1 CLASSIFICATION NOTES No CSA - DIRECT ANALYSIS OF SHIP STRUCTURES JANUARY 2011 Veritasveien 1, NO-1322 Høvik, Norway Tel.: Fax:
2 FOREWORD (DNV) is an autonomous and independent foundation with the objectives of safeguarding life, property and the environment, at sea and onshore. DNV undertakes classification, certification, and other verification and consultancy services relating to quality of ships, offshore units and installations, and onshore industries worldwide, and carries out research in relation to these functions. Classification Notes Classification Notes are publications that give practical information on classification of ships and other objects. Examples of design solutions, calculation methods, specifications of test procedures, as well as acceptable repair methods for some components are given as interpretations of the more general rule requirements. All publications may be downloaded from the Society s Web site The Society reserves the exclusive right to interpret, decide equivalence or make exemptions to this Classification Note. Main changes The main changes are: New class notation CSA-1 and CSA-FLS1 included. CSA-FLS1 has reduced fatigue scope compared to existing class notation CSA-FLS. CSA-1 includes requirements for ULS and CSA-FLS1. Existing notations CSA-FLS and CSA-2 are kept, but CSA-FLS is renamed CSA-FLS2. Include experience from recent project on ore carrier. The electronic pdf version of this document found through is the officially binding version Det Norske Veritas Any comments may be sent by to For subscription orders or information about subscription terms, please use Computer Typesetting (Adobe Frame Maker) by Det Norske Veritas If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of Det Norske Veritas, then Det Norske Veritas shall pay compensation to such person for his proved direct loss or damage. However, the compensation shall not exceed an amount equal to ten times the fee charged for the service in question, provided that the maximum compensation shall never exceed USD 2 million. In this provision "Det Norske Veritas" shall mean the Foundation Det Norske Veritas as well as all its subsidiaries, directors, officers, employees, agents and any other acting on behalf of Det Norske Veritas.
3 Page 3 CONTENTS 1. Introduction Objective General Definitions Programs Overview of CSA Analysis General Scope and acceptance criteria Procedures and analysis Documentation and verification overview Hydrodynamic Analysis Introduction Hydrodynamic model Roll damping Hydrodynamic analysis Design waves for ULS Load Transfer Fatigue Limit State Assessment General principles Locations for fatigue analysis Corrosion model Loads Component stochastic fatigue analysis Full stochastic fatigue analysis Damage calculation Ultimate Limit State Assessment Principle overview Global FE analyses local ULS Hull girder collapse - global ULS Structural Modelling Principles Overview General Global structural FE-model Sub models Mass modelling and load application Documentation and Verification General Documentation Verification References Appendix A. Relative Deflection Analysis Appendix B. DNV Program Specific Items Appendix C. Simplified Hull Girder Capacity Model - M U Appendix D. Hull Girder Capacity Assessment Using Non-linear FE Analysis Appendix E. PULS Buckling Code Design Principles Stiffened Panels... 66
4 Page 4 1. Introduction 1.1 Objective This Classification Note for Computational Ship Analysis, CSA, provides guidance on how to perform and document analyses required for compliance with the classification notations CSA-FLS1, CSA-FLS2, CSA-1 and CSA-2 as described in the DNV Rules for Classification of Ships, Pt.3 Ch.1. The aim of the class notations is to ensure that all critical structural details are adequately designed to meet specified fatigue and strength requirements. 1.2 General CSA-FLS1, CSA-FLS2, CSA-1 and CSA-2 are optional class notations for enhanced structural calculations of ships. All calculations are based on direct calculation of load and response. CSA-FLS1 and CSA-FLS2 cover fatigue analyses, while CSA-1 and CSA-2 additionally covers fatigue and ultimate strength analyses. The CSA notations have requirements for the structural parts and details of the ship hull. Tank systems and their supports are not a part of the scope for CSA. Likewise, structural details connected to moorings or offshore loading systems are outside the scope of CSA. Loads caused by slamming, sloshing and vibration are not included in the CSA notations. This Classification Note describes the following steps of the CSA analyses: scope of analysis (areas/details to be considered) procedures for: - modelling - hydrodynamic analyses - structural analysis - ULS post processing - FLS post processing. acceptance criteria documentation and verification of the analyses. The CSA notations are applicable to all ship types. Details to be analysed is specified for the following ship types: Tankers LNG carriers (Moss type and membrane type) LPG carriers Container ships Ore carrier. For other ship types the details are selected on case by case basis. The notations are especially relevant for vessels fulfilling one or more of the following criteria: novel vessel design increased size compared to existing vessel design operating in harsh environment operational challenges different from similar ships high requirements for minimizing off-hire. 1.3 Definitions Abbreviations The following abbreviations and definitions are used in this Classification Note. FLS ULS DNV CSA CSA-FLS1 CSA-FLS2 CSA-1 CSA-2 Fatigue Limit State Ultimate Limit State Det Norske Veritas Computational Ship Analysis Computational Ship Analysis - Fatigue Limit State with limited scope Computational Ship Analysis Fatigue Limit State with full scope Computational Ship Analysis - Fatigue Limit State with limited scope and Ultimate Limit State Computational Ship Analysis Fatigue Limit State with full scope and Ultimate Limit State
5 Page 5 CSR PLUS CN SCF Common Structural Rules Class Notation covering additional fatigue requirements based on rule loads Classification Note Stress concentration factor Symbols The following symbols are used in this Classification Note: D B T act K σ hot spot σ nominal θ ζ r p p d z wl N a m Δσ f m σ f f 1 σ e σ σ g σ 2 τ η A W A Wmod t p ρ a v p n g M S M W M UI M UD γ S γ D γ M V Moulded depth Moulded breadth Actual draught Stress concentration factor Stress at hotspot Nominal stress in structure Roll-angle Wave amplitude Correction factor for external pressure in waterline region Dynamic pressure amplitude Water head due to external wave pressure at waterline Number of cycles constant related to mean S-N curve S-N fatigue parameter Stress range Factor taking into account mean stress ratio Yield stress of material Material factor Nominal Von Mises stress Nominal stress Nominal stress from global bending/axial force Nominal stress from secondary bending (e.g. double bottom bending) Nominal shear stress Usage factor Effective shear area Modelled shear area thickness Pressure Density Vertical acceleration Fraction of time at sea in the different loading conditions Gravitational constant is the still water vertical bending moment is the wave vertical bending moment is the ultimate moment capacity of the intact hull girder is the ultimate moment capacity of the damaged hull girder Partial safety factors reflecting uncertainties and ensuring the overall required target safety margin with respect to the still water vertical bending moment Partial safety factors reflecting uncertainties and ensuring the overall required target safety margin with respect to the wave vertical bending moment Partial safety factors reflecting uncertainties and ensuring the overall required target safety margin with respect to the ultimate moment capacity maximum service speed in knots, defined as the greatest speed which the ship is designed to maintain in service at her deepest seagoing draught 1.4 Programs The CSA procedure requires programs with possibility for direct application of pressures and inertia from a 3D non-linear hydrodynamic program to a finite element (FE) analysis program with suitable applications and
6 Page 6 post-processing tools to ensure good documentation and verification possibilities for a third party to review. The Nauticus programs provided by DNV are well suited for these analyses. Relevant Nauticus applications are described in Section 8. Other programs may also be accepted. 2. Overview of CSA Analysis 2.1 General The requirements for the CSA notations are given in the Rules for Classification of Ships, Pt.3 Ch.1. CSA notations require compliance with NAUTICUS (Newbuilding) or CSR, whichever is applicable. For class notation CSR this implies that all CSR requirements are to be complied with and documented. For NAUTICUS (Newbuilding) the ULS analysis are to be complied with independent of CSA. However requirements for FLS need not be performed if compliance with CSA is documented and confirmed. All details except the stiffener-frame connections as defined by the PLUS notation shall also be included in CSA-FLS2 but only the details in 2.2 are to be included in the scope of CSA-FLS1. In case PLUS notation in addition to CSA is specified, calculations for stiffener frame connections have to be performed according to the procedure specified by the PLUS notation including low cycle fatigue requirements, while other requirements are documented and confirmed as part of CSA. 2.2 Scope and acceptance criteria The CSA procedure includes the following analysis and checks: CSA-FLS1 Fatigue of critical details in cargo hold area: - knuckles - discontinuities - deck openings and penetrations. CSA-FLS2 Fatigue of longitudinal end connections and frame connection in cargo hold area. Fatigue of bottom and side-shell plating connection to frame/stiffener in the cargo hold area. Fatigue of critical details in cargo hold area: - knuckles - discontinuities - deck openings and penetrations. CSA-1 FLS - Fatigue requirements as for CSA-FLS1. Local ULS - Yield and buckling strength of structure in the cargo hold area. Global ULS - Hull girder capacity of the midship section in intact and two damaged conditions. CSA-2 FLS - Fatigue requirements as for CSA-FLS2. Local ULS - Yield and buckling strength of structure in the cargo hold area. Global ULS - Hull girder capacity of the midship section in intact and two damaged conditions. Each project should together with the Society define the total scope of the calculations. Note that fatigue and strength analyses may also be required outside the cargo hold area if deemed necessary by the Society. Some details outside the cargo hold area are already specified in the Rules. The design life basis for CSA-analysis, is the minimum design life as defined by class notation NAUTICUS (Newbuilding) or CSR whichever is relevant, as defined in the Rules for Classification of Ships, Pt.3 Ch.1. The acceptance criteria for fatigue is stated in Section 4.7.1, while the acceptance criteria for Local-ULS and Global-ULS is given in Section and Section respectively. 2.3 Procedures and analysis The flowchart in Figure 2-2 shows the typical analysis procedure for a typical CSA.
7 Page 7 Figure 2-1 CSA calculation procedure All calculations shall be based on direct calculated wave loads using a 3D hydrodynamic program including effect of forward speed. The pressures and inertia loads from the hydrodynamic analysis shall be transferred to the FE-models maintaining the phasing definitions. For FLS two principal fatigue calculation methodologies are used to comply with CSA requirements: full stochastic (spectral) fatigue analysis (Section 4.6) DNV component stochastic method (Section 4.7). CSA-FLS1 require analysis with full stochastic analysis, while for CSA-FLS2 both analysis procedures are needed. Two types of ULS analyses are to be carried out, i.e. 1) Global FE analyses local ULS (Section 5.3) Is required for all structural members in the cargo hold area. Linear FE stress analyses are performed for verification of plating, stiffeners, girders etc. against buckling and material yield. The buckling and ultimate strength limits are evaluated using PULS buckling code. This is required for all structural members in the cargo hold area; however buckling is in general only performed for longitudinal members. 2) Hull girder collapse global ULS (Section 5.4) This ULS assessment is based on separate hull girder strength models accounting for buckling and nonlinear structural behaviour of plating, stiffeners, girders etc. in the cross-section. The purpose is to control and ensure sufficient overall hull girder strength preventing global collapse and loss of vessel. Simplified structural models (HULS) or advanced non-linear FE analyses may be used. Both intact and damaged hull sections are to be assessed.
8 Page 8 The CSA analysis is based on a set of different structural FE-models, (Section 6). A global FE-model is required for the analyses in addition to models with element definition applicable for evaluation of yield/ buckling strength and fatigue strength respectively. 2.4 Documentation and verification overview The analysis shall be verified in order to ensure accuracy of the results. Verification shall be documented and enclosed with the analysis report. The documentation shall be adequate to enable third parties to follow each step of the calculations. For this purpose, the following should, as a minimum, be documented or referenced: basic input (drawings, loading manual, weather conditions, etc.), assumptions and simplifications made in modelling/analysis, models, loads and load transfer, analysis, results (including quality control), discussion, and conclusion. Checklists for quality assurance shall also be developed before the analysis work commences. It is suggested that project-specific checklists be defined before the start of the project and to be included in the project quality plan. These checklists will depend on the engineering practices of the party carrying out the analysis, and associated software. 3. Hydrodynamic Analysis 3.1 Introduction Sea keeping and hydrodynamic load analysis for CSA-FLS1, CSA-FLS2, CSA-1 and CSA-2 shall be carried out using 3-D potential theory, with possibility of forward speed, with a recognized computer program. Nonlinear theory needs to be used for design waves for ULS assessment, where non-linear effects are considered important. The program shall calculate response amplitude operators (RAOs, transfer functions) and time histories for motions and loads in regular waves. The inertia loads and external and internal pressures calculated in the hydrodynamic analysis are directly transferred to the structural model. For FLS the reference loads shall represent the stresses that contribute the most to the fatigue damage, e.g. typical loading conditions with forward speed in typical trading routes. It is assumed that the loads contributing most to fatigue damage have short return periods and are therefore small but frequent waves. It is therefore sufficient to use linear analysis for fatigue assessments, since the linear wave loads give sufficient approximation of the loads for waves with small amplitudes or when ship sides are vertical. For linearization and documentation purposes, a reference load level of 10-4 is to be used, representing a daily load level. For ULS the loads representing the condition that leads to the most critical response of the vessel shall be found. Normally a design wave, representing the most critical response (load or stress), is applied, and the simultaneous acting loads (inertia and pressures) at the moment when maximum response is achieved, is transferred to the structural model. Several design waves are defined, representing different structural responses. In general the hydrodynamic loads should be represented by non-linear theory for design waves where the response is dominated by vertical bending moment and shear force. Other design waves may be based on linear theory, since the non-linear effects are negligible, or difficult to capture. Figure 3-1 shows a schematic overview of the work flow for the hydrodynamic analysis as part of the CSA- FLS1, CSA-FLS2, CSA-1 and CSA-2 calculations. Section 4.4 and Section defines loading conditions, environment conditions, etc. applicable for FLS and ULS hydrodynamic analysis, respectively.
