design of lock gates for ship collision

Version 3 – PIANC Short Course – 8th Sept 2015

Ship collision against lock gates

PIANC SHORT COURSE SMART RIVERS 2015, Argentina, Buenos Aires, 8th September 2015

Table of content

1) Introduction: Aims of PIANC WG 151 in terms of ship collision against

lock gates (20 min)

By Prof. Philippe RIGO, University of Liège (BE); INCOM Chairman ‐

[email protected]

2) Presentation of the WG 151 report: Design of lock gates for ship collision (45 min)

By Juan OLLERO, Inros‐Lackner AG (Germany) ‐ Juan.Ollero@inros‐lackner.de

Presentation of the data that have to be collected to correctly define the collision scenario

Brief review of the existing types of lock gates

Presentation of some impact protection systems

Description of the current practice and philosophy in different countries to protect lock

gates against ship collisions

Review of the potential consequences in case of impact

Presentation of four different methodologies to evaluate the crashworthiness:

o The CETMEF approach

o The analytical approach

o The numerical methods

o The use of physical models

Conclusion: recommended assessment procedure

3) Presentation of the experience of Panama (ACP) “How was considered ship collision in the design of

the new lock gates” (15 min)

By Johnny WONG, and Rogelio GORDON; ACP, Panama

[email protected] , [email protected]

4) Presentation of new advanced analytical methods to assess crashworthiness of lock gates (2 x 45 min)

By Dr. L. Buldgen: University of Liège (BE), [email protected]

Presentation of advanced analytical methods to evaluate the collision resistance for plane

lock gates

o Local deforming mode

o Global deforming mode

Extension of the simplified method to mitre lock gates

Validation of the analytical results with numerical solutions

o Description of the finite element models (LS‐DYNA)

o Comparison of the resistance and energy curves

Current development:

o Extension to double hull gates (as wheelbarrow rolling gates)

o Extension to impact on offshore wind structure (jacket and monopoles of wind

turbines)

PIANC SHORT COURSE

Design of lock gates for ship collision

(InCom WG151 report)

PIANC Smart Rivers Conference, September 2015, Buenos Aires

PIANC InCom WG 151

Design for lock gates for ship collision

ObjectiveWG151 was set up under the auspices of INCOM with the aim of defininggood practice and appropriate methodologies for the analysis and design oflock gates subjected to ship collision.

Members of WG 151Dr. Sören EHLERS (Chairman of Ship Collision Section)M. Juan OLLERODr. Hervé Le SOURNEDr. Loïc BULDGENDr. Ryszard DANIEL

Colin ROBERTSON (Chair of WG151)Prof. Philippe RIGO (Mentor)

PIANC InCom WG 151 - Design for lock gates for ship collision

VIDEO

Juan OLLERO, Inros-Lackner AG


The Speakers

Introduction: Prof. Philippe RIGO, Univ. of Liège; INCOM Chairman

Presentation of the WG 151 report: Juan OLLERO, Inros-Lackner AG (Germany) –

Experience of Panama (ACP) J. WONG, and R. GORDON; ACP, Panama

Advanced analytical methods to assess crashworthiness of lock gates Dr. L. Buldgen: University of Liège (BE),


Introduction

PIANC WG 151 - Ship collision against lock gates

Prof. Philippe RIGO,

University of Liège (BE); INCOM Chairman [email protected]


Agenda - Timing

2:15 pm : Presentation of the WG 151 report: Juan OLLERO, Inros-Lackner AG (Germany) –

3:00 pm Experience of Panama (ACP) J. WONG, and R. GORDON; ACP, Panama

3:30 BREAK

4:00 pm Advanced analytical methods to assess crashworthiness of lock gates Dr. L. Buldgen: University of Liège (BE),

5:30 pm Discussion with the floor


Presentation of the INCOM WG151 report

By Juan OLLERO, Inros-Lackner AG (Germany)

Brief review of the existing types of lock gates Presentation of some impact protection systems Alternatives to the installation of protection devices Design Criteria Risk Analysis Determination of the Collision Force Presentation of four different methodologies to evaluate the

crashworthiness:o The CETMEF approacho The analytical approacho The numerical methodso The use of physical models



Considerations of Ship Collision in the Design of New Lock Gates for the Panama Canal Expansion Project

By Johnny WONG and Rogelio GORDON, ACP, Panama

- DESIGN REQUIREMENTS- MODEL SET-UP (FEA)- RESULTS OF SHIP COLLISION ANALYSIS- CONCLUSIONS & RECOMMENDATIONS


Advanced analytical methods to assess crashworthiness of lock gates

By Dr. L. Buldgen: University of Liège (BE)

• Advanced analytical methods to assess collision resistance for plane lock gates

- Local deforming mode- Global deforming mode

•Extension of the simplified method to mitre lock gates

•Validation of the analytical results with numerical solutions•Description of the finite element models (LS-DYNA)•Comparison of the resistance and energy curves

•Current development:•Extension to double hull gates (as wheelbarrow rolling gates)•Extension to impact on offshore wind structure (jacket and monopoles of wind turbines)



HAVE A NICE SHORT COURSE

Do not hesitate to ask questionsat any time

Presentation of the WG 151 reportDesign of lock gates for ship collisionJuan Ollero

PIANC Smart Rivers Conference,07 – 11 September 2015, Buenos Aires

Design of Lock Gates for Ship Collision

PIANC InCom WG 151 Brief review of the existing types of lock gates Presentation of some impact protection systems Alternatives to the installation of protection devices Design Criteria Risk Analisys Determination of the Collision Force Presentation of four different methodologies to evaluate the

crashworthiness:o The CETMEF approacho The analytical approacho The numerical methodso The use of physical models


PIANC InCom WG 151

Design for lock gates for ship collision

ObjectiveWG151 was set up under the auspices of INCOM with the aim of defininggood practice and appropriate methodologies for the analysis and design oflock gates subjected to ship collision.

Members of WG 151

Professor Philippe RIGO (Mentor)Colin ROBERTSON (Chairman)Dr. Sören EHLERSDr. Hervé Le SOURNEDr. Loïc BULDGENDr. Ryszard A. DANIELJuan OLLERO

Funktion eines Schleusentores

Types of Navigation Locks

Navigation locks for inland waterwaysWidth 12,50 m ….. 25,00 m

Sea navigation locksWidth 32,00 m ….. 70,00 m

Function of a gate system

• A closure structure for a navigation lock• Part of a water regulation system• Part of a flood protection system• Closure structure of a harbour or shipyard dock.

Types of Navigation Lock Gates

Gates rotating on a vertical axis

Mitre Gates Sector Gates


Gates rotating on a horizontal axis

Floor-mounted flap gate Rising sector gate


Gates with vertical translation movement

Lifting gate system


Gates with horizontal translation movement

Sliding Gate System

Provisions and precautions

Provisions and precautions against ship collision

1. Installation of a protection system

2. Design of the lock gate structure to allow for the absorption of a certain impact energy


Protection Systems (1)

• Objective: Protection of the vessel• DIN 19704 prescribes the use of protection systems• Loads according to DIN 19703• Installation within the lock chamber in front of the lower head gate

upstream

downstream

upper head open lower head close

Protection device



• Vessel impact• Minimum 1 MN • Maximum 2 MN• 300 kN for sea navigation locks

• Velocity at collision • 1,0 m/s for motorised vessels• 0,9 m/s for pushing convoys

• The impact energy has to be totally absorbed by the protection system (hydraulic cylinder, elastomeric-buffer, cable….)



Protection device integrated in the gate

structureShock absorber beam Restraining Cable


Alternatives to the Installation of Protection Devices (1)

The installation of protection devices implies

1. Additional space (up to 5 m in the length)2. longer operating times of the lock3. additional construction and maintenance costs

Therefore, subject to certain conditions and allowing for certain exceptions one could abstain from installing protection devices

In this case a comprehensive risk analysis has to be performed taking into account the efficiency of the vessel traffic and a evaluation of the potential negative impacts on man, natureeconomics and technology


Alternatives to the Installation of Protection Devices (2)

Configuration and design of the lock gate structure in the impactarea such that, that the structure shows an optimal energy workcapacity.

