship can be considered as valid for a for non-linear response. This validity is only based on the assumption
that the ratio between the non-linear reponse and the linear response corresponding to the same probability of exceedence is
the same on both sea states. Using this assumption, it is interesting to compute the empirical cumulative distribution function
P’(x) on a higher sea state, in order to define the tail of the distribution P(x), and to be able to compute the short term extreme for
a long duration T and/or a low risk α. This method should only be used for the tail of the distribution P’(x) (for P’(x) > 0,8).
July 2015
Bureau Veritas
25
NR 583, App 1
4.1.3 Long term extreme
For a long-term condition, defined as a list of short-term conditions (scatter diagram or list of sea states), the maximum longterm response, corresponding to a return period Tr, exceeded with a risk α, is defined by:
α = 1–
∏ P (x)
Ni
i
i
p i Tr
N i = ---------Ti
where:
Tr
: Return period in seconds
i
: Index of the short term condition
Ni
: Number of response cycles in the return period, corresponding to the short term condition i
Ti
: Zero up-crossing period of the response in the short term condition i in seconds
pi
: Probability of the short term condition i
Pi(x)
: Cumulative distribution function of the response in the short term condition i.
Note 1: Usually the extreme long term response is defined as:
 N P (x)
i
i
= 1
i
For a return period larger than a few days, the risk α corresponding to this extreme response is 63%.
Note 2: The total number of response cycles in the return period Tr is given by:
N Tr =
N
i
i
For return periods of the order of 25 years, this number of response cycles is often of the order of 108. That is why the life time extreme response
is often called the 10-8 response. However the number of response cycles in 25 years depends on the ship length, and on the load type or stress
RAO. It is therefore more relevant to define the different extreme loads or stress response at the same return period Tr, rather than at the same
probability 10-8 , corresponding to different return periods.
The contribution of all short term conditions to the extreme value can be defined by:
1 – Pi ( x )
Ni
The most contributive conditions are the short term conditions having the highest contribution to the extreme value.
When the short term cumulative distribution functions are defined from linear computations, the cumulative distribution functions are based on Rayleigh distributions ( [3.7.1]). Hence the extreme long term response is perfectly known, whatever the reference duration and the associated risk is. However it is to be checked that the wave data from the scatter diagram are
sufficiently detailed in the highest sea states: the most contributive sea states should be inside the scatter diagram, and not at its
edge.
When the short term cumulative distribution functions are based on empirical distributions from time domain simulations,
extrapolation is needed to compute the long term extreme. The techniques explained in [4.1.2] should be applied. It is to be
checked that all the short term conditions having a significant contribution to the long term extreme have been extrapolated correctly, and that the statistical convergence is achieved.
4.2
Fatigue damage
4.2.1 Definition
The fatigue damage is computed from a time history of stress cycles and a S-N curve which is the characteristic of the structural
detail.
Fatigue damage can not be computed from a load response, except in a simplified case, when the stress response is supposed to
be proportional to a single load response.
4.2.2 Short term fatigue damage
In a short term condition of duration T, the fatigue damage can be computed from the cumulative distribution function of stress
ranges, and from the S-N curve.
A S-N curve is defined by the parameters mi and Ki as illustrated in Fig 13. The maximum number of cycles until the rupture is
given by:
Ki
…… ( S Qi – 1 < Δσ < S Qi )
N ( Δσ ) = ----------m
Δσ i
26
Bureau Veritas
July 2015
NR 583, App 1
Figure 13 : S-N curve
log S
K 3 , m3
SQ
2
K 2 ,m2
SQ
K 1 , m1
1
log N
NQ
NQ
2
1
The fatigue damage is computed using the assumption of linear cumulative damage proposed by Palmgreen-Miner:
∞
D =
n ( Δσ )
- dΔσ
 ---------------N ( Δσ )
0
T d
n ( Δσ ) = -------- ⋅ P ( Δσ )
T Δσ d x
where:
TΔσ
: Mean stress range period
T
: Duration of the sea state in seconds
P(Δσ)
: Cumulative distribution function of the stress range.
The cumulative distribution function can be based on a Rayleigh distribution ( [3.7.1]) or an empirical distribution based on a
Rainflow count ( [3.7.2]). In case of empirical distribution, this distribution should be based on a time domain simulation of at
least 1h to 3h, for a good statistical convergence of the hourly fatigue damage.
When the density function is a Rayleigh distribution, the fatigue damage can be computed analitically:
Nslope
T
D = -------T Δσ

2
2
mk
m S Qk – 1 
m S Qk 
1
----- ( 2 2m 0 )  Γ  1 + ------k ;---------– Γ  1 + ------k ;---------- 

2 8m 0
2 8m 0  
Kk
k=1
S Q0 = ∞ S QNslope = Threshold
4.2.3 Long term fatigue damage
For a long-term condition, defined as a list of short-term conditions (scatter diagram or list of sea states), the fatigue damage corresponding to a return period Tr is defined as the sum of the damage accumulated in all the short term conditions.
∞
D =
n i ( Δσ )
- dΔσ
  ---------------N ( Δσ )
i
0
Tr d
n i ( Δσ ) = p i --------- ⋅ P i ( Δσ )
T Δσi d x
where:
Tr
: Return period in seconds
i
: Index of the short term condition
TΔσi
: Mean stress range period in the short term condition i in seconds
pi
: Probability of the short term condition i
Pi(x)
: Cumulative distribution function of the response in the short term condition i.