9 Page 9 Figure 3-1 Flow chart of a hydrodynamic analysis for CSA This section describes the procedure for the hydrodynamic analysis. 3.2 Hydrodynamic model General There should be adequate correlation between hydrodynamic and structural models, i.e. both models should have: equal buoyancy and geometry equal mass, balance and centre of gravity.
10 Page 10 The hydrodynamic model and the mass model should be in proper balance, giving still water shear force distribution with zero value at FP and AP. Any imbalance between the mass model and hydrodynamic model should be corrected by modification of the mass model Hydrodynamic panel model The element size of the panels for the 3-D hydrodynamic analysis shall be sufficiently small to avoid numerical inaccuracies. The mesh should provide a good representation of areas with large transitions in shape, hence the bow and aft areas are normally modelled with a higher element density than the parallel midship area. The hydrodynamic model should not include skewed panels. The number of elements near the surface needs to be sufficient in order to represent the change of pressure amplitude and phasing, since the dynamic wave loads increases exponentially towards the surface. This is particularly important when the loads are to be used for fatigue assessment. In order to verify that the number of elements is sufficient, it is recommended to double the number of elements and run a head sea analysis for comparison of pressure time series. The number of panels needed to converge differs from code to code. Figure 3-2 shows an example of a panel model for the hydrodynamic code WASIM. Figure 3-2 Example of a panel model The panels should, as far as possible, be vertical oriented as indicated to the right in Figure 3-3. This is to ease the load transfer. For component stochastic fatigue analysis transverse sections with pressures are input to the assessment, which is easier with the model to the right. Figure 3-3 Schematic mesh model Mass model The mass of the FE-model and hydrodynamic model has to be identical in order to obtain balance in the structural analysis. Therefore the hydrodynamic analysis shall use a mass-model based on the global FE structural model. In many cases, however, the hydrodynamic analysis will be performed prior to the completion of the structural model. A simplified mass model may then be used in the initial phase of the hydrodynamic analysis. The structural mass model shall be used in the hydrodynamic analysis that establishes the pressure loads and inertia loads for the load transfer Simplified Mass model If the structural model is not available a simplified mass model shall be made. The mass model shall ensure a proper description of local and global moments of inertia around the longitudinal, transverse and vertical global ship axes. The determination of sectional loads can be particularly sensitive to the accuracy and refinement of the mass model. Mass points at every meter should be sufficient FE-based Mass model The FE-based mass model is described in Section 6.5.
11 Page Roll damping The roll damping computed by 3-D linear potential theory includes moments acting on the vessel hull as a result of the waves created when the vessel rolls. At roll resonance, however, the 3-D potential theory will underpredict the total roll damping. The roll motion will, consequently, be grossly over-predicted. To adequately predict total roll damping at roll resonance, the effect from damping mechanisms not related to wave-making, such as vortex-induced damping (eddy-making) near sharp bilges, drag of the hull (skin friction), skegs and bilge keels (normal forces and flow separation), should be included. Such non-linear roll damping models have typically been developed based on empirical methods, using numerical fitting to model test data. Example of non-linear roll damping methods for ship hulls includes those published by Tanaka /6/ and Kato /9//10/. Results from experiments indicate that non-linear roll damping on a ship hull is a function of roll angle, wave frequency and forward speed. As the roll angle is generally unknown and depends on the scatter diagram considered, an iteration process is required to derive the non-linear roll damping. The following 4-step iteration procedure may be used for guidance: a) Input a roll angle, θ input x, to compute non-linear roll damping. b) Perform vessel motion analysis including damping from a). c) Calculate long-term roll motion, θ update x, with probability level 10-4 for FLS or 10-8 for ULS, using design wave scatter diagram. d) If θ update x from c) is close to θ input x in step a), stop the iteration. Otherwise, set θ input x as the mean value of θ update x and θ input x, and go back to a). Viscous effects due to roll are to be included in cases where it influences the result. Roll motion can affect responses such as acceleration, pressure and torsion. Viscous damping should be evaluated for beam and quartering seas. The viscous roll damping has little influence in cases where the natural period of the roll mode is far away from the exciting frequencies. For fatigue it is sufficient to calibrate the viscous damping for beam sea and use the same damping for all headings. 3.4 Hydrodynamic analysis Wave headings A spacing of 30 degree or less should be used for the analysis, i.e. at least twelve headings Wave periods The hydrodynamic load analysis shall consider a sufficient range of regular wave periods (frequencies) so as to provide an accurate representation of wave energies and structural response. The following general requirements apply with respect to wave periods: The range of wave periods shall be selected in order to ensure a proper representation of all relevant response transfer functions (motions, sectional loads, pressures, drift forces) for the wave period range of the applicable scatter diagram. Typically wave periods in the range of 5-40 seconds can be used. A proper wave period density should be selected to ensure a good representation of all relevant response transfer functions (motions, sectional loads, pressures, drift forces), including peak values. Typically wave periods are used for a smooth description of transfer functions. Figure 3-4 shows an example of a poor and a good representation of a transfer function. For the transfer function with a poor representation, the range of periods does not cover the high frequency part of the transfer function and the period density is not high enough to capture the peak.
12 Page E+05 Transfer Function for Vertical Bending Moment 9.00E+05 Transfer Function for Vertical Bending Moment 8.00E E E E E+05 VBM / Wave Amplitude 5.00E E E E+05 VBM / Wave Amplitude 5.00E E E E E E E E Wave Period E Wave Period Figure 3-4 Poor representation of a transfer function on the left and on the right a transfer function where peak and shorter wave periods are well represented 3.5 Design waves for ULS General A design wave is a wave which results in a design load at a given reference value (e.g. return period). Using a design wave, the phasing between motions and loads will be maintained giving a realistic load picture. Normally it is assumed that maximising the load will result in also the maximised stress response. However some responses are correlated and the combined effect may give higher stresses than if each load is maximised. In such cases it is recommended to transfer the load RAO s and perform a full stochastic analysis. The stress RAO s of the most critical regions can then be used as basis for design waves. In case of linear design waves the response of the response variable shall be the same as the long term response described in Section For non-linear design waves, e.g. for vertical bending moment, the non-linear maximum response is not necessarily at the same location as the maximum linear response. Several locations need to be evaluated in order to locate the non-linear maximum response. The linear and non-linear dynamic response shall be compared, including the non-linear factor defined as the ratio between the maximum non-linear and linear dynamic response. Water on deck, also called green water, might occur during ULS design conditions. If the software does not handle water on deck in a physical way it is conservative to remove the elements and pressures from the deck. In a sagging wave the bow will be planted into a wave crest. Applying deck pressures in such case will reduce the sagging moment. There are several ways of generating design waves. The following presents two acceptable ways: regular design wave conditioned irregular extreme wave Regular design wave A regular design wave can be made such that a linear simulation results in a dynamic response equal to the long term response. The wave period for the regular wave shall be chosen as the period corresponding to the maximum value of the transfer function, see Figure 3-5. The wave amplitude shall be chosen as: ζ [ m] Long term response = Transfer function peak [ Nm] Nm m
13 Page E+ 05 Transfer Function for Vertical Bending Moment 8.00E E+ 05 VBM / Wave Amplitude 6.00E E E E E E E+ 00 Figure 3-5 Example of transfer function Wa ve Period The wave steepness shall be less than the steepness criterion given in DNV-RP-205 /3/. If the steepness is too large, a different wave period combined with the corresponding wave amplitude should be chosen. The regular response shall converge before results can be used Conditioned irregular extreme waves Different methods exist to make a conditioned irregular extreme wave (ref. /11/, /12/, /13/). In principle an irregular wave train which in linear simulations returns the long term response after short time is created. The same wave train can be used for non linear simulations in order to study the non-linear effects. 3.6 Load Transfer General The hydrodynamic loads are to be taken from the hydrodynamic load analysis. To ensure that phasing of all loads is included in a proper way for further post processing, direct load transfer from the hydrodynamic load analysis to the structural analysis is the only practical option. The following loads should be transferred to the structural model: inertia loads for both structural and non-structural members external hydro pressure loads, internal pressure loads from liquid cargo, ballast 1) viscous damping forces (see below). 1) The internal pressure loads may be exchanged with mass of the liquid (with correct center of gravity) provided that this exchange does not significantly change stresses in areas of interest (the mass must be connected to the structural model). Inertia loads will normally be applied as acceleration or gravity components. The roll and pitch induced fluctuating gravity component (g sin(θ) g θ) in sway and surge shall be included. Pressure loads are normally applied as normal pressure loads to the structural model. If stresses influenced by the pressure in the waterline region are calculated, pressure correction according to the procedure described in Section need to be performed for each wave period and heading. Viscous damping forces can be important for some vessels, particularly those vessels where roll resonance is in an area with substantial wave energy, i.e. roll resonance periods of 6-15 seconds. The roll damping may, depending on Metocean criteria, be neglected when the roll resonance period is above seconds. If torsion is an important load component for the ship, the effect of neglecting the viscous damping force should be investigated.
14 Page Load transfer FLS The loads from the hydrodynamic analysis are used in the fatigue analysis. For the full stochastic analysis the inertia is applied to the FE model and the inertia pressure of tank liquids and wave-pressures are transferred to the global FE model for all frequencies and headings of the hydrodynamic analysis. For the component stochastic analysis the load transfer functions at the applicable sections and locations are combined with nominal stress per unit load, giving nominal stress transfer functions. The loads of interest are the inertia pressures in the tanks, the sea-pressures, and the global hull girder loads, i.e. vertical and horizontal bending moment and axial elongation Inertia tank pressures The transfer functions for internal cargo and ballast pressures due to acceleration in x-, y- and z-direction are derived from the vessel motions. The acceleration transfer functions are to be determined at the tank centre of gravity and include the gravity component due to pitch and roll motions. Based on the free surface and filling level in the tank, the pressure heads to the load point in question is established, and the total internal transfer function is found by linear summation of pressure due to acceleration in x, y and z-direction for the load point in question (FE pressure panel for full stochastic and load point for component stochastic.) Effect of intermittent wet surfaces in waterline region The wave pressure in the waterline region is corrected due to intermittent wet and dry surfaces, see Figure 3-6. This is mainly applicable for details where the local pressure in this region is important for the fatigue life, e.g. longitudinal end connections and plate connections at the ship side. Water head f Extrapolated t Water head f Corrected Pressures at 10-4 probability Figure 3-6 Correction due to intermittent wetting in the waterline region Since panel pressures refer to the midpoint of the panel, the value at waterline is found from extrapolating the values for the two panels closest to the waterline. Above the waterline the pressure should be stretched using the pressure transfer function for the panel pressure at the waterline combined with the r p -factor. Using the wave-pressure at waterline, with corresponding water-head, at 10-4 probability level as basis, the wave-pressure in the region limited by the water-head below the waterline, is given linear correction, see Figure 3-6. The dynamic external pressure amplitude (half pressure range), p e, for each loading condition, may be taken as: p = r p where: e p d p d r p is dynamic pressure amplitude below the waterline is reduction of pressure amplitude in the surface zone
15 Page 15 z wl = 1.0 for z < T act z wl = Tact + zwl z 2zwl for T act z wl < z < T act + z wl = 0.0 for T act + z wl < z is distance in m measured from actual water line to the level of zero pressure, taken equal to water-head from pressure at waterline. = 3 p dt 4 ρg p dt is dynamic pressure at waterline T act In the area of side shell above z = T act + z wl it is assumed that the external sea pressure will not contribute to fatigue damage. Above waterline the wave-pressure is linearly reduced from the waterline to the water-head from the wavepressure Load transfer ULS In case of load transfer for ULS, the pressure and inertia forces are transferred at a snapshot in time. Every wetted pressure panel on the structural FE model shall have one corresponding pressure value while inertia forces in six degrees of freedoms are transferred to the complete model. 4. Fatigue Limit State Assessment 4.1 General principles Methodology overview The following defines fatigue strength analysis based on spectral fatigue calculations. Spectral fatigue calculations are based on complex stress transfer functions established through direct wave load calculations combined with subsequent stress response analyses. Stress transfer functions then express the relation between the wave heading and frequency and the stress response at a specific location and may be determined by either: component stochastic analysis full stochastic analysis. Component stochastic calculations may in general be employed for stiffeners and plating and other details with a well defined principal stress direction mainly subjected to axial loading due to hull girder bending and local bending due to lateral pressures. Full stochastic calculations can be applied to any kind of structural details. Spectral fatigue calculations imply that the simultaneous occurrence of the different load effects are preserved through the calculations and the uncertainties are significantly reduced compared to simplified calculations. The calculation procedure includes the following assumptions for calculation of fatigue damage: wave climate is represented by a scatter diagram Rayleigh distribution applies for the response within each short term condition (sea state) cycle count is according to zero crossing period of short term stress response linear cumulative summation of damage contributions from each sea state in the wave scatter diagram, as well as for each heading and load condition. The spectral calculation method assumes linear load effects and responses. Non-linear effects due to large amplitude motions and large waves are neglected, assuming that the stress ranges at lower load levels (intermediate wave amplitudes) contribute relatively more to the cumulative fatigue damage. Where linearization is required, e.g. in order to determine the roll damping or intermittent wet and dry surfaces in the splash zone, the linearization should be performed at the load level representing stress ranges giving the largest contribution to the fatigue damage. In general a reference load or stress range at 10-4 probability of exceedance should be used. Low cycle fatigue and vibrations are not included in the fatigue calculations described in this Classification Note Classification Note No Fatigue calculations for the CSA notations are based on the calculation procedures as described in Classification Note No /4/. This Classification Note describes details and procedures relevant for the
16 Page 16 CSA-notation. For further details reference is made to CN In case of conflicting procedure, the procedure as given in CN 30.7 has precedence. 4.2 Locations for fatigue analysis General Fatigue calculations should in general be performed for all locations that are fatigue sensitive and that may have consequences for the structural integrity of the ship. The locations defined by NAUTICUS (Newbuilding) or CSR, whichever is relevant, and PLUS, shall be documented by CSA fatigue calculations. The general locations are shown in Table 4-1 with some typical examples given in Figure 4-1 to Figure 4-7. Table 4-1 General overview of fatigue critical details Detail Location Selection criteria Stiffener end connection one frame amidships one bulkhead amidships All stiffeners included one frame in fwd. tank one frame in aft tank* ) Bottom and side shell plating one frame amidships All plating to be included connection to stiffener and one frame in fwd. tank frames one frame in aft tank* ) Stringer heels and toes one location amidships Based on global screening analysis and one location in fwd hold* ) evaluation of details other locations* ) Panel knuckles one lower hopper knuckle amidships other locations identified* ) Based on global screening analysis and evaluation of details Discontinuous plating structure between hold no. 1 and 2* ) between Machinery space and cargo region* ) Deck plating, including stress concentrations from openings, scallops, pipe penetrations and attachments. Based on global screening analysis and evaluation of details Based on global screening analysis and evaluation of details * ) Global screening and evaluation of design in discussion with the Society to be basis for selection For the stiffener end connections and shell plate connection to stiffeners and frames it is normally sufficient to perform component stochastic fatigue analysis using predefined load/stress factors and stress concentration factors. All other details, including those required by ship type, need full-stochastic analysis with use of stress concentration models with txt mesh (element size equal to plate thickness). Figure 4-1 Longitudinal end connection
17 Page 17 Figure 4-2 Plate connection to stiffener and frame Figure 4-3 Stringer heel and toe
18 Page 18 Figure 4-4 Example of panel knuckles Figure 4-5 Example of discontinuous plating structure
19 Page 19 Figure 4-6 Example of discontinuous plating structure Figure 4-7 Hotspots in deck-plating Details for fine mesh analysis In addition to the general positions as described in Section 4.2.1, fine mesh full stochastic fatigue analysis for defined ship specific details also need to be performed, see the Rules for Classification of Ships, Pt.3 Ch.1. The ship specific details are details either found to be specially fatigue sensitive and/or where fatigue cracks may have an especially large impact on the structural integrity. Typical vessel specific locations that require fine mesh full stochastic analysis are specified in the following. In the following the mandatory locations in need of fine mesh full stochastic analysis are listed for different vessel types. For vessel-types not listed, details to be checked need to be evaluated for each design. Tankers lower hopper knuckle upper hopper knuckle stringer heels and toes one additional critical location found on transverse web-frame from global screening of midship area.