Computations by means of Finite-Elemente-Method (FEM).

Research activities of CETMEF (The French Institute for Inland and Maritime Waterways)

Research activities of BAW (Federal Waterways Engineering and Research Institute) in cooperation with the TUHH (TechnischeUniversität Hamburg-Harburg). Siehe BAW-Mitteilungen Nr. 93 2011Starossek, U., Koppelmann J.: „Rechnerische Untersuchung zu Kollisionsbeanspruchungen von Stahlwasserbauten - Schiffsstoß auf Schleusentore“, Ergebnisbericht, TUHH - Technische Universität Hamburg-Harburg, 30.06.2005, unveröffentlicht.

Lehmann, E., Darie, I.: „Untersuchung zur Optimierung von Stemmtorkonstruktionen hinsichtlich Schiffsstoß“, Abschlussbericht, TUHH - Technische Universität Hamburg-Harburg, 30.09.2007, unveröffentlicht.

Design Criteria

Scenario selection and uncertainties

• The types of ships passing the lock (passenger ship, cargo vessel, barge…).

• The presence or not of a ship arrestor or collision protection system (cables, collision protection gate…).

• The direction of vessel movement prior to collision (e.g. if the ship coming from upstream or downstream).

• The approach velocity and eventual approach velocity limitations.

• The presence of other vessels in the lock.• The possibility of an oblique collision.

An appraisal of consequences and their risks of occurrence need to be considered in the design process.

Design Criteria

Required Parameters for the Striking Vessel

• Displacement of the ship and corresponding draught.• Added mass of water (Hydrodynamic mass): generally, the

added mass of a ship in its longitudinal direction is assumed to be 20% of its displacement. This value must be added to the mass of the ship.

• Bow geometry.• Bulb geometry if applicable• Initial ship velocity at collision.

Design Criteria

Required data for the lock and gate dimensions

• Geometry, scantling and constitutive material model of the gate.

• Boundary conditions between the gate and the lock structure.• Water levels within the lock chamber• If the lock is considered to be deformable, geometry and

constitutive material model for the lock.

Design Criteria

Required data for the contact area

• The contact point or contact area: dimensions and position.• The friction coefficient between the bow of the striking ship

and the gate. The coefficient may be different for contact below and above the free surface.

• Generally, the ship is assumed to strike the gate perpendicularly, but if the striking ship is much narrower than the lock, an oblique collision analysis may also be possible. In this case, a range of striking angles should be determined.

Risk Analysis

Risk Analysis / FMEA(Failure mode and effects analysis)

Determination of the consequences resulting from a ship collision

• sudden drop in water level upstream

• stranding of vessels

• emptying of the upstream waterway and potential flooding downstream

• These in turn can lead to loss of life, injury and economic and social costs amongst other consequences

Risk Analysis

Methodology / Design Approaches (1)

Existing Gate

Determination of the critical collision velocity for the design (representative) vessel, above which unacceptable gate damage would occur. Examinations at different locations under different collision angles.

Risk Analysis

Methodology / Design Approaches (2)

New Gate

In the frame work of the early pre-design phase to optimaze thestructural behaviour of the lock gate regarding ist collisionresistance.

In the course of the subsequent design phases gate deformations and reaction loads for a given representative ship and a range of possible collision scenarios are to be calculated

Risk Analysis

Accepted Level of Damages

Difficult to determine since it is dependent on the specific requirements of the project under consideration

Three (3) Criteria are to be considered:

• Watertightness: specially for lock gates as part of a global flood protection sytem

• operation of the lock: specially for highly frequented waterways, high economic losses

• Overall stability of the structure: A total collapse of the gate structure is not acceptable since the risk of human losses is very high.

Determination of the Collision Forces

Definition of the unfavourable scenario

• Collision takes place in the upper part of the structure

• The hydrostatic pressure is acting unfavorably

• The probability of occurrence is relatively high


Quasi-static Method (1)CETMEF / ROSA 2000

The French Institute for Inland and Maritime Waterways

V = velocity of vessel at collision

M0 = Mass of the vessel / displacement

Cm = mass coefficient, usually 1,20 however depends shape of the striking bow

Cc = Confinement coefficient to account for the mass of water confined between vessel and gate Cc ˂ 1,0

Cs = Ship coefficient to account for the amount of energy that is also dissipated by the deforming bow


Quasi-static Method (2)CETMEF / ROSA 2000

The French Institute for Inland and Maritime Waterways

Calculation of the collision force acc. to the Meier-Dörnberg Formula

Collision force (quasi-static)

Assumptions: • Collision against a unlimited rigid structure• Deformations take place on the ship hull


Analysis Methods

Empirical methods

Simplified analysis methods have been developed to assess the energy absorbed during a collision incident.

Minorsky (1959) proposed the most well-known simplified analysis method, in which the collision process is split into an external and an internal part. The central element of the external part is the evaluation of ship motions under the action of external forces.

Analysis Methods

Analytical Methods (1)

Ship collision can be analysed in a rigorous manner using non-linear finite element methods.

Procedures to analyse collisions between two ships are available and this provides a basis for developing analytical procedures for collisions with certain but not all gate types.

Analysis Methods


Local crushing and plastic deformations in a gate are similar to those experienced by a ship in collision with another vessel. However, unlike a ship to ship collision, the collision energy is also likely to be dissipated through an overall bending deformation of the gate. As a consequence, the total resistance is provided by two deforming modes:

The local mode: behaviour is similar to that in ship to ship collisions

The global mode: this involves an overall deformation of the gate. This type of behaviour is not considered in ship to ship collisions.

Analysis Methods


For the local mode, the structure is decomposed into large structural entities, called super-elements. Buldgen and Le Sourne (2012) extended the method to study the local resistance of gates in collision with a vessel.

For the global mode, the resistance is evaluated by assuming that the gate is submitted to an overall bending deformation.

The total resistance is found by combining the local and the global ones. Buldgen and Le Sourne (2012) assumed that for small values of penetration, the local mode is predominant. With increasing penetration of the gate, the resistance is dominated by the global mode.

Analysis Methods


Local and global modes according to Buldgen (2012)

Analysis Methods


Typical positions and shapes of ships in collision with the gate of the new set of locks in the Panama Canal (Iv-Groep, 2010), (Daniel et al., 2013)

Analysis Methods


Example of local gate deformation in ships collision analysis for the new set of locks in the Panama Canal (Iv-Groep, 2010), (Daniel et al., 2013)

Analysis Methods

Numerical Methods (1)

1. Quasi-static approaches

Finite element-based analyses of ship collision simulations have been performed in many commercial codes, such as LS-DYNA, ABAQUS, and MSC/DYTRAN. Commonly, the nonlinear material behaviour is selected in the form of a power law

Analysis Methods

Numerical Methods (2)

1. Dynamic approaches

In order to realistically assess the structural deformation, the distribution of energy between structural deformations and ship motions needs to be evaluated. Therefore, coupled dynamic collision simulations are the method of choice for a precise description of the entire collision process. Le Sourne et al. (2001) formulated the external dynamics of collisions in a three-dimensional space and included all the major external forces through a subroutine MCOL implemented into LS-DYNA. The coupling between the ship motions and the structural deformations was carried out simultaneously with the help of structural analysis with the finite element method.