July 2015
Bureau Veritas
27
NR 583, App 1
The contribution of each short term condition to the total damage can be defined by:
∞
n i ( Δσ )
- dΔσ
 ---------------N ( Δσ )
0
The most contributive conditions are the short term conditions having the highest contribution to the total damage.
Another way to compute the long term fatigue damage is first to compute the long term distribution of stress ranges by summing
the stress ranges distributions over all the short term conditions, and in a second step to compute the damage using the Miner
sum:
n ( Δσ ) =
 n ( Δσ )
i
i
∞
D =
n ( Δσ )
- dΔσ
 ---------------N ( Δσ )
0
5
5.1
Long term analysis methods
General
5.1.1 Definition
A long term analysis consists in simulating the ship behaviour over a very long period of time (usually 25 years), where the ship
will encounter many different environmental conditions. The objective of the long term analysis is to compute:
• the extreme response over that period of time (extreme stress, motion or load)
• the fatigue damage.
5.1.2 Input data
In order to do a long-term analysis a complete description of the environmental conditions is needed. This description can
come from some hindcast data, or from a scatter diagram (see [2.1]).
To compute the hydro-structure ship response on every sea state of the environmental conditions, a proper model of the ship
should be chosen (see [3]) and its operational profile should be given (see Sec 1, [3.2]).
5.1.3 Output data
The output of a long-term analysis is the distribution of stress cycles, or load cycles, in all the short term conditions composing
the long term environmental conditions. From these distributions of cycles, it is possible to compute:
• the extreme response in term of stress, or load
• the fatigue damage.
A secondary output of the long-term analysis is the list of the most contributive conditions (heading, sea state) to the extreme
response or to the fatigue damage.
5.1.4 Analysis methods
Several methods can be employed to perform a long term analysis. The most complex ones simulate all the life time ship
response, while the simplified methods, under given assumptions, focus on a limited number of simulations cases. All these
methods are described hereafter.
5.2
Fully long-term analysis
5.2.1 General case
A fully long-term analysis consists in simulating the ship response in all the sea states of the environmental conditions. This
analysis may be very time consuming if the model chosen for calculating the ship hydro structure response is not very time efficient (time domain model, including non-linearity).
5.2.2 Linear long-term analysis
If the ship response is considered to be linear, the long-term analysis is done very easily. The ship behaviour is characterised by
its linear RAOs defined in [3.3.1]. It can be a load RAO (Vertical Bending Moment, Torsion Moment, Acceleration...) or a stress
RAO. A load RAO only needs the results of a seakeeping computation, while a stress RAO needs in addition the results of FE
analysis.
The extreme response corresponding to any return period and any risk can be computed with the procedure described in
[4.1.3].
28
Bureau Veritas
July 2015
NR 583, App 1
The fatigue damage corresponding to any return period can be computed from the procedure described in [4.2.3].
Both for extreme and fatigue, a very useful result is the identification of the most contributive short term condition, in terms of
heading and sea state.
5.3
5.3.1
Design Sea States Approach
Principle
The principle of the Design Sea States approach is to focus the computation on a limited number of short term conditions (sea
states and heading). These conditions are the ones having the highest contribution to the extreme response, or to the fatigue
damage.
5.3.2
Choice of Design Sea States based on a linear long term analysis results
When the non-linear ship response is supposed to be partly governed by the linear ship response, it may be useful to choose the
Design Sea States among the short term conditions having the highest contributions to the linear extreme response or total linear
fatigue damage.
5.3.3
Computation of extreme response and fatigue damage
The Design Sea States approach is an iterative process:
• A first set of sea states and headings is chosen, and short term computation is done on these conditions.
• The extreme response, or the fatigue damage, is then computed using only these sea states, and neglecting the contribution
of all the other conditions ( [4.1.3] and [4.2.3]).
• The contribution of each computed condition to the extreme response, or total fatigue damage is computed. It is to be
checked that the contribution on the edge of the chosen conditions can be neglected. If not, new short term conditions are
added, and the process is started again.
5.4
5.4.1
Single Design Sea State
Principle
Under certain conditions, when it can be assumed than the non-linear ship response is just a correction of its linear response, it
might be enough to compute the non-linear ship response for a single short term condition, and to use the results of this short
term condition to correct the linear result.
5.4.2
Choice of the Design Sea State
For extreme response analysis, the Single Design Sea State should be the short term condition having the highest contribution to
the linear extreme response.
For fatigue damage analysis, the Single Design Sea State should be the short term condition having the highest contribution to
the linear fatigue damage.
5.4.3
Computation of the extreme response
The linear extreme response is computed at first using the linear long term analysis method ( [5.2.2]). On the chosen Design Sea
State, the risk of exceeding this linear extreme response is computed (see [4.1.2]). The short term non-linear extreme response
corresponding to the same risk is then derived from the non-linear simulation. To limit the duration of the non-linear simulation,
a fitting function may be used, or the Design Sea State significant wave height may be increased, as explained in [4.1.2].
This short term extreme response is considered to be the long term extreme response.
5.4.4
Computation of the fatigue damage
The linear fatigue damage is first computed using the linear long term analysis method ( [5.2.2]). On the chosen Design Sea
State, the linear fatigue damage and the non-linear fatigue damage are computed (see [4.2.2]). A correction factor is defined as
the increase of fatigue damage due to non-linear effects.
This correction factor is applied to the long term linear fatigue damage to compute the long term non-linear fatigue damage.
July 2015
Bureau Veritas
29
NR 583, App 1
30
Bureau Veritas
July 2015