20 Page 20 Membrane type LNG carriers lower hopper knuckle upper hopper knuckle stringer heels and toes dome opening and coaming lower and upper chamfer knuckles longitudinal girders at transverse bulkhead trunk deck at transverse bulkhead termination of tank no. 1 longitudinal bulkhead aft trunk deck scarfing. Moss type LNG carriers lower hopper knuckle stringer heels and toes tank cover to deck connection tank skirt connection to foundation deck inner side connection to foundation deck in the middle of the tank web frame longitudinal girder at transverse bulkhead. LPG carriers dome opening and coaming lower and upper side bracket longitudinal girder at transverse bulkhead. Container vessel top of hatch coaming corner (amidships, in way of E/R front bulkhead, and fore-ship) upper deck hatch corner (amidships in way of E/R front bulkhead, and fore-ship hatch side coaming bracket in way of E/R front bulkhead scarfing brackets on longitudinal bulkhead in way of E/R critical stringer heels in fore-ship stringer heel in way of HFO deep tank structure (where applicable). Ore carrier inner bottom and longitudinal bulkhead connection horizontal stringer toe and heel in ballast tank cross-tie connection in ballast tank hatch corner hatch coaming brackets upper stool connection to transverse bulkhead additional critical locations found from screening of midship frame. 4.3 Corrosion model Scantlings All structural calculations are to be carried out based on the net-scantlings methodology as described by the relevant class notation. This yields for both global and local stresses. E.g. for oil tankers with class notation CSR 50% of the corrosion addition is to be deducted for local stress and 25% of the corrosion addition is to be deducted for global stress. For other class notations the full corrosion addition is to be deducted. 4.4 Loads Loading conditions Vessel response may differ significantly between loading conditions. Therefore the basis of the calculations should include the response for actual and realistic seagoing loading conditions. Only the most frequent loading conditions should be included in the fatigue analysis, normally the ballast and full load condition, which should be taken as specified in the loading manual. Under certain circumstances, other loading conditions may be considered Time at sea For vessels intended for normal, world wide trading, the fraction of the total design life spent at sea, should not be taken less than The fraction of design life in the fully loaded and ballast conditions, p n, may be taken
21 Page 21 according to the Rules for Classification of Ships, Pt.3 Ch.1, summarised in Table 4-2. Table 4-2 Fraction of time at sea in loaded and ballast condition Vessel type Tanker Gas carrier Bulk carrier Container vessel Ore carrier Loaded condition Ballast condition Other fractions may be considered for individual projects or on owners request Wave environment The wave data should not be less severe than world wide or North Atlantic for vessels with NAUTICUS (Newbuilding) notation or CSR notation, respectively. The scatter-diagrams for World Wide and North Atlantic are defined in CN Other wave data may also be considered in addition, if requested by owner. This could typically be a sailing route typical for the specific ship. Fatigue is governed by the daily loads experienced by the vessel, hence the reference probability level for fatigue loads and responses shall be based on 10-4 probability level. Weibull fitting parameters are normally taken as 1, 2, 3 and 4. A Pierson-Moskowitz wave spectrum with a cos 2 wave spreading shall be used. If a different wave data is specified, it is recommended to perform a comparative analysis to advice which of the scatter diagram gives worse fatigue life. If one yields worse results, this scatter diagram may be used for all analysis. If the results are comparative, fatigue life from both wave environments may need to be established Hydrodynamic analysis A vessel speed equal to 2/3 of design speed should be used, as an approximation of average ship speed over the lifetime of the vessel. All wave headings (0 to 360 ) should be assumed to have an equal probability of occurrence and maximum 30 spacing between headings should be applied. Linear wave load theory is sufficient for hydrodynamic loads for FLS, since the daily loads contribute most to the fatigue damage. Reference is made to Section 3 for hydrodynamic analysis procedure Load application The loads from the hydrodynamic analysis are used in the fatigue analysis. For the full stochastic analysis the following hydrodynamic loads are applied to the global structural model for all headings and frequencies: external panel pressures internal tank pressures inertia loads due to rigid body accelerations. For the component stochastic analysis the loads at the applicable sections and locations are combined with stress transfer functions representing the stress per unit load. The loads to be considered are: inertial loads (e.g. liquid pressure in the tanks), sea-pressure global hull girder loads: - vertical bending moment - horizontal bending moment and - axial elongation. Details are described in Section Component stochastic fatigue analysis Component stochastic fatigue analysis is used for stiffener end connections and plate connection to stiffeners and frames, see Section The component stochastic fatigue calculation procedure is based on linear combination of load transfer functions calculated in the hydrodynamic analysis and stress response factors representing the stress per unit load. The nominal stress transfer functions for each load component is combined with stress concentration factors before being added together to one hot spot transfer function for the given detail. The flowchart shown in Figure 4-8 gives an overview of the component stochastic calculation procedure giving a hot-spot stress transfer function used in subsequent fatigue calculations. If the geometry and dimensions of
22 Page 22 the given detail does not have predefined SCFs, the stress concentration factor need to be found through a stress analysis using a stress concentration model for the detail, see CN 30.7 /4/. In such cases the procedure and results shall be documented together with the results from the fatigue analysis. A short overview of the procedure for stiffener end connections and plate connections is given in Section and Section 4.5.3, respectively. Figure 4-8 DNV component stochastic fatigue analysis procedure Considered loads The loads considered normally include: vertical hull girder bending moment horizontal hull girder bending moment hull girder axial force internal tank pressure external (panel) pressures. In the surface region the transfer function for external pressures should be corrected by the r p factor as explained in Section , and as given in CN 30.7 /4/, to account for intermittent wet and dry surfaces. The tank pressures are based on the procedure given in Section
23 Page Stiffener end connections Fatigue calculations for stiffener end connections are to be carried out for end connections at ordinary frames and at transverse bulkheads. Note that the web-connection of longitudinals (cracks of web-plating) is not covered by the CSA-notations. This is covered by PLUS notation only, and shall follow the PLUS procedure Nominal stress per unit load The stresses considered are stress due to: global bending and elongation local bending due to internal and external pressure relative deflections due to internal and external pressure. Stress from double side or double bottom bending may be neglected in the CSA analyses since these stresses are relative small and varies for each frame. The stress due to relative deflection is only assessed for the bulkhead connections, where the stress due to relative deflection will add on to the stress due to local bending and hence reduce the fatigue life. A description of the relative deflection procedure is given in Appendix A. Formulas for nominal stress per unit load are given in CN They may alternatively be found from FEanalysis Hotspot stress The nominal stress transfer function is further multiplied with stress concentration factors as defined in CN For end connections of longitudinals, they are typically defined for axial elongation and local bending. The total hotspot stress transfer function is determined by linear complex summation of the stresses due to each load component Plating Fatigue calculations for plating are carried out for the plate welds towards stiffeners/longitudinals and frames as illustrated in Figure 4-3. The stress in the weld for a plate/frame connections consist of the following responses: local plate bending due to external/internal pressure global bending and elongation. For a plate/longitudinal connection the global effects may be disregarded and only the contributions from stresses in transverse directions are included. The total stress in the welds for a plate/longitudinal connection is mainly caused by the following responses: local plate bending relative deflection between a stringer/girder and the nearby stiffener rotation of asymmetrical stiffeners due to local bending of stiffener. These three effects are illustrated in Figure 4-9. Figure 4-9 Nominal stress components due to local bending (left), relative deflection between stiffener and stringers/girders (middle) and rotation of asymmetrical stiffeners (right) The local plate bending is the dominating effect, but relative deflection and skew bending may increase the stresses with up to 20%. This effect should be considered and investigated case by case. As guidance, the following factors can be used to correct the stress calculations for a plate/longitudinal connection: plate weld towards stringer/girder 1.15 plate weld towards L-stiffener 1.1
24 Page 24 The combined nominal stress transfer function is determined by linear complex summation of the stresses due to each load component Hotspot stress The nominal stress transfer function is further multiplied with stress concentration factors as defined in CN The total hotspot stress transfer function is determined by linear complex summation of the stresses due to applicable load components. 4.6 Full stochastic fatigue analysis General A full stochastic fatigue analysis is performed using a global structural model and local fine-mesh sub-models. This method requires that the wave loads are transferred directly from the hydrodynamic analysis to the structural model. The hydrodynamic loads include panel pressures, internal tank pressures and inertia loads due to rigid body accelerations. By direct load transfer the stress response transfer functions are implicitly described by the FE analysis results, and the load transfer ensures that the loads are applied consistently, maintaining load-equilibrium. Quality assurance is important when executing the full stochastic method. The structural and hydrodynamic analysis results should have equal shape and magnitude for the bending moment and shear force diagrams. Also, the reaction forces due to unbalanced loads in the structural analysis should be minimal. Figure 4-10 shows a flow chart for the full stochastic fatigue analysis using a global model. References to relevant sections in this CN are given for each step. Figure 4-10 Full stochastic fatigue analysis procedure The analysis is based on a global finite element model including the entire vessel in addition to local models of specified critical details in the hull. Local models are treated as sub models to the global model and the
25 Page 25 displacements from the analysis are transferred to the local model as boundary displacements. From local stress concentration models the geometric stress transfer functions at the hot spots are determined by the t x t elements that pick up the stress increase towards the hotspot. The hotspot transfer functions are combined with the wave scatter diagram and S-N data and the fatigue damage is summarised from each heading for all sea states in the scatter diagram (wave period and wave height) Global screening analysis The global screening analysis is a full stochastic fatigue analysis performed on the global model, or parts of the global model, using a SCF typical for the details investigated. The global screening analysis generally has four different purposes: calculate allowable stress concentrations in deck find the most fatigue critical detail from a number of similar or equal details establish a fatigue ratio between identical details evaluate if there are fatigue critical details that are not covered in the specification. Note that the global screening analysis only includes global effects as global bending and double bottom bending. Local effects from stiffener bending, etc. are not included Allowable stress concentration in deck A significant part of the total fatigue cracks occur in the deck region. This is mainly due to the large nominal stresses in parts of this area and the fact that there are many cut-outs, attachments, etc. leading to local stress increases. A crack in the deck is considered critical since a crack propagating in the deck will reduce the effective hull girder cross section. Even if a crack in the deck will be discovered at an early stage due to easy inspection and high personnel activity, it is important to control the fatigue of the deck area. The nominal stress level in the deck varies along the ship, normally with a maximum close to amidships. Larger openings, structural discontinuities, change in scantlings or additional structure will change the stress flow and lead to a variation of stress flow both longitudinally and transversely. The information from the fatigue screening analysis may be used together with drawing information about details in the deck. Typical details that need to be taken into consideration are: deck openings butt weld in the deck (including effect of eccentricity and misalignment) scallops cut outs, pipe-penetrations and doubling plates. The stress concentrations for each of these details need to be compared to the results from the global screening analysis in order to show that the required fatigue life is obtained for all parts of the deck area Finding the most critical location for a detail A ship will have many identical or similar details. It is not always evident which ones are more critical, since they are subject to the same loads, but with different amplitudes and combinations. Through a global screening analysis, the most critical location might be identified, by comparing the global effects. Local effects, which may be of major importance for the fatigue damage, are not captured in the global screening analysis. Element mesh must be identical for the positions that are compared; otherwise the effect of changing the mesh may override the actual changes in loads. An example of the result from a global screening for one detail type is shown in Figure 4-11 where relative damage between different positions in a ship is shown for three different tanks.