Evaluation of Computation Methods

Methods Analysis effort ResultsModelling Computation Energy Loads Stress

Analytical methods

Least in volume, large in expertise

Least, special programs required, often unavailable

yes partially yes

Numerical methods -quasi-static approaches

Moderate in volume and expertise

Moderate, specialist programs required and available

partially partially yes

Numerical methods -dynamic approaches*

Extensive in volume and expertise

Time consuming and expensive. Extensive and dedicated software required

yes yes yes

Conclusion and recommendation

THANK YOU VERY MUCH FOR YOUR ATTENTION

Johnny Wong

Rogelio Gordon

Considerations of Ship Collision in the Design of New Lock Gates for the

Panama Canal Expansion

Buenos Aires, Argentina, 7-11 September 2015

“SMART RIVERS 2015”

PIANC Short Course on Ship Collision Against Lock Gates

28-9-2015 “SMART RIVERS 2015”

Design Requirements

Gate collision requirements• New rolling gates must be able to resist the impact

of a 160,000 ton displacement ship travelling at a speed of 1 knot (0.514 m/s)

• After collision lock must be operable– Gate must be able to be retracted into slot

– Gate must hold water from upstream source

– Gate must keep its floation within limit

– Gate must keep in its track

• Note: Agreement with PIANC WG-151 report on designof lock gates for ship collision (published 2014)

PIANC Smart Rivers 2015

Design vessel• Neopanamax vessel 366 m LOA; 48.8 m beam;

15.2 m draft TFW; 13000 TEU containership

• Third set of locks 27 m lift in three consecutivechambers, dimensions: 458 m long, 55 m wide, 18.3 m to 27.5 m deep


Vessel models• One containership modeled with bulbous bow,

blockage 0.65, displacement 222,000 tons

• One tanker/bulker modeled with vertical V-shapebow, blockage 0.48, displacement 224,000 tons

• Ships assisted with tugs modeled 34 m length, 12 m beam, 2.8 m draft, blockage 0.53


Gate design• Each lock has four pairs of rolling gates 8-10 m

wide; 22-33 m tall; 57 m long; weight 2400-4200 ton

• Gate built with S355 and S460 grade steel

• Horizontal bearing pads on gate sides and bottomconstrain the horizontal movement and transmitloads to the concrete structure

• Gate built with 19 vertical block rows

• Buoyancy chambers set at bottom of gate


28-9-2015 “SMART RIVERS 2015”

Model Setup

Ship direction and bow shape• Downlockage from lake to ocean of a ship with

bulbous bow– Water level at 27.13 m, draft of bulbous bow at 18.23 m,

so collision location will be 8.9 m below water line– During a downlockage a ship with bulbous bow will not

reach the buoyancy chambers from the upstream side

• Downlockage bulkcarrier with V-shaped bowcollision will be near top of gate

• Uplockage ship with bulbous bow will collide nearthe buoyancy chambers (V-shaped bow will notreach the buoyancy chambers)


Ship eccentricity• Ship can impact gate at its center• Ship can also impact gate off-center with maximum

eccentricity of 4.5m • Since vertical frames are spaced at 3.2 m a ship can

collide a row or in-between rows, therefore only the midthree rows can be hit during collision– The analysis showed that the local skin damage is comparable

in both, the collision at a row, and with that of a collision betweenthe rows.

– A collision at a web gives a more direct global response, resulting in higher increase of load distribution to the horizontal bearings and is more severe for the vertical framing


FE model

• Collision modeling by TNO Center for Mechanicaland Maritime Constructions, NL

• Using LSDYNA Finite Element based on ANSYS model used for the structural design and drawings


FE model

• Model changes were made to make it suitable forcrash analysis

• Model validated by comparing global deformations, stresses and reaction forces for the hydrostaticloading of ANSYS for similarity of results


28-9-2015 “SMART RIVERS 2015”

Results of Ship Collision Analysis

Downlockage bulk carrier• After collision, the analysis showed that no

excessive failure is expected:– The required energy absorption is reached after

penetration of 1.06 m


– No rupture of the shell plating willoccur and the structure behind theshell will only show local fracture

– The horizontal reaction force due tocollision is 63 MN, which is anincrease of 29% of the hydrostaticload forces

– The maximum global horizontal deflection of the gate is 0.145 m, anelastic deformation that will return toposition after the vessel has stopped

Downlockage bulbous bow

• The resulting analysis showed that after a collisionno excessive failure is expected for this scenario: – The required energy absorption by the gate is reached

after a penetrarion of 0.879 m

– The upstream shell plating remains intact and the structurebehind the shell shows very limited fracture


– The horizontal reaction force dueto collision is estimated at 62 MN, which is 28% of the reaction forcesdue to hydrostatic loading.

– The global horizontal deflection of the gate is about 0.08 m, within itselastic range and will recuperateafter the ship has stopped

Uplockage bulbous bow• Analysis showed that this will not result in flooding of

its buoyancy chambers for this collision scenario:– Buoyancy chambers and shell plating will remain intact

– A small fracture may occur behind the shell plating in some webs


– The required energy absorption isreached after a penetration of 0.76 m

– The maximum total horizontal reactionforce on the gate is 82 MN from thecollision

– The vertical reaction forces on the upperand lower wagon of the gate oscilatesbetween -2.77 MN and 3.26 MN, thus thewagon will remain in place

Other cases and results• The larger ships will be assisted with tugs ahead

and astern during lockage. The collision analysisincluded the case where a large ship pushed a harbor tug against the gate– This scenario is similar to the case where a ship with a

bulbous bow penetrates the gate. The bow of the tug is 5 m which will create a deeper penetration into the gate

– But it will cause less damage to the gate than the 8 m widebulbous bow of the containership which remains thegoverning case


Conclusions• The analysis performed for the

different operating scenariosand ship types shows that theoverall structural integrity of thelock gate is not compromised bythe ship impact

• The damage will be limited tolocal plastic deformation with no rupture of critical structuralelements.

• In general, the gate remainselastic and it will be possible toretract the gate into its recess


Conclusions• The analysis shows no puncture

of the buoyancy chambers and any possible loss of buoyancy willbe below the 25% allowed by thegate design

• The increase of horizontal loadingon the bearing surfaces of thegate resulting from the shipimpact does not impair the gatefunction

• All cases analyzed show verylimited temporary vertical uplift in the range of 1 to 2 millimeters off the gate from the supportwagons. The connection of thewagons to the gate allows forrelative large displacement, therefore the wagons will remainin place


Panama Canal Third Set of LocksSet to Open on April 2016


Presentation ofnewanalytical methods toassess thecrashworthiness oflock gates

PIANCSMARTRIVERSCONFERENCE

7– 11September 2015BuenosAires

LoïcBuldgen

University ofLiège(Belgium)

1.Introduction

2.Generalbackground

3.Required data

4.Analytical derivation

5.Numerical comparisons

6.Extensiontomitrelock gates

7.Conclusions


1.Introduction

2.Generalbackground

3.Required data




7.Conclusions

1.1


1.INTRODUCTION

1.1.Overview ofthewaterborne transportinEurope

1.2.Collisionanalysis oflock gates

1.3.Aim oftheanalytical methods

1.2

1.INTRODUCTION




1.2

1.INTRODUCTION1.1.Overview ofthewaterborne transportinEurope

0

1000

2000

3000

4000

5000

6000

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

2011

2012

2013

2014

2015

Freighttransport(10

6tkm)

Year

©European Environment Agency

• Increasing freight transport since 1995

1.3



• Road transport is predominant

76%

18%

6%

Road Rail Inlandnavigation

©Eurostat

1.4‐1


©Eurostat

123

22,830,9

0

20

40

60

80

100

120

140

Roadtransport Railtransport Inlandnavigation

CO2em

issions(g/tkm

)


• Road transport is predominant⟶ high CO2 emissions

76%

18%

6%


1.4‐2


©Eurostat

Truckscongestion


• Road transport is predominant⟶ high CO2 emissions

• Limited road capacity

76%

18%

6%


1.4‐3


TruckscongestionWaterbornetransport

Shift

1barge≃200trucks


• Roadtransportis predominant⟶high CO2 emissions ⟹Newmodalsplit

• Limited road capacity

1.4‐4


• New modal split: increase waterbone transport

‐ CO2 emissions

‐ Air quality

‐ Noise nuisance

‐ Safety

‐ Land take

‐ Same infrastructure cost per tkm

1.5



• European situation:

‐ Important sea ports

‐ Network: 40 000 km

‐ Currently under‐utilized

1.6‐1







• European policy: NAIADES I and II

1.6‐2







• European policy: NAIADES I and II

DesignnewlocksImprove existing ones

1.6‐3

1.INTRODUCTION




1.7

1.INTRODUCTION1.2.Collisionanalysis oflock gates

DesignnewlocksImprove existing ones

• Need to account for accidental actions

1.8‐1


DesignnewlocksImprove theexisting ones


‐ Keep the structure undamaged

1.8‐2




‐ Keep the structure undamaged

‐ Proportionate consequences

1.8‐3




• Crucial point: pre‐design

1.8‐4





• Ship impact is a key issue

‐ Little information in international standard

‐ Little information in the literature

1.8‐5



Howtointegrate ship impact inthepre‐designoflocks ?



• Ship impact is a key issue

1.8‐6



• Perform finite element analyses

1.9‐1


Howtointegrate ship impactinthepre‐designoflocks ?


‐ Detailed results

‐ Realistic model

1.9‐2




‐ Build the models (Gate and vessel)

‐ Critical scenarios (Impact point)

‐ Run simulations (Dynamic non‐linear)

‐ Post‐processing (Voluminous)

1.9‐3




• Time demanding

1.9‐4



1.9‐5


• Time demanding

• Licenses



1.9‐6

Expansive…


• Time demanding

• Licenses



1.9‐7


• Time demanding

• Licenses

…orillegal




• Time demanding

• Licenses

• Not suited for optimization (Iterations)

1.9‐8



Anefficienttool is missing


• Time demanding

• Licenses

• Not suited for optimization

1.9‐9

1.INTRODUCTION




1.10

1.INTRODUCTION1.3.Aim oftheanalytical methods

Anefficienttool is missing tointegrate ship impactinthepre‐designoflock gates

1.11‐1



⟶ Simplified analytical tool to evaluate:

1.11‐2




• The collision force

1.11‐3





• The collision energy

1.11‐4






⟶ Complementary tool to finite elements

1.11‐5






⟶ Complementary tool to finite elements

• Finite elements: accurate results final design

• Analytical tool: approximate results pre‐design

1.11‐6

1.Introduction

2.Generalbackground

3.Required data




7.Conclusions

2.1


2.GENERALBACKGROUND

2.1. Procedure toderive analytical solutions

2.2. Theupper‐bound method

2.3. Theequilibriummethod

2.4. Summary

2.2

2.GENERALBACKGROUND




2.4. Summary

2.2

2.GENERALBACKGROUND2.1.Procedure toderive analytical solutions

• Experimental methods

‐ Individual component

‐ Technical challenge

‐ Financial challenge

2.3‐1






• Finite element methods

‐ Complex model

‐ Refined analyses

2.3‐2







‐ Complex model


• Analytical methods

‐ Simplified model

‐ Global results

2.3‐3





‐ Complex model





Validation


‐ Global results

2.3‐4





‐ Complex model





Validation


‐ Global results

2.3‐5


• Derive closed‐form solutions for the impact force

2.4‐1



• Rigorous theoretical basis for analytical methods

‐ Finite displacements

‐ Plasticity

2.4‐2





‐ Plasticity

⟶ No simplified formulation

2.4‐3





‐ Plasticity

⟶ No simplified formulation

• Approximate theories

‐ Upper‐bound method

‐ Equilibrium method

2.4‐4

2.GENERALBACKGROUND




2.4. Summary

2.5

2.GENERALBACKGROUND2.2.Theupper‐bound method

• Particularly suited for shells but also applicable to beams

2.6‐1



• Energy balance:

2.6‐2


External powerofthecrushing force

2.6‐3


• Energy balance:


Internal energyrate

2.6‐4

External powerofthecrushing force


• Energy balance:


2.6‐5


• Energy balance

• Small displacements


2.6‐6


• Energy balance

• Small displacements but extended to moderate ones:


Green‐Lagrangeplastic:strain rate

2.6‐7


• Energy balance



2.6‐8

Green‐Lagrangetensor:


• Energy balance



2.6‐9



• Energy balance



2.6‐10

⟶InitialaxesX1,X2,X3



• Energy balance



2.6‐11

⟶Undeformedconfiguration

⟶InitialaxesX1,X2,X3



• Energy balance



2.6‐12

Plasticflowstress



• Energy balance




2.6‐13


• Energy balance

• Small displacements but extended to moderate ones

Example:impactonaplasticbeam


2.7‐1

Example: impact on a plastic beam (upper‐bound method)

‐ Displacement field:


2.7‐2



‐ Green‐Lagrange strain:


2.7‐3




‐ Plastic rotation:


2.7‐4





‐ Internal forces: Membrane tension NBending momentM


2.7‐5







2.7‐6







2.7‐7


‐ Internal power:


2.7‐8


‐ Internal power:

‐ External power:


2.7‐9


‐ Internal power:

‐ External power:

‐ Upper‐bound:


2.7‐10


‐ Internal power:

‐ External power:

‐ Upper‐bound:


2.7‐11


‐ Internal power:

‐ External power:

‐ Upper‐bound:


2.7‐12


‐ Internal power:

‐ External power:

‐ Upper‐bound:

Smalldisplacements


2.7‐13


‐ Internal power:

‐ External power:

‐ Upper‐bound:

SmalldisplacementsLarge

displacements

2.GENERALBACKGROUND




2.4. Summary

2.8

2.GENERALBACKGROUND2.3.Theequilibriummethod

• More suited for beams

2.9‐1



• Static equilibrium equations:

2.9‐2

‐ Rotational equilibrium:

‐ Translational equilibrium:




2.9‐3






2.9‐4



Only intheimpactplane


2.9‐5


• Static equilibrium equations

• Deformed configuration to account for moderate displacements


2.9‐6


• Static equilibrium equations

• Deformed configuration to account for moderate displacements

Example:impactonaplasticbeam


2.10‐1

Example: impact on a plastic beam (equilibrium method)

‐ Large displacements ⟶membrane force N

‐ Large rotations ⟶ inclination angle θ


2.10‐2



⟶Equilibrium in the deformed configuration:



2.10‐3



⟶Equilibrium in the deformed configuration:Strongly nonlinear…



2.10‐4


‐ Moderate rotations ⟶ inclination angle θ≪Strongly nonlinear…

⟶ Equilibrium in the deformed configuration:



2.10‐5


‐ Moderate rotations ⟶ inclination angle θ≪

⟶Equilibrium in the deformed configuration:Analytically tractable



2.10‐6




Same result astheupper‐bound method



2.10‐7




Exact solution


2.GENERALBACKGROUND




2.4. Summary

2.11

2.GENERALBACKGROUND2.4.Summary

2.12‐1

• The upper‐bound method

‐ Particularly suited for shells but also applicable to beams

‐ Based on an energy balance

‐ Valid for small displacements but extended to moderate ones


2.12‐2


‐ Particularly suited for shells but also applicable to beams

‐ Based on an energy balance

‐ Valid for small displacements but extended to moderate ones

• The equilibrium method

‐ More suited for beams

‐ Based on static equilibrium equations

‐ Deformed configuraiton to account for moderate displacements




2.12‐3

Equivalentforsmall displacements

(principle ofvirtual velocities)

2.GENERALBACKGROUND2.1.Generalbackground



Validity of these methods ?