26 Page 26 Lower Chamfer Knuckle Screening Results TBHD Pos. Local Model Result 1.5 Fatigue Damage [-] Distance from AP [mm] Figure 4-11 Fatigue screening example relative damage between different positions Fatigue ratio between different positions The fatigue calculations used for relative damage between different positions for identical details helps evaluate where reinforcements are necessary. E.g. if local reinforcements are necessary in the middle of the cargo hold for the example shown in Figure 4-11, it may not be needed towards the ends of the cargo hold. New detailed fatigue calculations should be performed in order to verify fatigue lives if different reinforcement methods are selected Finding critical locations not specified for the vessel By specifying a critical level for relative damage the model can be scanned for elements that exceed the given limit, indicating that it may be a fatigue critical region. Since not all effects are included the results are not reliable, but will give an overview of potential problem areas. This exercise will also help confirm assumed critical areas from the specifications stage of the project in addition to point at new critical areas Local fatigue analysis The full stochastic detailed analysis is used to calculate fatigue damages for given details. The analysis is normally performed either for details where the stress concentration is unknown, or where it is not possible to establish a ratio between the load and stress. Full stochastic calculations may also be used for stiffener end connections and bottom/side shell plating, and will in that case overrule the calculations from the component stochastic analysis. Several types of models can be used for this purpose: local model as a part of the global model local shell element sub-model local solid element model. If sub-models are used, the solution (displacements) of the global analysis is transferred to the local models. The idea of sub-modelling is in general that a particular portion of a global model is separated from the rest of the structure, re-meshed and analysed in greater detail. The calculated deformations from the global analysis are applied as boundary conditions on the borders of the sub-models, represented by cuts through the global model. Wave loads corresponding to the global results are directly transferred from the wave load analysis to the local FE models as for the global analysis. It is not always easy to predefine the exact location of the hotspot, or the worst combination of stress
27 Page 27 concentration factor and load level, and therefore the fine-mesh model frequently does not include fine mesh in all necessary locations. The local model shall be screened outside the already specified hotspot to evaluate if other locations in close proximity may be prone to fatigue damage, requiring evaluation with mesh size in the order of t t. This can be performed according to the procedure shown in Section Determination of hotspot stress General From the results of the local structural analysis, principal stress transfer functions at the notch are calculated for each wave heading. In general, quadratic shaped elements with length equal to the plate thickness are applied at the investigated details, and the geometry of the weld is not represented in the model. Since the stresses are derived in the element gauss points, it is necessary to extrapolate the stresses to the considered point. The extrapolation procedure is given in CN30.7 /4/. Alternatively to the extrapolation procedure, the stress at t/2 multiplied with 1.12 is also appropriate for the stress evaluation at the hotspot Cruciform connections At web stiffened cruciform connections the following fatigue crack growth is not linear across the plate, and the stresses need to be specially considered. The procedures for the cruciform joints and extrapolation to the weld toe are described in CN 30.7 /4/ Stress concentration factor The total stress concentration K is defined as: Also other effects, like eccentricity of plate connections, need to be considered together with the stress-results from the fine-mesh analysis. This needs to be included in the post-processing. 4.7 Damage calculation σ K = σ hot spot no min al Acceptance criteria Calculated fatigue damage shall not be above 1.0 for the design life of the vessel. Owner may require lower acceptable damage for parts of the vessel. The fatigue strength evaluation shall be carried out based on the target fatigue life and service area specified for the vessel, but minimum 20 years world wide, for vessels with Nauticus (Newbuilding), or 25 years North Atlantic, for vessels with CSR notation. The owner may require increased fatigue life compared to the minimum requirement Cumulative damage Fatigue damage is calculated on basis of the Palmgrens-Miner rule, assuming linear cumulative damage. The damage from each short term sea state in the scatter diagram is added together, as well as the damage from heading and load condition S-N curves The fatigue accumulation is based on use of S-N curves that are obtained from fatigue tests. The design S-N curves are based on the mean-minus-two-standard-deviation curves for relevant experimental data. The S-N curves are thus associated with a 97.6% probability of survival. Relevant S-N curves according to CN 30.7 /4/ should be used. It is important that consistency between S-N curves and calculated stresses is ensured Effect of corrosive environment Corrosion has a negative effect on the fatigue life. For details located in corrosive environment (as water ballast or corrosive cargo) this has to be taken into account in the calculations. For details located in water ballast tanks with protection against corrosion or where the corrosive effect is small, the total fatigue damage can be calculated using S-N curve for non-corrosive environment for parts of the design life and S-N curve for corrosive environment for the remaining part of the design life. Guidelines on which S-N curve to use and the fraction in corrosive and non-corrosive environment are specified by CN 30.7 /4/.
28 Page 28 For details without corrosion protection, a S-N curve for corrosive environment has to be used in the calculations for the entire lifetime Thickness effect The fatigue strength of welded joints is to some extent dependent on plate thickness and on the stress gradient over the thickness. Thus for thickness larger than 25 mm, the S-N curve in air reads where t is thickness (mm) through which the potential fatigue crack will grow. This S-N curve in general applies to all types of welds except butt-welds with the weld surface dressed flush and with small local bending stress across the plate thickness. The thickness effect is less for butt welds that are dressed flush by grinding or machining. The above expression is equivalent with an increase of the response with Mean stress effect The procedure for the fatigue analysis is based on the assumption that it is only necessary to consider the ranges of cyclic principal stresses in determining the fatigue endurance. However, some reduction in the fatigue damage accumulation can be credited when parts of the stress cycle are in compression. A factor, f m, accounting for the mean stress effect can be calculated based on a comparison of static hotspot stresses and dynamic hotspot stresses at a 10-4 probability level Base material For base material, f m varies linearly between 0.6 when stresses are in compression through the entire load cycle to 1.0 when stresses are in tension through the entire load cycle Welded material For welded material, f m varies between 0.7 and Improvement of fatigue life by fabrication It should be noted that improvement of the toe will not improve the fatigue life if fatigue cracking from the root is the most likely failure mode. The considerations made in the following are for conditions where the root is not considered to be a critical initiation point for fatigue cracks. Experience indicates that it may be a good design practice to exclude this factor at the design stage. The designer is advised to improve the details locally by other means, or to reduce the stress range through design and keep the possibility of fatigue life improvement as a reserve to allow for possible increase in fatigue loading during the design and fabrication process. It should also be noted that if grinding is required to achieve a specified fatigue life, the hot spot stress is rather high. Due to grinding a larger fraction of the fatigue life is spent during the initiation of fatigue cracks, and the crack grows faster after initiation. This implies use of shorter inspection intervals during service life in order to detect the cracks before they become dangerous for the integrity of the structure. The benefit of weld improvement may be claimed only for welded joints which are adequately protected from corrosion. The following methods for fatigue improvement are considered: weld toe grinding (and profiling) TIG dressing hammer peening. m t log N = loga log mlogδσ 4 25 Δ σ resp t 25 = Among these three, weld toe grinding is regarded as the most appropriate method, due to uncertainties regarding quality assurance of the other processes. The different fatigue improvements by welding are described in CN 30.7 /4/. 1 4
29 Page Ultimate Limit State Assessment 5.1 Principle overview General The Ultimate Limit State (ULS) analyses shall cover necessary assessments for dimensioning against material yield, buckling and ultimate capacity limits of the hull structural elements like plating, stiffeners, girders, stringers, brackets, etc. in the cargo region. ULS assessments shall also ensure sufficient global strength in order to prevent hull girder collapse, ductile hull skin fracture and compartment flooding. Two levels of ULS assessments are to be carried out, i.e. global FE analyses - local ULS hull girder collapse - global ULS. The basic principles behind the two types of assessments are described in more detail in the following Global FE analyses local ULS The local ULS design assessment is based on a linear global FE model with automatic load transfer from hydrodynamic wave load programs. The design of the structural elements in different areas of the ship, are covered by different design conditions. Each design condition is defined by a loading condition and a governing sea state/wave condition, which together are dimensioning for the structural element. For each design condition the calculation procedure follows the flow chart in Figure 5-1, i.e. the static and hydrodynamic wave loads for the loading condition are transferred to the structural FE model for a linear nominal stress assessment. The nominal stresses are to be measured against material yield, buckling and ultimate capacity criteria of individual stiffened panels, girders etc. The material yield checks cover von Mises stress control using a cargo hold model, and for high peak stressed areas using local fine-mesh models. The local ULS buckling control follow two different principles, allowing and not allowing elastic buckling, depending on the elements main function in the global structure, using PULS /8/. The procedure for local ULS assessment is further described in Section Hull girder collapse - global ULS The hull girder collapse criteria are used to check the total hull section capacity against the corresponding extreme global loads. This is to be carried out for the mid-ship area for one intact and two damaged hull conditions. Specially developed hull girder capacity models based on simplified non-linear theory or fullblown FE analyses are to be used for assessing the hull capacity. The extreme loads are to be based on direct calculations and the static + dynamic load combination giving the highest total hull girder moment shall be used, including both the extreme sagging and hogging condition. For some ship types other sections than the mid-ship area may be relevant to be checked, if deemed necessary by the Society. This applies in particular to hull sections which are transversely stiffened, e.g. engine room of container ships etc. The procedure for the global ULS assessment is further described in Section Scantlings/corrosion model All FE calculations shall be based on the net scantlings methodology as defined by the relevant class notations NAUTICUS (Newbuilding) or CSR. The buckling calculations are to be carried out on net scantlings. 5.2 Global FE analyses local ULS General The local ULS design assessment is based on a linear global FE analysis with automatic load transfer from hydrodynamic programs, as schematically illustrated in Figure 5-1.
30 Page 30 Figure 5-1 Flowchart for ULS analysis: Load transfer: Hydro Global FE model Selection of design loads, and procedures for selection of stress and application of the yield and buckling criteria is described in the following Designloads General This section is closely linked to Section 3, which explains how hydrodynamic analyses are to be performed Design condition and selection of critical loading conditions The design loading conditions are to be based on the vessels loading manual and shall include ballast, full load and part load conditions as relevant for the specific ship type. The loading conditions and dynamic loads are selected such that they together define the most critical structural response. Depending on the purpose of the design condition, e.g. the region to be analysed and failure mode (yield/buckling) for the structural elements, different loading conditions and design waves are required to ensure that the relevant response is at its maximum. Any loading condition in the loading manual that, combined with its hydrodynamic extreme loads, may result in the design loads should be evaluated. For each loading condition, hydrodynamic analysis shall be performed, forming the basis for selection of design waves and stress assessment. For areas where non-linear effects are not necessary to consider (e.g. for transverse structural members) a design wave need not be defined. The design stress is then based on long-term stress, where the stress at 10-8 probability level for the loading condition is found. A design wave is required if non-linear effects need to be considered. The design wave may be defined based on structural response, or wave load, depending on the purpose of the design condition.
31 Page 31 Table 5-1 gives an overview of the design conditions that need to be evaluated, and should at a minimum be covered. Additional design conditions need to be evaluated case by case, depending on the ships structural configuration, trading/operational conditions, etc, which may require several design conditions to ensure that all the structures critical failure modes are covered Hydrodynamic analysis The hydrodynamic analyses are to be performed for the selected critical loading conditions. A vessel speed of 5 knots is to be used for application of loads that are dominated by head seas. For design conditions where the driving response is dominated by beam or quartering seas, the speed is to be taken as 2/3 of design speed Design life and wave environment Wave environment is minimum to be the North Atlantic wave environment as defined in the CN 30.7 /4/. If other wave environment is required by design, it should not be less severe than the North Atlantic wave environment. The hydrodynamic loads are to be taken as 10-8 probability of exceedance according to Pt.3 Ch.1 Sec.3 B300 and Pt.8 Ch.1 Sec.2 for Nauticus (Newbuilding) and CSR respectively, using a cos 2 wave spreading function and equal probability of all headings Design waves The design waves used in the hydrodynamic analysis should basically cover the entire cargo hold area. Different design waves are used to check the capacity of different parts of the ship. It is important that the design waves are not used outside the area for which the design wave is valid, i.e. a design wave made for tank no.1 must not be used amidships. An overview of the relation between the design loads and areas they are applicable for should be checked against the different design loads is given in Table 5-1. The design conditions together with its applicable loading condition and design load need to be reviewed on project basis. It can be agreed with Classification Society that some design conditions can be removed based on review of design together with loading conditions and operational profile. It is considered that only design waves which represents vertical bending moment and vertical shear force need to be performed with non-linear hydrodynamic analysis Load transfer A load transfer (snap-shot) from the hydrodynamic analysis to the structural analysis shall be performed when the total load/response from the hydrodynamic time-series is at its maximum/minimum. The load transfer shall include both gravitational and inertial loads, and the still water and wave pressures, see Section 3.6. Table 5-1 Guidance on loading condition selection Design Condition Reference Design area Loading condition Typical loading ID load/response pattern (Dominant or max load/response) 1A 1B 2A 2B 3A 3B hogging bending moment Sagging bending moment Hogging + double bottom bending Sagging + double bottom bending Shear force at aft quarter length Shear force at fwd quarter length Midship (global hull) Midship (global hull) Midship double bottom Transverse bulkheads Midship double bottom Aft hold shear elements Fwd hold shear elements Max/large hogging bending moment Max/large sagging bending moment Large hogging combined with deep draft Large sagging combined with shallow draft Max shear force aft Max shear force fwd Loading condition & design loads Tanks/hold empty across with adjacent tanks/hold full Tanks/hold full across with adjacent tanks/hold empty Design wave (maximised response/load) Max hogging wave moment Max sagging wave moment Max hogging wave moment Max sagging wave moment Max wave shear force at aft quarterlength Max wave shear force at fwd quarter length
32 Page 32 Table 5-1 Guidance on loading condition selection (Continued) Design Condition Loading condition & design loads Reference Design area Loading condition Typical loading Design wave load/response pattern (maximised response/load) ID (Dominant or max load/response) 4A 4B 5 6 Internal pressure/ load in no.1 tank/hold External pressure at no.1 tanks/hold Combined vertical, horizontal and torsional bending Maximum transverse loading Tank no 1 double bottom Tank no.1 double bottom Entire cargo region Entire cargo region Loaded at shallow draft fwd Loaded at deep draft fwd Loaded condition with large GM combined with large hogging for hogging vessels or large sagging for sagging vessels Loaded with maximum GM Design stress General Based on the global FE analysis a nominal stress flow in the hull structure is available. This nominal stress flow shall be checked against material yield and acceptable buckling criteria (PULS). The nominal stresses produced from the FE analysis will be a combination of the stress components from several response effects, which in a simplistic manner can be categorized as follows: hull girder bending moment hull girder shear force hull girder axial loads (small) hull girder torsion and warping effects (if relevant) double side/bottom bending local bending of stiffener local bending of plates transverse stresses from cargo and sea pressure transverse and shear stresses from double hull bending other stress effects due to local design issues; knuckles, cut-outs etc. Guidelines for determining design stresses are given in the following. No.1 tanks/hold full across with no.2 tanks/hold empty No.1 tanks/hold empty across with no.2 tanks/hold full Maximum vertical accelerations at no.1 tanks/hold in head sea Maximum bottom wave pressure at no.1 tanks/hold in head seas Design wave(s) in quartering/beam sea condition: maximised torsion maximised horizontal bending maximised stress at hatch corners/ large openings Maximum transverse acceleration Material yield assessment In the material yield control all effects are to be included apart from local bending stress across the thickness of the plating. This means that the yield check involves the von Mises stress based on membrane stresses and shear stresses in the structure evaluated in the middle plane of plating, stiffener webs and stiffener flanges. For cases where large openings are not modelled in the FE-analysis, either as cut-outs or by reduced thickness, see Section , the von Mises stress should be corrected to account for this. In areas with high peaked stress, where the von Mises stress exceeds the acceptance criteria, the structure should be evaluated using a stress concentration model (t x t mesh). Frame and girder models (stiffener spacing mesh or equivalent) that reflect nominal stresses should not be used for evaluation of strain response in yield areas. Areas above yield from the linear element analysis may give an indication of the actual area of plastification. Non-linear FE analysis may be used to trace the full extent of plastic zones, large deformations, low cycle fatigue etc. but such analyses are normally not required. For evaluation of large brackets, the stress calculated at the middle of a bracket s free edge is of the same magnitude for models with stiffener spacing mesh size as for models with a finer mesh. Evaluation of brackets of well-documented designs, may be limited to a check of the stress at the free edge. When 4-node elements are used, fictitious bar elements are to be applied at the free edge to give a straightforward read-out of the critical edge stress. For brackets where the design needs to be verified, a fine mesh model needs to be used.
33 Page 33 σ = Figure 5-2 Bracket stress to be used Buckling assessment In order to be consistent with available buckling codes the nominal stress pattern has to be simplified, i.e. stress gradients has to be averaged and the local bending stress due to lateral pressure effects has to be eliminated. The membrane stress components used for buckling control shall include all effects listed in Section , except for the stresses due to local stiffener and plate bending, since these effects are included in the buckling code itself. When carrying out the local ULS-buckling checks the nominal FE stress flow has to be simplified to a form consistent with the local co-ordinate system of the standard buckling codes. In the PULS buckling code the biaxial and shear stress input reads (see Figure 5-3): σ 1 axial nominal stress in primary stiffener and plating (normally uniform*) (sign convention in buckling code (PULS): positive stress in compression, negative stress in tension) σ 2 transverse nominal stress in plating. Normally uniform stress distribution, but it can vary linearly across the plate length in the PULS code, also into the tension range; σ 2,1 σ 2,2 at plate ends) τ 12 nominal in-plane shear stress in plating (uniform and as assessed by Section p net uniform (average) lateral pressure from sea or cargo (positive pressure acting on flat plate side). Primary stiffeners x - direction 1 Secondary stiffeners x 2- direction (if any) Figure 5-3 PULS nominal stress input for uni-axially or orthogonally stiffened panels (bi-axial + shear stresses)
34 Page 34 Note: Varying stress along the plate edge can be considered by checking each stiffener for the stress acting at that position. Since the PULS buckling model only consider uniform stresses, a fictive PULS model have to be used with the actual number of stiffener between rigid lateral supports (girders etc.) or limited by maximum 5 stiffeners) The local plate bending stress is easily excluded by using membrane stresses in the plating. The stiffener bending stress can not directly be excluded from the stress results unless stresses are visualised in the combined panel neutral axis. This is, for most program systems, not feasible. Figure 5-4 Stiffener bending stress - mesh variations The magnitude of the stiffener bending stress included in the stress results depends on the mesh division and the element type that is used. This is shown in Figure 5-4 where the stiffener bending stress, as calculated by the FE-model, is shown dependent on the mesh size for 4-node shell elements. One element between floors results in zero stiffener bending. Two elements between floors result in a linear distribution with approximately zero bending in the middle of the elements. When a relatively fine mesh is used in the longitudinal direction the effect of stiffener bending stresses should be isolated from the girder bending stresses for buckling assessment. For the buckling capacity check of a plate, the mean shear stress, τ mean is to be used. This may be defined as the shear force divided on the effective shear area. The mean shear stress may be taken as the average shear stress in elements located within the actual plate field, and corrected with a factor describing the actual shear area compared to the modelled shear area when this is relevant. For a plate field with n elements the following apply: where: A W A Wmod ( τ + τ τ ) = effective shear area according to the Rules for Classification of Ships, Pt.3 Ch.1 Sec.3 C503 = shear area as represented in the FE model Local buckling assessment - plates, stiffeners, girders etc General Buckling control of plating, stiffeners and girders/floors shall be carried out according to acceptable design principles. All relevant failure modes and effects are to be considered such as plate buckling local buckling of stiffener and girder web plating torsional/sideways buckling and global (overall) buckling of both stiffeners and girders interactions between buckling modes, boundary effects and rotational restraints between plating and stiffeners/girders free plate edge buckling to be excluded by fitting edge stiffeners unless detailed assessments are carried out. The buckling design of stiffened panels follows two main principles, namely: τ mean = 1 2 n n A A Wmod W
35 Page 35 Method 1 Ultimate Capacity (UC): The stiffened panels are designed against their ultimate capacity limit thus accepting elastic buckling of plating between stiffeners and load redistributions from plating to stiffeners/girders. No major von Mises yielding and development of permanent sets/buckles should take place. Method 2 Buckling Strength (BS): The stiffened panels are designed against the buckling strength limit. This means that elastic buckling of neither the plating nor the stiffeners are accepted and thus redistribution of loads due to buckling are avoided. The buckling strength (BS) is the minimum of the Ultimate Capacity (UC) and the elastic buckling strength (minimum Eigenvalue). The load bearing limits using Method 1 and Method 2 will be coincident for moderate to slender designs while they will diverge for slender structures with the Method 1 giving the highest load bearing capacity. This is due to the fact that Method 1 accept elastic plate buckling between stiffeners and utilize the extra post-buckling capacity of flat plating ( overcritical strength ) while Method 2 cuts the load bearing capacity at the elastic buckling load level. From a design point of view Method 1 principle imply that thinner plating can be accepted than using Method 2 principle. These principles are implemented in PULS buckling code /8/, which is the preferred tool for buckling assessment, see Appendix E Application Method 1 design principles are in general used for stiffened panels relevant for the longitudinal strength, or the main elements that contribute to the hull girder, while Method 2 design principles are used for the primary support members of the hull girder, e.g. panels that form the web-plating of girders, stringers and floors. Table 5-2 summarises which method to use for different structural elements. Table 5-2 Application of Method 1 and Method 2 Method 1 Method 2 1) bottom-shell side-shells deck inner bottom longitudinal bulkheads transverse bulkheads girders stringers floors 1) Webs that may be considered to have fixed in-plane boundary-conditions, e.g. girders below longitudinal bulkheads, can utilize Method 1 For Method 1 the panel can be uni-axially stiffened or orthogonally stiffened. The latter arrangement is illustrated in Figure 5-5. In general the application of Method 1 versus Method 2 follows the same principles as IACS-CSR Tanker Rules, see the Rules for Classification of Ships, Pt.8 Ch.1 App. D.5.2.
36 Page 36 Figure 5-5 Schematic illustration of elastic plate buckling (load in x 2 -direction); load shedding from plating towards the stiffeners takes place when designing according to Method 1 principle (i.e. reduced effective plate width/stiffness due to buckling) Other structures Pillars, brackets etc For designs where the buckling strength of structural members apart from the longitudinal material in cargo region, the following guidelines may be used as reference for assessment: Pillars, IACS/CSR Sec.10, Part Brackets, IACS/CSR Sec.10, Part Cut-outs, openings IACS/CSR Sec.10, Part and Part Reinforcements of free edges, i.e. in way of openings, brackets, stringers, pillars etc. IACS/CSR Sec.10, Part The buckling and ultimate strength control of unstiffened and stiffened curved panels (e.g. bilge) may be performed according to the method as given in DNV-RP-C202, Ref. /2/ Acceptance criteria General Acceptance requirements are given separately for material yield control and buckling control even though the latter also includes yield checks locally in plate and stiffeners. The yield check is related to the nominal stress flow in the structure, i.e. the local bending across the plate thickness is not included. The buckling check is also based on the nominal stress flow idealized as described in Section to be consistent with input to the PULS buckling code. The check includes secondary stress effects due to imperfections and elastic buckling effects, thus preventing major permanent sets Material yield check The longitudinal hull girder and main girder system nominal and local stresses derived from the direct strength calculations are to be checked according to the criteria specified listed below. Allowable equivalent nominal von Mises stresses (combined with relevant still water loading) are given in Table 5-3: Table 5-3 Allowable stress levels von Mises membrane stress Seagoing condition General σ e = 0.95 σ f N/mm 2
37 Page 37 For areas with pronounced geometrical changes local linear peak stresses (von-mises membrane) of up to 400 f 1 may be accepted provided plastic mechanisms are not developed in the associated structural parts Buckling check The ULS local buckling check for stiffened panels follows the guidelines as given in Section using the PULS buckling code. For other structures the guidelines in Section apply. The acceptance level is as follows: the PULS usage factor shall not exceed 0.90 for stiffened panels, girder web plates etc. This applies for Method 1 and Method 2 principle Alternative methods non-linear FE etc Alternative non-linear capacity assessment of local panels, girders etc. using recognised non-linear FE programs are acceptable on a case by case evaluation by the Society. In such cases, inclusion of geometrical imperfections, residual stresses and boundary conditions needs careful evaluation. The models should be capable of capturing all relevant buckling modes and interactions between them. The accept levels are to be specially considered. 5.3 Hull girder collapse - global ULS General The hull girder collapse criteria shall ensure sufficient safety margins against global hull failure under extreme load conditions and the vessel shall stay afloat and be intact after the incident. Buckling, yielding and development of permanent sets/buckles locally in the hull section are accepted as long as the hull girder does not collapse and break with hull skin cracking and compartment flooding. The hull girder collapse criteria involve the vertical global bending moments in the considered critical section and have the general format γ S M S + γ W M W M U / γ M where: M s = the still water vertical bending moment M w = the wave vertical bending moment M U = the ultimate moment capacity of the hull girder γ = a set of partial safety factors reflecting uncertainties and ensuring the overall required target safety margin. The actual loads M s and M w, giving the most severe combination in sagging and hogging respectively are to be considered. The hull girder capacity M U shall be assessed using acceptable methods recognized by the Society. Acceptable simplified hull capacity models are given in Appendix C. Appendix D describes alternative methods based on advanced non-linear FE analyses. The hull girder collapse criteria shall be checked for both sagging and hogging and for the intact and two damaged conditions, see Section The ultimate sagging and hogging bending capacities of the hull girder is to be determined for both intact and damaged conditions and checked according to criteria in Table 5-4. Global ULS shear capacity is to be specially considered if relevant for actual ship type and operating loading conditions Damage conditions There are two different damaged conditions to be considered; collision and grounding. The damage extents are shown in Figure 5-6 and further described in Table 5-4.