‐ Literature

‐ Experimental validations

‐ Numerical validations

2.12‐4

Equivalentforsmall displacements

(principle ofvirtual velocities)

1.Introduction

2.Generalbackground

3.Required data




7.Conclusions

3.1


3.REQUIREDDATA

3.1. Definition ofthegate

3.2. Definition ofthevessel

3.3. Definition oftheimpactscenario

3.2

3.REQUIREDDATA




3.2

3.REQUIREDDATA3.1.Definition ofthegate

• Description of the gate

‐ Single plating

3.3‐1



‐ Single plating

‐ Orthogonal reinforcement

3.3‐2



‐ Single plating


3.3‐3



‐ Single plating


‐ Simple supports at the lock walls

3.3‐4



‐ Single plating



‐ Free sliding at the lock walls

3.3‐5



‐ Single plating



‐ Free sliding at the lock walls

‐ Eventually: simple supports at the bottom

3.3‐6


• Required data for the gate

N° Y hw tw hf tf

Girders 1 … … … … …

2 … … … … …

⋮

Fram

es

1 … … … … …

2 … … … … …

⋮Stiffeners 1 … … … … …

2 … … … … …

⋮

Plating thickness tp …

‐ Geometrical properties

3.4‐1


• Required data for the gate

3.4‐2


‐ Material properties

YoungModulus E …

Yield stress σ0 …

3.REQUIREDDATA




3.5

3.REQUIREDDATA3.2.Definition ofthevessel

• Description of the vessel

3.6

Raked bow Bulbous bow



‐ Idealized bow shape

3.7‐1




‐ Parabolic stem

3.7‐2




‐ Parabolic stem

3.7‐3




‐ Parabolic stem

‐ Elliptic bulb

3.7‐4




‐ Parabolic stem

‐ Elliptic bulb

3.7‐5


• Required data for the vessel

3.8‐1


Stem

X radiusofthestem q …

Z radiusofthestem p …

Height ofthestem hb …

Stemangle ϕ …

Side angle ψ …

Bulb

X radiusofthebulb RX …

Y radius ofthebulb RY …

Z radiusofthebulb RZ …


• Required data for the vessel

3.8‐2

‐ Material properties⟶ useless: perfectly rigid vessel


3.REQUIREDDATA




3.9

3.REQUIREDDATA3.3.Definition oftheimpactscenario

• Definition of the impact scenario

‐ Location of the impact point

‐ Initial kinetic energy

3.10


• Required data for the collision scenario

3.11‐1

Impact

point X horizontalposition XI …

Yverticalposition YI …

Z horizontal position ZI …

Bulb Totalmass M0 …

Initial velocity V0 …



3.11‐2

Impact






⟶ Very few parameters to introduce


3.11‐3

⟶ Very few parameters to introduce ≠ Pre‐processing with finiteelement software

Impact







1.Introduction

2.Generalbackground

3.Required data




7.Conclusions

4.1



4.1. Deformation sequence

4.2. Totalresistance

4.3. Localresistance

4.4. Globalresistance

4.5. Summary

4.2






4.5. Summary

4.2

4.Analytical derivation4.1.Deformation sequence

• Decomposition of the total displacement

Totaldisplacement

=

Global displacement +Localdisplacement

4.3‐1



Totaldisplacement

=

Global displacement +Local displacement

4.3‐2



Totaldisplacement

=


Example: Von Mises stresses (Pa)in a vertical frame

4.3‐3



Totaldisplacement

=

Global displacement +Localdisplacement

4.3‐4




Totaldisplacement

=


4.3‐5



• Decomposition of the total displacement (δ < δt)

Hypothesis:

Phase1: δ <δt⟶Local displacement

4.4‐1




Hypothesis:


4.4‐2




Hypothesis:


4.4‐3



• Decomposition of the total displacement (δ > δt)

Hypothesis:

Phase1: δ <δt⟶Localdisplacement

Phase2: δ >δt⟶Global displacement

4.4‐4




Hypothesis:


Phase2: δ >δt⟶Globaldisplacement

⟶Two successivemotions

4.4‐5




Hypothesis:


Phase2: δ >δt⟶Globaldisplacement

⟶Two successivemotions

⟶Two decoupled motions

4.4‐6







4.5. Summary

4.7

4.Analytical derivation4.2.Totalresistance

• Resistance

4.8‐1

‐ δ < δt : Phase 1

PL Local resistance due to localized crushing


• Resistance



Pt Force to activate a global plastic mechanism

4.8‐2


• Resistance

4.8‐3




‐ δ = δt : Transition when PL = Pt


• Resistance

4.8‐4




‐ δ = δt : Transition when PL = Pt

‐ δ > δt : Phase 2

PG Global resistance due to overall bending


• Resistance

‐ Total resistance P :

If δ < δt : P = PL

If δ > δt : P = PG

4.8‐5


• Resistance

Not realistic: local and global coupling if δ < δt


If δ < δt : P = PL ⟶Not realistic

If δ > δt : P = PG ⟶OK

4.8‐6


• Resistance




‐ Correction:

Elastic calculation of PG if δ < δt

4.8‐7


• Resistance




‐ Correction:

Elastic calculation of PG if δ < δt

Transition when min(PL ; PG) = Pt

4.8‐8


• Resistance


If δ < δt : P = min(PL ; PG)


4.8‐9


• Resistance




4.8‐10

Resistanceduringthelocal mode

Local mode


• Resistance




4.8‐11

Resistanceduringthelocalmode

Resistanceduringtheglobal mode

Localmode Global mode


• Resistance




4.8‐12


Resistanceduringtheglobalmode

PL Local resistance

PG Global resistance

Pt Force to activate a global plastic mechanismLocalmode Globalmode


• Resistance




4.8‐13


Resistanceduringtheglobalmode

PL Local resistance

PG Global resistance


⟶ PL, PG, Pt ?Localmode Globalmode






4.5. Summary

4.9

4.Analytical derivation4.3.Localresistance

4.10‐1

• Reminder

Decomposition of the total resistance P :

‐ If δ < δt : P = min(PL ; PG)

‐ If δ < δt : P = PG


4.10‐2

• Reminder





4.10‐3

Localresistance

• Reminder





• Decomposition of the gate into large entities

4.11‐1



• Gate = assembly of super‐elements

‐ SE1: Plating

4.11‐2




‐ SE1: Plating

‐ SE2: Horizontal girdersVertical frames

4.11‐3




‐ SE1: Plating

‐ SE2: Horizontal girdersVertical frames

‐ SE3: Intersections

4.11‐4


SE2

SE1

SE3• Three super‐element types:

‐ SE1: Plating

‐ SE2: VerticalframesHorizontalgirders


• Hypothesis: all the super‐elements are decoupled

4.12‐1


SE2

SE1

SE3• Three super‐element types:

‐ SE1: Plating

‐ SE2: VerticalframesHorizontalgirders


• Hypothesis: all the super‐elements are decoupled

⟶ No interaction

Activation only if contact with the bow

4.12‐2


• Decoupling⟶ hypothesis on the boundary conditions:

‐ SE1: Plate supported on four edges

Out‐of‐plane impact load

4.13‐1





‐ SE2: Plate supported on three edges

In‐plane impact load

4.13‐2





‐ SE2: Plate supported on three edges

In‐plane impact load

‐ SE3: X or T elements supported along their axis

Impacted along their axis

4.13‐3


• How to evaluate the local resistance PL?

‐ Boundary conditions


‐ Mechanical properties

SE1

SE2

SE3

Closed‐formexpressions

Super‐element i ResistancePi

4.14‐1






SE1

SE2

SE3


Super‐element i ResistancePi

4.14‐2






SE1

SE2

SE3


‐ Upper‐bound method

‐ Equilibrium method

4.14‐3


• Closed‐form solution for SE1

⟶ Plating

4.15‐1



⟶ Plating

⟶ Upper‐bound method (suited for shells)

4.15‐2



⟶ Plating

⟶ Upper‐bound method (suited for shells)

⟶ Write an energy balance:

4.15‐3


• Closed‐form solution for SE1 (Plating)

1. Postulate u(y,z)


‐ Geometry: a1, a2, b1, b2

‐ Bow shape

⟶ Realistic

4.16‐1



1. Postulate u(y,z)

2. Calculate the strain rates

4.16‐2



1. Postulate u(y,z)


3. Calculate the plastic internal energy rate

4.16‐3



1. Postulate u(y,z)



4. Apply the upper‐bound method:

4.16‐4



1. Postulate u(y,z)




4.16‐5



1. Postulate u(y,z)




SE1resistance

4.16‐6



⟶ Comparison with numerical results

4.17




0

1

2

3

4

5

6

0 0,1 0,2 0,3 0,4 0,5

Resistance(MN)

δ (m)