38 Page 38 Figure 5-6 Damage extent collision (left) and grounding (right) Table 5-4 Damage parameters Damage extent Single side/bottom Double side/bottom Height: h/d Collision in ship side Length: l/l Breath: b/b Grounding in ship bottom Length: l/l L - ship length, l - damage length All structure within a breath of B/16 is regarded as damaged for the collision case, while structure within a height of B/15 is regarded as damaged for the grounding case. Structure within the boxes shown in Figure 5-6 should have no structural contribution when hull girder capacity is calculated for the collision or grounding damage case. When assessing the ultimate strength (M U ) of the damaged hull sections the following principles apply: damaged area as defined in Table 5-4 carry no loads and is to be removed in the capacity model the intact hull parts and their strength depend on the boundary supports towards the damaged area, i.e. loss of support for transverse frames at shipside etc. The modelling of such effects need special considerations reflecting the actual ship design. The changes in still-water and wave loads due to the damages are implicitly considered in the load factors γ S and γ W, see Table 5-5. No further considerations of such effects are needed Hull girder capacity assessment (MU) - simplified approach Assuming quasi-static response the hull girder response is conveniently represented as a moment-curvature curve (M - κ) as schematically illustrated in Figure 5-6. The curve is non-linear due to local buckling and material yielding effects in the hull section. The moment peak value M U along the curve is defined as the ultimate capacity moment of the total hull girder section. For ships with varying scantlings in the longitudinal direction, changing stiffener spans, etc. the momentcurvature relation of the critical hull section should be analysed. Critical sections are normally found within the mid-ship area, but for some ship designs, like container vessels, critical sections can be outside 0.4 L, e.g. in the engine room area.
39 Page 39 Figure 5-7 Moment-curvature (M-κ) curve for hull sections, schematic illustration in sagging (quasi static loads) Accept criteria intact and damaged The ultimate hull girder capacity is calculated according to the accept criteria and limits shown in Table 5-5. Table 5-5 Hull girder strength check: accept criteria required safety factors Intact strength Damaged strength M S + γ W1 M W M UI /γ M γ S M S + γ W2 M W M UD /γ M where: where: M S = Still water moment M W = Design wave moment (20 year return period North Atlantic) M UI = Ultimate intact hull girder capacity γ W1 = 1.1 (partial safety factor for environmental loads) γ M = 1.15 (material factor) in general γ M = 1.30 (material factor) to be considered for hogging checks and designs with bi-axial/shear stresses conditions in bottom area, e.g. double bottoms etc. M S = Still water moment M W = Design wave moment (20 year return period North Atlantic) M UD = Damaged hull girder capacity γ S = 1.1 (factor on M S allowing for moment increase with accidental flooding of holds) γ W2 = 0.67 (hydrodynamic load reduction factor corresponding to 3 month exposure in world-wide climate) γ M = 1.0 in general γ M = 1.10 (material factor) to be considered for hogging checks and designs with bi-axial/shear stresses conditions in bottom area, e.g. double bottoms etc.
40 Page Structural Modelling Principles 6.1 Overview Model types The CSA analysis is based on a set of different structural FE-models. This section gives an overview of the structural (and mass) modelling required for a CSA analysis. The structural models as shown in Table 6-1 are normally included in a CSA analyses. Table 6-1 Structural models used in CSA analyses Model type Characteristics Used for The whole structure of the vessel Global analysis (FLS and ULS) S S mesh (girder spacing mesh) Cargo systems May include cargo hold model (stiffener Global structural model Buckling stresses spacing mesh) May include fine mesh (t t type mesh) Includes mass-model Cargo hold model Stress concentration model Part of vessel (typical cargo-hold model) s x s mesh (stiffener spacing mesh) May include fine mesh (t t type mesh) Includes mass-model, particularly when used as sub-model Fine mesh, (t t type mesh) Sub-model Size such that boundary effects are avoided Mass-model normally not included Global fatigue screening Yield stresses Buckling stresses Relative deflection analysis Detailed fatigue analysis Yield evaluation Figure 6-1, Figure 6-2 and Figure 6-3 show typical structural models used in a CSA analysis. Figure 6-1 Global model example, with cargo hold model included (port side shown)
41 Page 41 Figure 6-2 Stiffener spacing mesh (structural model of No.1 hold on left, and Midship cargo hold model on right) Figure 6-3 Stress concentration model Global structural model The global structural model is intended to provide a reliable description of the overall stiffness and global stress distribution in the primary members in the hull. The following effects shall be taken into account: vertical hull girder bending including shear lag effects, vertical shear distribution between ship side and bulkheads, horizontal hull girder bending including shear lag effects, torsion of the hull girder (if open hull type) transverse bending and shear. The mesh density of the model shall be sufficient to describe deformations and nominal stresses due to the effects listed above. Stiffened panels may be modelled by a combination of plate and beam elements. Alternatively, layered (sandwich) elements or anisotropic elements may be used. Since it is required to use a regular mesh density for yield evaluation and for global fatigue screening, it is recommended to model a region of the global model with stiffener spacing type mesh, by means of suitable element transitions to the coarse mesh model, see Figure 6-1. Since a full-stochastic fatigue analysis may include as much as 200 to 300 complex load cases the region of regular mesh density might need to be restricted to reduce computation time. If it is unpractical to include all desired areas with a regular mesh density, the
42 Page 42 remaining parts should be modelled as sub-models, see Section 6.4. The fatigue analysis and high stress yield areas require even denser mesh than that provided by regular mesh type. Including these meshes in the global model will increase the number of degrees of freedom and computational time even more, resulting in a database that is not easy to navigate. It is therefore normal to have separate sub-models with finer mesh regions complementing the global model. Figure 6-4 Global model with stiffener spacing mesh in Midship/cargo region Cargo hold model The cargo hold model is used to analyse the deformation response and nominal stress in primary structural members. It shall include stresses caused by bending shear and torsion. The model may be included in the global model as mentioned in Section , or run separately with prescribed boundary deformations or boundary forces from the global model. The element size for cargo hold models is described in ship specific Classification Notes and in CN 30.7 /4/. Vessels with CSR notation may follow the net-scantlings methodology of CSR, and the FE-model used for CSR assessment may also be used during CSA analysis. It should however be noted that stiffeners modelled co-centric for CSR shall be modelled eccentric for CSA Stress concentration model The element size for stress concentration models is well described in ship specific Classification Notes and in Classification Note No It is therefore not described here, even if it is a part of the global structural model. 6.2 General Properties All structural elements are to be modelled with net scantlings, i.e. deducting a corrosion margin as defined by the actual notation Unit system The unit system as given in Table 6-2 is recommended as this is consistent and easy to use in the DNV programs.
43 Page 43 Table 6-2 Unit System Measure Unit Length Millimetre [mm] Mass Metric tonne [Te] Time Second [s] Force Newton [N] Pressure and stress 10 6 Pascal [MPa or N/mm 2 ] Gravitation constant [mm/s 2 ] Density of steel [Te/mm 3 ] Young s modulus [N/mm 2 ] Poisson s ratio 0.3 [-] Thermal expansion coefficient 0.0 [-] Co-ordinate system The following co-ordinate system is proposed; right hand co-ordinate system, with the x-axis positive forward, y-axis positive to port and z-axis positive vertically from baseline to deck. The origin should be located at the intersection between aft perpendicular, baseline and centreline. The co-ordinate system is illustrated in Figure 6-5. z, up baseline y, port x, fwd centreline A.P. Figure 6-5 Co-ordinate system 6.3 Global structural FE-model Model extent The entire ship shall be modelled including all structural elements. Both port and starboard side need to be included in the global model All main longitudinal and transverse structure of the hull shall be modelled. Structure not contributing to the global strength of the vessel may be disregarded. The mass of disregarded elements shall be included in the model. The superstructure is generally not a part of the CSA scope and may be omitted. However, for some ships it will also be required to model the superstructure as the stresses in the termination of the cargo area are influenced by the superstructure. It is recommended to include the superstructure in order to easily include the mass Model idealisation Elements and mesh size of plates and stiffeners Where possible, a square mesh (length to breadth of 1 to 2 or better) should be adopted. A triangular mesh is
44 Page 44 acceptable to avoid out of plane elements, but not necessary since this can be handled by the analysis system. Plate elements should be modelled with linear (4- and 3-node) or quadratic (8- and 6-node) elements. Stiffeners may be modelled with two or three node elements (according to shell element type). The use of higher level elements such as 8-node or 6-node shell or membrane elements will not normally lead to reduced mesh fineness. 8-node elements are, however, less sensitive to element skewness than 4-node elements, and have no out of plane restrictions. In addition, 6-node elements provide significantly better stiffness representation than that of 3-node elements. Use of 6-node and 8-node elements is preferred but can be restricted by computer capacity. The following rules can be used as a guideline for the minimum element sizes to be used in a global/stiffness structural model using 4-node and/or 8 node shell elements (finer mesh divisions may be used): General: One element between transverse frames/girders Girders: One element over the height Beam elements may be used for stiffness representation Girder brackets: One element Stringers: One element over the width Stringer brackets: One element Hopper plate: One to two elements over the height depending on plate size Bilge: Two elements over curved area Stiffener brackets: May be disregarded. All areas not mentioned above should have equal element sizes. One example of suitable element mesh with suitable element sizes is illustrated by the fore and aft-parts of Figure 6-1. The eccentricity of beam elements should be included. The beams can be modelled eccentric, or the eccentricity may be included by including the stiffness directly in the beam section modulus Modelling of girders Girder webs shall be modelled by means of shell elements in areas where stresses are to be derived. However, flanges may be modelled using beam and truss elements. Web and flange properties shall be according to the actual geometry. The axial stiffness of the girder is important for the global model and hence reduced efficiency of girder flanges should not be taken into account. Web stiffeners in direction of the girder should be included such that axial, shear and bending stiffness of the girder are according to the girder dimensions. The mean girder web thickness in way of cut-outs may generally be taken as follows for r co values larger than 1.2, (r co > 1.2): Figure 6-6 Mean girder web thickness where: t mean h h = h r co co t W t w = web thickness r co = co ( h h ) 2 co l co = length of cut-out h co = height of cut-out l
45 Page 45 h = height of girder web For large values of r co (> 2.0), geometric modelling of the cut-out is advisable Boundary conditions The boundary conditions for the global structural model should reflect simple supports that will avoid built-in stresses. A three-two-one fixation, as shown in Figure 6-7, can be applied. Other boundary conditions may be used if desirable. The fixation points should be located away from areas of interest, as the loads transferred from the hydrodynamic load analysis may lead to imbalance in the model. Fixation points are often applied at the centreline close to the aft and the forward ends of the vessel. Figure 6-7 Example of boundary conditions Ship specific modelling Membrane type LNG carrier The stiffness of the tank system is normally not included in the structural FE-model. Pressure loads are directly transferred to the inner hull Spherical LNG carriers The spherical tanks shall be modelled sufficiently accurate to represent the stiffness. A mesh density in the order of 40 elements around the circumference of a tank will normally be sufficient. However, the transition towards the hull will normally have a substantially finer mesh. The mesh density of the cover has to be consistent with the hull mesh. Special attention should be given to the deck/cover interaction as this is a fatigue critical area LPG/LNG carrier with independent tanks The tank supports will normally only transfer compressive loads (and friction loads). This effect need to be accounted for in the modelling. A linearization around the static equilibrium will normally be sufficient. 6.4 Sub models General The advantage of a sub-model (or an independent local model), as illustrated in Figure 6-2, is that the analysis is carried out separately on the local model, requiring less computer resources and enabling a controlled step by step analysis procedure to be carried out. For this sub model, the mass data must be as for the global model in order to ensure correct inertia loads. The various mesh models must be compatible, i.e. the coarse mesh models shall produce deformations and/ or forces applicable as boundary conditions for the finer mesh models (referred to as sub-models). Sub-models (e.g. finer mesh models) may be solved separately by use of the boundary deformations/ boundary forces and local internal loads transferred from the coarse model. This can be done either manually or, if submodelling facilities are available, automatically by the computer program. The sub-models shall be checked to ensure that the deformations and/or boundary forces are similar to those obtained from the coarse mesh model. Furthermore, the sub-model shall be sufficiently large that its boundaries are positioned at areas where the deformation/ stresses in the coarse mesh model are regarded as accurate. Within the coarse model, deformations at web frames and bulkheads are usually accurate, whereas
46 Page 46 deformations in the middle of a stiffener span (with fewer elements) are not sufficiently accurate. The sub-model mesh shall be finer than that of the coarse model, e.g. a small bracket is normally included in a local model, but not in global model Principle Sub-models using boundary deformations/forces from a coarse model may be used subject to the following rules. The rules aim to ensure that the sub-model provides correct results. These rules can, however, vary for different program systems. The sub-model shall be compatible with the global (parent) model. This means that the boundaries of the sub-model should coincide with those elements in the parent model from which the sub-model boundary conditions are extracted. The boundaries should preferably coincide with mesh lines as this ensures the best transfer of displacements / forces to the sub-model. Special attention shall be given to: 1) Curved areas. Identical geometry definitions do not necessarily lead to matching meshes. Displacements to be used at the boundaries of the sub-model will have to be extrapolated from the parent model. However, only radial displacements can be correctly extrapolated in this case, and hence the displacements on sub-model can consequently be wrong. 2) The boundaries of the sub-model shall coincide with areas of the parent model where the displacements/ forces are correct. For example, the boundaries of the sub-model should not be midway between two frames if the mesh size of the parent model is such that the displacements in this area cannot be accurately determined. 3) Linear or quadratic interpolation (depending on the deformation shape) between the nodes in the global model should be considered. Linear interpolation is usually suitable if coinciding meshes (see above) are used. 4) The sub-model shall be sufficiently large that boundary effects, due to inaccurately specified boundary deformations, do not influence the stress response in areas of interest. A relatively large mesh in the parent model is normally not capable of describing the deformations correctly. 5) If a large part of the model is substituted by a sub model (e.g. cargo hold model), then mass properties must be consistent between this sub-model and the parent model. Inconsistent mass properties will influence the inertia forces leading to imbalance and erroneous stresses in the model. 6) Transfer of beam element displacements and rotations from the parent model to the sub-model should be especially considered. 7) Transitions between shell elements and solid elements should be carefully considered. Mid-thickness nodes do not exist in the shell element and hence special transition elements may be required. The model shall be sufficiently large to ensure that the calculated results are not significantly affected by assumptions made for boundary conditions and application of loads. If the local stress model is to be subject to forced deformations from a coarse model, then both models shall be compatible as described above. Forced deformations may not be applied between incompatible models, in which case forces and simplified boundary conditions shall be modelled Boundary conditions The boundary conditions for the sub-model are extracted from the parent model, as displacements applied to the edges of the model, and pressures are applied to the outer shell and tank boundaries. Sub-model nodes are to be applied to the border of the models which are given displacements as found in parent model. 6.5 Mass modelling and load application General The inertia loads and external pressures need to be in equilibrium in the global FE-analysis, keeping the reaction forces at a minimum. The sum of local loads along the hull needs to give the correct global response as well as local response for further stress evaluation. Since the inertia and wave pressures are obtained and transferred from the hydrodynamic analysis, using the same mass-model for both structural analysis and hydrodynamic analysis ensure consistent load and response between structural and hydrodynamic analysis. This means that the mass-model used need to ensure that the motion characteristics and load application is properly represented. In the hydrodynamic analysis the mass needs to be correctly described to produce correct motions and sectional
47 Page 47 forces, while global/local stress patterns are affected by the mass description in the structural analysis. The mass modelling therefore needs to be according to the loading manual, i.e. have the same: total weight longitudinal centre of gravity vertical centre of gravity transverse centre of gravity rotational mass in roll and pitch. Experience shows that the hydrodynamic analysis will give some small modification to the total mass and centre of gravity, where the buoyancy is decided by the draft and trim of the loading condition in question. Each loading condition analysed needs an individual mass-model. The lightship weight is consistent for all the models, but the draft and cargo load/ballast distribution is different from one loading condition to another. To obtain the correct mass-distribution in the FE model, an iteration process for tuning the mass distribution has to be carried out in the initial phase of the global analysis Light weight Light weight is defined as the weight that is fixed for all relevant loading conditions, e.g. steel weight, equipment, machinery, tank fillings (if any), etc. The steel weight should be represented by material density. Missing steel weight and distributed deadweight can be represented by nodal masses applied to shell and beam elements. The remaining lightweight should be represented by concentrated mass points at the centre of gravity of each component, or by nodal masses, whichever is more appropriate for the mass in question. The point mass representation should be sufficiently distributed to give a correct representation of rotational mass and to avoid unintended results. Point masses should be located in structural intersections such that local response is minimised Dead weight Dead weight is defined as removable weight, i.e. weight that varies between loading conditions. The most common are: liquid cargo and ballast containers bulk cargo. Different ship-types and tank/cargo types may need special consideration to ensure that the mass is modelled in a way that both represent the motion characteristics of the vessel, at the same time as the inertia load is properly applied. The following contains some guidelines/best practice for some ship-types/mass-types. Other methods may also be applicable Ballast and liquid cargo In most cases liquid should be represented by distributed pressure in the FE-analysis, at least within the areas of interest. In the hydrodynamic analysis the pressure is represented as mass-points distributed within the tankboundaries of the tank Container cargo The weight of containers need to give the correct vertical forces at the container supports, but also forces occurring in the cell guides due to rolling and pitching need to be included Bulk / ore cargo For bulk cargo the correct centre of gravity and the roll radii of gyration need to be ensured. The forces need to be applied such that the lateral forces, but also friction forces of the bulk cargo are correctly applied. This can be achieved by modelling part of the load as mass-points and part of the load as pressure-loads, where the pressure loads will ensure some lateral pressure on the transverse and longitudinal bulkheads and the masspoints will ensure that most of the load is taken by the bottom structure. The ratio between cargo modelled by mass-points and by pressure load depends on the inclination of the supporting transverse/longitudinal structure Spherical tanks For spherical tanks there are two important effects that need to be considered, i.e.;
48 Page 48 the rotational mass of the cargo cargo distribution has a correct representation of how the load from the cargo is transferred into the hull. For spherical tanks, the inner side of the tank is without any stiffening arrangement, and only the friction between the tank surface and the liquid (in addition to the drag effect of the tower) will make the liquid rotate. Hence the rotational mass from this effect can normally be neglected and only the Steiner contribution (mr 2 ) of the rotational mass should be included. By neglecting the rotational mass, the roll Eigen period will be slightly under estimated from this procedure. This is conservative since a lower Eigen period normally will give higher roll acceleration of the vessel. Normally the weight of the cargo can be assumed to be uniformly distributed along the skirt of the tank. 7. Documentation and Verification 7.1 General Compliance with CSA class notations shall be documented and submitted for approval. The documentation shall be adequate to enable third parties to follow each step of the calculations. For this purpose, the following should, as a minimum, be documented or referenced: basic input assumptions and simplifications made in modelling/analysis models loads and load transfer analysis results discussion, and conclusion. The analysis shall be verified in order to ensure accuracy of the results. Verification shall be documented and enclosed with the analysis report. Checklists for quality assurance shall also be developed before the analysis work commences. It is suggested that project-specific checklists are defined before the start of the project and are included in the project quality plan. These checklists will depend on the shipyard s or designer s engineering practices and associated software. The following contains the documentation requirements to each step (Section 7.2) and some typical verification steps (Section 7.3) that compiles the total delivery. Input files and result files may be accepted as part of the verification. 7.2 Documentation Basic input The following basis for the analysis need to be included in the documentation: basic ship information, including revision number - drawings - loading manuals - hull-lines. deviations, simplifications from ship information assumptions scope overview - analysis basis - loading conditions - wave data - design waves (including purpose) - time at sea. requirements/acceptance criteria Models All models used should be documented, where the use and purpose of the model is stated. In addition the following to be included: units boundary conditions
49 Page 49 coordinate system Loads and hydrodynamic analysis Typical properties to be documented are listed below and should be based on the selected probability level for long-term analysis: viscous damping level mass properties (radii of gyration) motion reference point long term responses with corresponding Weibull shape parameter and zero-crossing period for - motions - sectional loads within cargo region - accelerations within cargo region - sea pressures. design waves parameters with corresponding basis and non-linear results (if relevant). It is recommended that the documentation of the hydrodynamic parameters is initiated in the start of the project in order to have comparable numbers throughout the project Load transfer The following to be documented, confirming that the individual and total applied loads are correct.: pressures transfer global loads (vertical bending moment and shear force) between hydro-model and structural model the same Structural analysis Overview of which structural analysis are performed Fatigue damage assessment Following to be documented: reference to or methodology used welding effects included factors accounting for effects not present in structural analysis (correction of stress) SN curves used damage, including mean stress effect if any stress patterns global screening Ultimate limit state assessment local yield and buckling Following to be documented: results showing compliance based on yielding criteria results showing compliance based on buckling criteria results from fine mesh evaluation special considerations, corrections and assumptions made need to be summarized amendments needed to achieve compliance Ultimate limit state assessment - hull girder collapse Following to be documented: reference to evaluation method reference to special considerations results showing compliance for intact conditions, including loads and capacity results showing compliance for damaged conditions, including loads and capacity. 7.3 Verification General Each step of the procedure should be verified before next step begins. As major verification milestones, the following should at a minimum be documented before the work is continued: FE model scantlings, geometry, etc load cases and boundary conditions test-run to ensure that FE-model is OK to be performed
50 Page 50 Mass-model total mass and centre of gravity still water vertical bending moment and shear force (of structural and hydro model). Hydro-analysis hydro-model transfer-functions long-term responses design waves (if relevant). Load transfer vertical bending moments and shear forces equilibrium load patterns. FE analysis responses global displacement patterns/magnitudes local displacement patterns global sectional forces stress level and distribution sub-model boundary displacements/forces and stress reaction forces and moments. Verification steps should be included as Appendix or Enclosed together with main report/documentation Verification of Structural Models For proper documentation of the model, requirements given in the Rules for Classification of Ships, Pt.3 Ch.1 Sec.13 should be followed. Some practical guidance is given in the following. Assumptions and simplifications are required for most structural models and should be listed such that their influence on the results can be evaluated. Deviations in the model compared with the actual geometry according to drawings shall be documented. The set of drawings on which the model is based should be referenced (drawing numbers and revisions). The modelled geometry shall be documented preferably as an extract directly from the generated model. The following input shall be reflected: plate thickness beam section properties material parameters (especially when several materials are used) boundary conditions out of plane elements (4-node elements, see Section 6) mass distribution/balance Verification of Hydrodynamic Analysis Model The mass model should have the same properties as described in the loading manual, i.e. total mass, centre of gravity and mass distribution. The linking of the hydrodynamic and structural models shall be verified by calculating the still water bending moments and shear forces. These shall be in accordance with the loading manual. Note that the loading manuals do not include moments generated by pressures with components acting in the longitudinal direction. These pressures are illustrated by the two triangular shapes in Figure 7-1.
51 Page 51 Figure 7-1 End pressures contributing to vertical bending moment Two ways of including the longitudinal forces are presented. One way is to add the moment given by: where d B ΔM 5 = ρgd (Z 2 ρ = sea-water density g = acceleration of gravity d = draught B = breadth Z N.A. = distance from the keel to the neutral axis. The correction is not correct towards the ends since the vessel is not shaped like a box. Figure 7-2 shows an example of the procedure above. The loading manual corresponds with the potential theory as long as the transverse section has a rectangular shape. N.A. d - ) Still water bending moment Loding Manual Loading Man. Corr. Potential theory Still water bending moment Longitudinal position of the vessel Figure 7-2 Example of verification of still water loads Another option is to apply pressures acting only in longitudinal direction to the structural model and integrate the resulting stresses to bending moments. In this way the potential theory shall match the corrected loading
52 Page 52 manual all over the vessel. When the internal tanks have large free surfaces the metacentric height might change significantly. This will affect the roll natural frequency. If there is wave energy present for this frequency range these free surface effects should be included in the model. The viscous and potential code should use the same physics and thereby give the same natural frequency for roll. Correction of metacentric height in the potential code Wasim can be included by modifying the stiffness matrix. where C ρ g = the stiffness matrix, = the water density = the acceleration of gravity. ΔC = ρg Volume Displacement 44 GM correction Roll damping If the method in Section 3.3 is used the roll angle given as input to the damping module should be the same as the long term roll angle which is based on the final transfer functions. In general increased motion will result in increased damping. It is therefore normally more viscous damping for ULS than for FLS Transfer functions The transfer functions shall be reviewed and verified. For short waves, all motion responses (6 degrees of freedom) shall be zero. For long waves, transfer function for heave shall be equal to one. When the roll and pitch transfer functions are normalized with the wave amplitude it shall be zero for long waves, and normalized with wave steepness they shall be constant for long waves. Transfer functions for surge in head and following sea should be equal to one for long periods, while transfer functions for sway should be one in beam sea. All global wave load components shall be equal to zero for long and short waves Design waves for ULS For linear design waves, the dynamic response of the maximized response shall be the same as the long term response described in Section 3.5. For non-linear design waves, the comparisons of linear and non-linear results shall be presented. It is important that if the non-linear simulation is repeated in linear mode the result would be the linear long term response Verification of loads Inaccuracy in the load transfer from the hydrodynamic analysis to the structural model is among the main error sources for this type of analysis. The load transfer can be checked on basis of the structural response and on basis on the load transfer itself. It is possible to ensure the correct transfer in loads by integrating the stress in the structural model and the resulting moments and shear forces should be compared with the results from the hydrodynamic analysis. Figure 7-3 and Figure 7-4 compares the global loads from the hydrodynamic model with that resulting from the loads applied to the structural model.