Analytical LS‐DYNA

4.18




0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0 0,1 0,2 0,3 0,4 0,5

Energy(MJ)

δ (m)


4.19



⟶Horizontal girders

Vertical frames

4.20‐1




Vertical frames

⟶ Folding process: upper‐bound method

4.20‐2




Vertical frames


⟶ Beam behaviour: equilibrium method

4.20‐3


• Closed‐form solution for SE2 (Stiffeners)

‐ Folding mechanism

⟶OK if hw≫

4.21‐1




⟶OK if hw≫

‐ Bending mechanism

⟶ Combination

4.21‐2


• Closed‐form solution for SE2 (Stiffeners) – Folding mechanism

4.22‐1



‐ Two triangles of height H

4.22‐2



‐ Two triangles

‐ Three plastic hinges

4.22‐3



‐ Two triangles


⟶ Rotation in the hinges

Bending energy rate Ėb

4.22‐4



‐ Two triangles




⟶ Axial elongation of the triangles

Membrame energy rate Ėm

4.22‐5



‐ Two triangles




⟶ Axial straining of the triangles

Membrame energy rate Ėm

Folding resistance

4.22‐6


• Closed‐form solution for SE2 (Stiffeners) – Transition

‐ The central section is crushed during the folding process

4.23‐1




‐ The residual bending strength is:

Fullcross‐sectionbending strength

4.23‐2





Reductioncoefficient

Fullcross‐sectionbending strength

4.23‐3





‐ Equilibrium method⟶ force P * to activate a bending process:

4.23‐4





‐ Equilibrium method⟶ force P * to activate a bending process:

Decreasing function ofδ

4.23‐5



Transition from the folding to the bendingmechanism:

4.24‐1



Transition from the folding to the bendingmechanism:

Bending mechanism if δ > δ*

4.24‐2


• Closed‐form solution for SE2 (Stiffeners) – Bending mechanism

‐ Bending mechanism if δ > δ*

4.25‐1




‐ Reduced bending moment in the central section

4.25‐2





‐ Moderate displacements⟶ tensile membrane forces

4.25‐3





‐ Moderate displacements⟶ tensile membrane forces

‐ Static equilibrium of the beam⟶ bending resistance Pb

4.25‐4



‐ If δ < δ*: P = Pf ⟶Folding mechanism

4.26‐1




‐ If δ = δ*: P = P* ⟶ Transition

4.26‐2





‐ If δ > δ*: P = Pb ⟶Bending mechanism

4.26‐3






4.26‐4




4.27‐1



0

1

2

3

4

5

0 0,2 0,4 0,6 0,8 1 1,2

Resistance(MN)

δ (m)


4.27‐2


0

1

2

3

4

5

0 0,2 0,4 0,6 0,8 1 1,2

Resistance(MN)

δ (m)



δ*

Transition

4.27‐3


0

0,5

1

1,5

2

2,5

0 0,2 0,4 0,6 0,8 1 1,2

Energy(MJ)

δ (m)



4.27‐4



⟶ Intersections

4.28‐1



⟶ Intersections


4.28‐2



⟶ Intersections


⟶ Beam behaviour: equilibrium method

4.28‐3


• Closed‐form solution for SE3 (Intersections)


‐ Bending mechanism

4.29


• Closed‐form solution for SE3 (Intersections) – Folding mechanism

‐ 4wings aresimultaneously crushed

‐ Each wing is madeoftwo parts:

4.30‐1





① Centralpart

4.30‐2





① Centralpart

② Connectionpart

4.30‐3



⟶Upper‐bound method: 1. Compatibledisplacement field for① and②

4.31‐1




2. MembraneenergyrateĖm

Membrane deformationsinthetriangles+bendingintheplastichinges

4.31‐2





3. BendingenergyrateĖb

Membranedeformationsinthetriangles +bending intheplastichinges

4.31‐3





3. BendingenergyrateĖb

⟶Totalinternal energy:

Folding resistance

4.31‐4


• Closed‐form solution for SE3 (Intersections) – Bending mechanism

‐ Forδ =δ*: Transition

‐ Forδ >δ*: Bending mechanism

Displacement ofthenodalpoint

4.32‐1



‐ Each wing is submitted tobending

4.32‐2




‐ Reduced bending resistance ξ*M0

4.32‐3




‐ Reduced bending resistance ξ*M0

‐ Additional membraneforces

Equilibrium method⟶ bending resistance Pb

4.32‐4






4.33




4.34



0

1000

2000

3000

4000

5000

6000

7000

8000

0 0,2 0,4 0,6 0,8 1 1,2

Resistance(kN)

δ (m)

Analytical

LS‐DYNA

4.35‐1



0

1000

2000

3000

4000

5000

6000

7000

8000

0 0,2 0,4 0,6 0,8 1 1,2

Resistance(kN)

δ (m)

Analytical

LS‐DYNA

δ*

Transition

4.35‐2



0

0,5

1

1,5

2

2,5

0 0,2 0,4 0,6 0,8 1 1,2

Energy(MJ)

δ (m)

Analytical

LS‐DYNA

4.36


• Local resistance calculation

4.37‐1



4.37‐2

Totalnumber ofsuper‐elements



4.37‐3

Totalnumber ofsuper‐elements

‐ Pi = 0 if the super‐element is not activated

‐ Pi ≠ 0 if the super‐element is impacted by the bow

⟶ analytical formulae of SE1, SE2 or SE3

Individual resistance ofeach super‐element:






4.5. Summary

4.38

4.Analytical derivation4.4.Globalresistance

4.39‐1

• Reminder





4.39‐2

• Reminder





4.39‐3

Globalresistance

• Reminder





• Local deforming mode:

‐ Decoupled super‐elements

‐ Idealized boundary conditions

4.40‐1





⟶ Able to capture the localized crushing

4.40‐2





⟶ Able to capture the localized crushing

⟶ Unable to capture the overall bending

Globalmode

4.40‐3


• Observations:

‐ The frames ∼ rotate as rigid bodies

4.41


• Observations during the global mode:


‐ They do not dissipate a lot of energy

4.42‐1





Localmode(crushing)

4.42‐2





Globalmode(rotation)

4.42‐3




‐ They do not dissipate a lot of energyNegligible contributiontoPG

4.42‐4





• Energy dissipated during the global mode

= Contribution from the girders

Negligible contributiontoPG

4.42‐5







the plating


4.42‐6







the plating

the stiffeners


4.42‐7




Grosscross‐sectionofthegirder

4.43‐1




the plating

the stiffeners

Grosscross‐sectionofthegirder

Collaborating partoftheplating

4.43‐2


• Gate model

‐ Set of horizontal beams

4.43‐3


• Gate model


‐ Connected by the frames

4.43‐4


• Gate model



‐ Submitted to

4.43‐5


• Gate model



‐ Submitted to

an out‐of‐plane displacement field u

4.43‐6


• Gate model



‐ Submitted to


an in‐plane displacement field w

4.43‐7


• Gate model



‐ Submitted to



Impactlocation

Bowshape

Bulb

Sill

4.43‐8


• Gate model



‐ Submitted to



• Global resistance

4.43‐9


• Mechanical model of a beam i

4.43‐10



4.43‐11



⟶Beam theory with u and w

4.43‐12




⟶Individual resistance Pi of beam i

4.43‐13




⟶Individual resistance Pi of beam iElastic

Plastic

4.43‐14




⟶Individual resistance Pi of beam iElastic⟶Resistanceduring thelocal mode

Plastic⟶Resistanceduring theglobalmode

4.43‐15

Localmode Globalmode




⟶Individual resistance Pi of beam iElastic⟶Resistanceduring thelocalmode

Plastic⟶Resistanceduring theglobal mode

4.43‐16

Localmode Global mode


• Elastic solution

‐ Small displacements

‐ Negligible lateral displacements: w≪

4.44‐1





⟶Beam theory:

4.44‐2





⟶Beam theory:

⟶ Equilibrium method to get an elastic solution for Pi

Localindentation

4.44‐3





⟶Beam theory:


Localindentation

Maynotexceedthecross‐sectionbendingresistance

4.44‐4





⟶Beam theory:


Localindentation

Maynotexceedthecross‐sectionbendingresistance

Classification

4.44‐5



‐ If the girder is simultaneously crushed during the local mode

Localindentation

4.46‐1

Bending resistance isreached




Localindentation

Decreasingresistanceuntilδ =δt(globalplasticmechanism)

4.46‐2




‐ If the girder is not crushed during the local mode

Bendingresistanceisreached

Nolocalindentation

4.46‐3




‐ If the girder is not crushed during the local mode

Nolocalindentation

4.46‐4

Constantresistanceuntilδ =δt(globalplasticmechanism)


• Plastic solution

‐ If the bending resistance is reached for all the beams⟶ δ = δt

4.46‐5

δ =δt aglobalplasticmechanism isactivated overtheentire gate



‐ If the bending resistance is reached for all the beams⟶ δ = δt

‐ A plastic solution is needed to calculate PGwhen δ > δt

4.46‐6

Need aplasticsolutionforPG ifδ >δt

? ?