53 Page E E+05 Vertical shear force [kn] 5.00E E E E E+05 WASIM CUTRES -2.00E+05 Length [m] Figure 7-3 Example of QA for section loads Vertical Shear Force 1.00E E+06 Vertical bending moment [knm] 6.00E E E E E+06 Length [m] WASIM CUTRES Figure 7-4 Example of QA for sectional loads Vertical Bending Moment 10 sections are usually sufficient in order to establish a proper description of the bending moment and shear force distribution along the hull. However, this may depend on the shape of the load curves. The first and last sections should correspond with the ends of the finite element model. In case of problems with the load transfer, it is recommended to transfer the still water pressures to the structural
54 Page 54 FE model in order to verify the models and tools. Pressures applied to the model can be verified against transfer-functions of shell pressure in the hydrodynamic analysis. For use of sub-models, it shall be verified that the pressure on the sub-model is the same as that from the parent model Verification of structural analysis Verification of Response The response should be verified at several levels to ensure that the analysis is correct. The following aspects should be verified as applicable for each load considered: global displacement patterns/magnitude local displacement patterns/magnitude global sectional forces stress levels and distribution sub model boundary displacements/forces reaction forces and moments Global displacement patterns/magnitude In order to identify any serious errors in the modelling or load transfer, the global action of the vessel should be verified against expected behaviour/magnitude Local displacement patterns Discontinuities in the model, such as missing connections of nodes, incorrect boundary conditions, errors in Young s modulus etc., should be investigated on basis of the local displacement patterns/magnitude Global sectional forces Global bending moments and shear force distributions for still water loads and hydrodynamic loads should be according to the loading manual and hydrodynamic load analysis respectively. Small differences will occur and can be tolerated. Larger differences (>5% in wave bending moment) can be tolerated provided that the source is known and compensated for in the results. Different shapes of section force diagrams between hydrodynamic load analysis and structural analysis indicate erroneous load transfer or mass distribution and hence should not normally be allowed. When transferring loads for FLS, at least two sections along the vessel should be chosen and transfer functions for sectional loads from hydrodynamic and structural FE model shall be compared, e.g. one section amidships and one section in the forward or aft part of the vessel as a minimum. When ULS is considered, the sectional loads from the hydrodynamic model at time of load transfer shall be compared with the integrated stresses in the structural FE model Stress levels and distribution The stress pattern should be according to global sectional forces and sectional properties of the vessel, taking into account shear lag effects. More local stress patterns should be checked against probable physical distribution according to location of detail. Peak stress areas in particular should be checked for discontinuities, bad element shapes or unintended fixations (4-node shell elements where one node is out of plane with the other three nodes). Where possible, the stress results should be checked against simple beam theory checks based on a dominant load condition, e.g. deck stress due to wave bending moment (head sea) or longitudinal stiffener stresses due to lateral pressure (beam sea) Sub-model boundary displacements/forces The displacement pattern and stress distribution of a sub-model should be carefully evaluated in order to verify that the forced displacements/forces are correctly transferred to the boundaries of the sub-model. Peak stresses at the boundaries of the model indicate problems with the transferred forces/displacements Reaction forces and moments Reacting forces and moments should be close to zero for a direct structural analysis. Large forces and moments are normally caused by errors in the load transfer. The magnitude of the forces and moments should be compared to the global excitation forces on the vessel for each load case.
55 Page References /1/ DNV Rules for Classification of Ships, Pt.3 Ch.1 Hull Structural Design, Ships with Length 100 metres and above, July 2008 /2/ DNV Recommended Practice DNV-RP-C202, Buckling Strength of Shells, April 2005 /3/ DNV Recommended Practice DNV-RP-C205, Environmental Conditions and Environmental Loads, October 2008 /4/ DNV Classification Note 30.7, Fatigue assessment of ship structures, October 2008 /5/ DNV Classification Note 34.2, PLUS - Extended fatigue analysis of ship details, April 2009 /6/ Tanaka, A study of Bilge Keels, Part 4, on the Eddy-making Resistance to the Rolling of a Ship Hull, Japan Soc. of Naval Arch., Vol. 109, 1960 /7/ DNV Rules for Classification of Ships, Pt.8 Ch.2 Common Structural Rules for Double Hull Oil Tankers above 150 metres of length, October 2008 /8/ DNV Recommended Practice DNV-RP-C201 Part 2, Buckling strength of plated structures, PULS buckling code, Oct /9/ Kato, On the frictional Resistance to the Rolling of Ships, Journal of Zosen Kiokai, Vol. 102, 1958 /10/ Kato, On the Bilge Keels on the Rolling of Ships, Memories of the Defence Academy, Japan, Vol IV No.3 pp , 1966 /11/ Friis-Hansen, P., Nielsen, L.P., On the New Wave model for kinematics of large ocean waves, Proc. OMAE, Vol. I-A, pp , 1995 /12/ Pastoor, L.W., On the assessment of nonlinear ship motions and loads, Ph.D. thesis, Delft University of Technology, 2002 /13/ Tromans, P.S., Anaturk, A.R., Hagemeijer, P., A new model for the kinematics of large ocean waves - application as a design wave, Proc. ISOPE conf., Vol. III, pp , 1991.
56 Page 56 Appendix A Relative Deflection Analysis A.1 General The following gives the procedure for finding the relative deflection to be used in component stochastic analysis for bulkhead connections. A FE analysis using a cargo-hold model is performed to calculate relative deflections at the midship bulkhead. A.2 Structural modelling A cargo-hold model representing the midship region is used, with ½ ½ cargo holds, or 3 cargo holds. See vessel types individual class notation for modelling principles and boundary conditions. Plating is represented by 6- and 8-node shell elements and stiffeners are represented by 3-node beam elements. An image of the model is shown in Figure A-1. The model is to be based on net scantlings, unless other is stated by class notation. Figure A-1 3-D Cargo Hold Model
57 Page 57 A.3 Load cases The applied load cases are described in Table A-1. Table A-1 Midship model fatigue load cases LC no Loading condition Load component Figure LC1 Full load condition Dynamic sea pressure LC2 Full load condition Dynamic cargo pressure (vertical acceleration) LC4 Ballast condition Dynamic sea pressure LC5 Ballast condition Dynamic ballast pressure (vertical acceleration) A.4 Loads The loads are to be based on the hydrodynamic analysis for FLS for each loading condition respectively. The loads are to be taken at 10-4 probability level and are to be based on the defined scatter-diagram with cos 2 spreading. A.4.1 Sea pressure The panel pressures from hydrodynamic analysis at midship section are subtracted and the long-term values are found. The pressure is applied to the cargo-hold model with same value along the model. If panels do not match the pressures, they are to be interpolated according to coordinates. The pressure in the intermittent wet/dry region on the side-shell is to be corrected according to the procedure specified in Section (see also CN 30.7). A.4.2 Cargo load/tank pressure The cargo load/pressure due to vessel accelerations applied is to be based on accelerations at 10-4 probability level. Loads from accelerations in vertical, transverse and longitudinal direction are to be considered on project basis. For most vessels it is sufficient to apply the loads due to vertical acceleration only, but some designs may need to consider transverse and longitudinal acceleration also. The acceleration is to be taken at the centre of gravity of the tank(s)/hold in the midship region. and the reference point for the pressure distribution is to be taken at the centre of free surface. The density is to be taken as tonnes/m 3 for ballast water in ballast tanks and as cargo density/load as specified in the loading manual for full load condition.
58 Page 58 The long term acceleration is to be used for the pressures calculation. The pressure distribution due to positive acceleration shall apply. It is sufficient to use the same acceleration for the tank(s) forward and aft of the tank(s)/hold in question without taking into account the phasing or difference in long term value between adjacent tanks forward and aft. A.5 Boundary conditions The boundary conditions are to be taken according to vessels applicable CN for strength assessment. A.6 Post-processing A.6.1 Subtracting results The relative deflection between the bulkhead and the closest frame is found from the FE-analysis. Based on the relative deflection the stress due to the deflection can be calculated based on beam theory, see CN 30.7 /4/. The deflection of each detail is further normalised based on the load it is caused by (e.g. the wave pressure or acceleration at 10-4 probability level), giving the nominal stress per unit load. By combining it with the transfer function of the response, the nominal stress due to relative deflection is found. The stress concentration factor is added, and the transfer-function can be added to the total stress transfer function.
59 Page 59 Appendix B DNV Program Specific Items B.1 General There are several steps and different programs that are necessary for an analysis that involve direct calculation of loads and stress including a load transfer. Typical programs are given in the following: HydroD WASIM WAVESHIP PATRAN_PRE SESTRA SUBMOD PRESEL STOFAT XTRACT POSTRESP CUTRES NAUTICUS HULL is an interactive application for computation of hydrostatics and stability, wave loads and motion response for ships and offshore structures. The wave loads and motions are computed by Wadam or Wasim in the SESAM suite of programs. linear and non-linear 3D time domain program. WASIM in its linear mode calculates transfer functions for motions, sea pressure and sectional forces of the vessel. In its nonlinear mode, time series of the specified responses are generated, and additional Froude- Krylov and hydrostatic forces from wave action above still-water level are included. Vessel speed effects are accounted for in WASIM, and the vessel is kept directional and positional stable by springs or auto-pilot. is a linear 2D frequency domain program. WAVESHIP can be applied for calculation of viscous roll damping. is a general pre-processor for graphical geometry modelling of structures and generation of Finite Element Models. is a program for linear static and dynamic structural analysis within the SESAM program system. Program for retrieval of displacements on a local part (sub-model) of a structure from a global (complete) model for refined or detailed analysis. is a program for assembling super-elements (part models) to form the complete model to be analysed. It also has functions for changing coordinate system to easily allow part models to be moved. is an interactive postprocessor performing stochastic fatigue calculation of welded shell and plate structures. The fatigue calculations are based on responses given as stress transfer functions. STOFAT also has an application for calculation of statistical long term post-processing of stresses. is the model and results visualization program of SESAM. It offers general-purpose features for selecting, further processing, displaying, tabulating and animating results from static and dynamic structural analysis as well as results from various types of hydrodynamic analysis. is a wave statistical post-processor for determination of short and long term responses of motions and loads. is a post-processing tool for sectional results calculating the force distribution throughout the cross section, and integrate the force to form total axial force, shear forces, bending moments and torsional moment for the cross section. has an application for component stochastic fatigue analysis, the program (Component) Stochastic Fatigue in Section Scantlings is a tool for performing stochastic fatigue analysis of longitudinal stiffeners with corresponding plates according to Classification Note The program uses all the structural input specified in Section Scantlings together with result and specified data from the wave analysis to calculate stochastic fatigue life. B.2 Modelling B.2.1 General mass modelling In order to tune the position of the centre of gravity and verify the weight distribution, it is recommended to divide the vessel in longitudinal and transverse blocks. This allows easy specification of individual mass and material properties for each block. B.2.2 External loads To be able to transfer the hydrodynamic loads a dummy hydro pressure must be applied to the hull. This must be load case no. 1 (SESAM). The pressure shall be defined by applying hydro pressure (PROPERTY LOAD x HYDRO-PRESSURE) acting on the shell (all parts of the hull may be wetted by the wave). The pressure shall point from the water onto the shell. A constant pressure may be applied since the real pressure distribution will be calculated in WASIM and directly transferred to the structural model. The model must also have a mesh line at or close to the respective waterlines for each of the draft loading conditions (full load and ballast) to be considered.
60 Page 60 B.2.3 Ballast and liquid cargo Using SESAM tools require that the tanks are predefined in the FE-model as separate load cases. Each load case consists of dummy-pressures applied to the tank-boundaries of the tank. In the interface between the hydro-analysis and structural analysis, each tank is given a density and a filling level, producing a surface, centre of gravity and weight of the liquid in the tank. Based on these properties the mass points for the tank can be generated for the hydrodynamic analysis and a tank-pressure distribution based on the inertia for the structural analysis. If above procedure cannot be applied, the following is an alternative procedure: General One separate super element covering all tanks (ballast and cargo) is made. Each tank is defined with a set name identical to the one used for the structural model. Each tank is specified with one specific density, i.e. one material to be defined for each tank. Ballast tanks The frames for each ballast tank (excluding ends of tank) are meshed, see Figure B-1. The same mesh as used in the global/mid-ship model may be used. Alternatively, a new mesh may be created. Shell or solid elements may be used. This mesh only needs to be fine enough to capture global geometry changes. Typical mesh size: - one mesh between each frame (for solid elements) - one mesh between each stringer/girder. Cargo tanks The tank is modelled with solid elements. The mesh only needs to be fine enough to capture global geometry changes. Typical mesh size; One mesh between each frame One mesh between each stringer/girder. End frames Figure B-1 Mass model ballast tanks B.2.4 Container cargo Containers may be modelled as boxes by using 8 QUAD shell elements. The changing the thickness will give a total weight of the containers in the holds. By connecting the containers to the bulkheads with springs, the force from roll and pitch are transferred.
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