‐ Lateral displacements w1 and w2

‐ Out‐of‐plane displacement u

4.47‐1





‐ Membrane force N

4.47‐2






‐ Rotation θ

4.47‐3






‐ Rotation θ

Plastichinge(Class1)

4.47‐4



‐ Class 1: plastic resistances ξpMp and Np

4.48‐1




‐ Interaction criteria forM and N

4.48‐2




‐ Interaction criteria forM and N

‐ Equilibrium method⟶ Pi

4.48‐3






‐ Rotation θ

Buckling(Class>1)

4.49‐1



‐ Class > 1: no plastic hinge but early buckling

⟶ Post‐buckling resistance: thin‐walled structure

4.49‐2




‐ Approximate buckling pattern

Webofahorizontalgirder

Post‐bucklingmechanism

4.49‐3





Webofahorizontalgirder

Post‐bucklingmechanism

Analyticalmodel

4.49‐4





4.49‐5





‐ Upper‐bound method⟶ Pi

4.49‐6



‐ If the girder has been previously crushed before the transition

Class1 Class>1

4.50‐1

? ?




Class1 Class>1

4.50‐2




‐ If the girder has not been crushed before the transition

Class1 Class>1

4.50‐3

? ?




‐ If the girder has not been crushed before the transition

Class1 Class>1

4.50‐4


• Global resistance calculation

4.51‐1



4.51‐2

Totalnumber ofhorizontalbeams



4.51‐3

Totalnumber ofhorizontalbeams

‐ δ < δt : Elastic solution for Pi

‐ δ > δt : Plastic solution for Pi

Individual resistance ofeach beam:






4.5. Summary

4.52

4.Analytical derivation4.5.Summary

• How to calculate the total resistance?

4.53‐1



‐ If δ < δt⟶Resistance during the local mode

4.53‐2




1) Calculate the local resistance PL

4.53‐3





4.53‐4

Individual resistance ofeach super‐element

(SE1,SE2,SE3)





4.53‐5





2) Calculate the global resistance PG

4.53‐6






4.53‐7

Individual resistance ofeach beam

(Elastic regime)






4.53‐8






3) Calculate P = min(PL , PG)

4.53‐9




‐ If δ = δt⟶Transition

4.53‐10





1) Calculate the force to activate a global plasticmechanism Pt

4.53‐11





1) Calculate the force to activate a global plasticmechanism Pt

2) The transition occurs when P = min(PL , PG) = Pt

4.53‐12





‐ If δ < δt⟶Resistance during the global mode

4.53‐13







4.53‐14







4.53‐15

Individual resistance ofeach beam

(Plasticregime)







4.53‐16







2) Calculate P = PG

4.53‐17






4.53‐18

Globalmode

Localmode

1.Introduction

2.Generalbackground

3.Required data




7.Conclusions

5.1



5.1. Descriptionofthefinite element models

5.2. Example 1:gate supported byasill

5.3. Example 2:gate freeat thebottom

5.2





5.2

5.Numerical comparisons5.1.Descriptionofthefinite element models

• Finite element software

5.3

Pre‐processing

Simulations

Post‐processing


• Boundary conditions

5.4‐1



‐ Lock walls: X: constrainedY: freeZ: free

5.4‐2



‐ Lock walls: X: constrainedY: freeZ: free

‐ Sill: X: constrainedY: constrainedZ: free

5.4‐3


• Gate modelling

‐ Belytschko‐Tsay shell elements

5.5‐1


• Gate modelling


‐ Elastoplastic material:

MAT_PIECEWIESE_LINEAR_PLASTICITY

Parameters

E 210 000MPa

ET 10 180MPa

σ0 235MPa

ρ 7850kg/m3

ν 0.3

5.5‐2


• Vessel modelling


5.6‐1




‐ Perfectly rigid material:

MAT_RIGID

5.6‐2




‐ Perfectly rigid material

‐ Idealized parabolic bow shape

Parameters

p 3.5m

ET 7m

hb 8m

ϕ 70°

ψ 79°

5.6‐3




‐ Perfectly rigid material

‐ Idealized parabolic bow shape

‐ Fictitious rigid boby:

PART_INERTIA

Parameters

M 4000t

V 2m/s

5.6‐4


• Contact modelling

‐ LS‐DYNA standard penalty formulation:

CONTACT_AUTOMATIC_SURFACE_TO_SURFACE

Contact

5.7‐1



‐ LS‐DYNA standard penalty formulation:

CONTACT_AUTOMATIC_SURFACE_TO_SURFACE

CONTACT_AUTOMATIC_GENERAL

Self‐contact

5.7‐2



‐ LS‐DYNA standard penalty formulation

‐ Default values of the contact parameters

5.7‐3


• Gate mesh (PATRAN)

‐ Regular rectangular elements

5.8‐1




‐ Dimension ≤ ℓe in the impact area

5.8‐2





‐ Dimension ≤ ℓe at the boundaries

5.8‐3






‐ Dimension ≤ 2ℓe otherwise

5.8‐4






‐ Dimension ≤ 2ℓe otherwise

⟶ ℓe = 5 cm (mesh convergence)

5.8‐5


• Vessel mesh (PATRAN)

‐ Dimension ∼ ℓe near the impact

‐ Coarser mesh otherwise

5.9





5.10

5.Numerical comparisons5.2.Example 1:gate supported byasill

• Example 1 (LS‐DYNA)

‐ Typical lock gate

‐ Supported by a sill

5.10‐1



Vessel:

M0 =4000t

V0 =2m/s

E0 =8MJ

5.10‐2


0

2

4

6

8

10

12

0 0,3 0,6 0,9 1,2 1,5

Resistance(MN)

δ (m)

LS‐DYNA

Analytical

• Example 1: Resistance

5.10‐3


• Example 1: Energy

0

1

2

3

4

5

6

7

8

9

0 0,3 0,6 0,9 1,2 1,5

Energy(MJ)

δ (m)

LS‐DYNA

Analytical

8%

5.10‐4


• Example 1: Consistency

⟶ Ideally: experimental validation

5.11‐1



⟶ Ideally: experimental validation

⟶Practically:technical difficulties

financial difficulties

5.11‐2



‐ Conservation of the total energy

‐ Hourglass energy

‐ Mesh convergence

5.11‐3


• Example 1: Consistency – Total energy

0

1

2

3

4

5

6

7

8

9

0 0,3 0,6 0,9 1,2 1,5

Energy(MJ)

δ (m)

Internal

Kinetic

Total

5.12


• Example 1: Consistency – Hourglass energy

0

0,1

0,2

0,3

0,4

0,5

0,6

0 0,3 0,6 0,9 1,2 1,5

Ratio(%)

δ (m)

Hourglassratio

<5%

5.13


• Example 1: Consistency – Mesh convergence illustration

0

2000

4000

6000

8000

10000

12000

14000

16000

0 0,5 1 1,5 2 2,5

Resistance(kN)

δ (m)

20cm

5.14‐1



0

2000

4000

6000

8000

10000

12000

14000

16000

0 0,5 1 1,5 2 2,5

Resistance(kN)

δ (m)

20cm

10cm

0

2000

4000

6000

8000

10000

12000

14000

16000

0 0,5 1 1,5 2 2,5

Resistance(kN)

δ (m)

20cm

10cm

5.14‐2



0

2000

4000

6000

8000

10000

12000

14000

16000

0 0,5 1 1,5 2 2,5

Resistance(kN)

δ (m)

20cm

10cm

7.5cm

5.14‐3



0

2000

4000

6000

8000

10000

12000

14000

16000

0 0,5 1 1,5 2 2,5

Resistance(kN)

δ (m)

20cm

10cm

7.5cm

5cm

5.14‐4



0

2000

4000

6000

8000

10000

12000

14000

16000

0 0,5 1 1,5 2 2,5

Resistance(kN)

δ (m)

20cm

10cm

7.5cm

5cm

4cm

⟶ℓe =5cm

5.14‐5


• Example 1: Influence of failure

Plasticdeformation>εr

5.15‐1



Element thickness/lengthratio

5.15‐2



0

2

4

6

8

10

12

0 0,3 0,6 0,9 1,2 1,5

Resistance(MN)

δ (m)

LS‐DYNA

Analytical

Withfailure

5.15‐3



0

1

2

3

4

5

6

7

8

0 0,3 0,6 0,9 1,2 1,5

Energy(MJ)

δ (m)

LS‐DYNA

Analytical

Withfailure

5.15‐4





5.16

5.Numerical comparisons5.2.Example 2:gate freeat thebottom


‐ Typical lock gate

‐ Not supported by a sill

5.16‐11



Vessel:

M0 =4000t

V0 =2m/s

E0 =8MJ

5.16‐2



5.16‐3


• Example 2: Resistance

0

1

2

3

4

5

6

7

0 0,3 0,6 0,9 1,2 1,5 1,8

Resistance(MN)

δ (m)

LS‐DYNA

Analytical

Collapse

5.16‐4


• Example 2: Energy

0

1

2

3

4

5

6

7

8

9

0 0,3 0,6 0,9 1,2 1,5 1,8

Energy(MN)

δ (m)

LS‐DYNA

Analytical

10%

5.16‐5

1.Introduction

2.Generalbackground

3.Required data




7.Conclusions

6.1


6.EXTENSIONTOMITRELOCKGATES

6.1. Analytical modifications

6.2. Numerical comparisons

6.2




6.2

6.EXTENSIONTOMITRELOCKGATES6.1.Analytical modifications

• Up to now:

6.3

‐ Plane lock gate

‐ Single plating


Example:liftinglock gate ofMeinderich(Rhine‐Hernecanal,Germany)


• Extension:

6.4‐1

‐ Mitre lock gate

‐ Single plating



• Extension:

6.4‐2

‐ Mitre lock gate

‐ Single plating


Mitreangleβ


• Derivation of the local resistance

‐ SE1: Plating

‐ SE2: Horizontal girders and vertical frames


6.5



⟶ Analytical derivation…

SE1 SE2– Vertical SE2– Horizontal

6.6‐1




…withdueconsiderationforβ

6.6‐2




…withdueconsiderationforβ

…consistentwithplanegatesifβ→0

6.6‐3


• Derivation of the global resistance


6.7‐1





6.7‐2





‐ Global out‐of‐plane displacement

6.7‐3





‐ Global out‐of‐plane displacement

≡Obliqueimpact

6.7‐4


• Combination of the local and global resistances

‐ Same philosophy as for plane gates

6.8‐1

If δ < δt : P = min(PL ; PG) ⟶ Local mode

If δ < δt : P = PG ⟶Global mode

PL Localresistance

PG Globalresistance

Pt Forcetoactivate aglobalplasticmechanism


• Combination of the local and global resistances

‐ Same philosophy as for plane gates

‐ But corrections are required for off‐centered impact (see hereafter)

6.8‐2




6.9

6.EXTENSIONTOMITRELOCKGATES6.2.Numerical comparisons

• Results: off‐centered impact M0 = 4000 t ; V0 = 2m/s ; E0 = 8MJ

(Pre‐loading:hydrodstatic pressure)

6.10‐1


(Pre‐loading:hydrodstatic pressure)

• Results: off‐centered impact M0 = 4000 t ; V0 = 2m/s ; E0 = 8MJ

6.10‐2


• Results: off‐centered impact

Progressivelossofcontact

6.10‐3



Coulombslidingcriteria

LS‐DYNA:frictioncoefficientof0.3


6.10‐4



0

1500

3000

4500

6000

7500

0 0,2 0,4 0,6 0,8 1 1,2

Resistance(kN)

δ (m)

Analyticalsolution Numericalsolution


6.10‐5



Impossibletodissipatetheentireinitialkineticenergy


6.10‐6



0

1

2

3

4

5

6

0 0,2 0,4 0,6 0,8 1 1,2

Energy(MJ)

δ (m)


∼60%ofE0

6.10‐7


• Results: centered impact M0 = 4000 t ; V0 = 2m/s ; E0 = 8MJ

6.11‐1


0

2000

4000

6000

8000

10000

12000

14000

16000

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Resistance(kN)

δ (m)


• Results: centered impact

6.11‐2


0

1

2

3

4

5

6

7

8

9

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Energy(MJ)

δ (m)


• Results: centered impact

100%ofE0

6.11‐3


0

1

2

3

4

5

6

7

8

9

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9

Energy(MJ)

δ (m)


• Results: centered impact2%

6.11‐4

1.Introduction

2.Generalbackground

3.Required data




7.Conclusions

7.1


7.CONCLUSIONS

7.1.Applicability

7.2.Limitationsandperspectives

7.2

7.CONCLUSIONS

7.1.Applicability


7.2

7.CONCLUSIONS7.1.Applicability

• Different collision scenarios

‐ Plane lock gates

7.3‐1




‐ Mitre lock gates

7.3‐2





‐ Raked bow

7.3‐3





‐ Raked bow

‐ Bulbous bow

7.3‐4



• Application to new lock gates

‐ Pre‐design: Optimization

7.4‐1


FEM

7.4‐2




‐ Final design: Worst scenarios


7.4‐3




‐ Final design: Worst scenarios

⟶ Aid for designers


7.4‐4



• Application to existing lock gates

‐ Rapid strength assessment


7.4‐5





‐ Protection devices


7.4‐6





‐ Protection devices

⟶ Aid for authorities

7.CONCLUSIONS

7.1.Applicability


7.7

7.CONCLUSIONS7.2.Limitationsandperspectives

• Limitations due to the analytical method

‐ No local field (σ, ε…)

7.8‐1


• Limitations due to the analytical method

‐ No local field (σ, ε…)

‐ Rupture: Numerical treatment of rupture is not always reliable

Approximate analytical treatment of rupture is possible

Difficult to account for various rupture modes

7.8‐2


• Perspectives of analytical methods

‐ Other gate types: Double‐side gates

7.8‐.3




Sector gates

7.8‐4




Sector gates

‐ Other vessels: Barges

7.8‐5




Sector gates


Other types

7.8‐6




Sector gates


Other types

‐ Other structures: OWT jackets

7.8‐7




Sector gates


Other types


OWTmonopiles

7.8‐8




Sector gates


Other types


OWTmonopiles

7.8‐9

Underdevelopment



7.10

JacketofOWT

MonopileOWT

Impactofriverbarges




Sector gates


Other types


OWTmonopiles

7.11

Shipcol researchprogram

7.CONCLUSIONS

• Acknowledgements

7.12

Government oftheWalloon Region ofBelgium

Financial contribution to the research projectShipcol on vessel collisions against lock gatesand offshore wind turbines.

MSCSoftwareCorporation

Technical support to the use of the softwarePatran and Nastran to create numerical modelsand perform finite element analyses.

7.CONCLUSIONS 7.13

design of lock gates for ship collision

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