Schedule for Presentation Meeting of Master-Degree Thesis in 2017
International Course of Maritime & Urban Engineering

Name

Date :
Venue :

August 2nd (Wednesday) starting from 10:00
S1-312 Lecture RoomSupervisor

Title of thesis

No.

Time

1

10:00 – 10:25

Hossain MD. Alfaz

Toda

Force, Motion and Nominal Wake Prediction for KCS Model with Heave and Pitch
Free Condition in Head Waves

Aoki

2

10:25 – 10:50

Ma Jianping

Kashiwagi

Study on the Cloaking Phenomenon in Shallow Water Waves by Designing theGeometry of Seabed

Aoki

3

10:50 – 11:15

Silva Kukulege Bhathisha
Araki
AkalankaRole of Beach Morphology in a Tsunami Event - A Numerical Case Study Based on
2004 and 2011 Tsunami Disasters

Aoki

4

11:15 – 11:40

Su Sandy Htun

Water-on-Deck Effects on Roll Motions of an Offshore Supply Vessel in Regular
Stern Quartering Waves

Aoki

Umeda

Chairman

Lunch Break5

13:15 – 13:40

Sumanto Nugroho

Kita

6

13:40 – 14:05

Htike Aung Kyaw

Toda

7

14:05 – 14:30

Ahmad Zakky

Osawa

A Study on Socio-spatial Structure of Informal Settlements by Analyzing
Relationships between Physical Environment and Human Behaviors in the Inner-city
Kampung, Jakarta
Flow Field Measurement Around Self-Propelled KRISO Container Ship Model in
Head Waves
Numerical Study on Determination Technique for Equivalent Distributed StressBreak

14:45 –

at S1-323

Meeting for Evaluating Mater-thesis Presentations, and Steering Committee Meeting

Meeting for Evaluation: From 14:45 at S1-323 Meeting Room
Members are Steering committee members and the supervisors

Fujikubo
Fujikubo
Fujikubo

International Course of Maritime & Urban Engineering / Abstract of Master Thesis

July 28, 2017

Force, Motions and Nominal Wake Prediction for KCS Model with
Heave and Pitch Free Conditions in Head Waves
Md Alfaz Hossain
Hull Form Design Sub-Area, Department of Naval Architecture and Ocean Engineering
Key Words: CFD, Ship Motions, Added Resistance, Nominal Wake, Head Waves

1. Introduction
The prediction of ship motions and added resistance is very
important for safe and economic operation of the ship. Fuelconsumption of a ship is strongly related to the ship motions andadded resistance. The wake profile and behavior has influence on
the propeller performance and hence on the fuel consumption as
well. The Marine Environment Protection Committee (MEPC) of
International Maritime Organization’s (IMO) has imposed
regulations for seagoing ships to maintain a minimum energy
efficiency level, which is determined by Energy Efficiency
Design Index (EEDI) and Energy Efficiency Operational
Indicator (EEOI). Therefore, it is of vital importance to make areliable prediction of ship motions, added resistance and nominal
wake to meet criteria of EEDI and EEOI.

Fig. 2-4 respectively, made good agreement on the trend. In shortwaves, typically λ/L<0.5, z/A and θ/Ak are near zero indicatingsmall vertical motions and corresponding lower σAW due to wave
diffraction hitting the ship bow. With the increase of λ/L, verticalmotions increase and consequently σAW increases until it reach tothe peak value at λ/L=1.15 (wave resonance condition). In longwaves, especially λ/L>1.15, z/A and θ/Ak both are close to one
which indicates the ship moves up vertically as the wave
amplitude and the pitch angle follows the wave slope. As a result,σAW drops down.

2. Methodology
CFD has been used to predict the force, motions and nominal
wake of the KRISO Container Ship (KCS) model (without
propeller) for Froude number 0.261, with heave and pitch freeconditions, in calm water and in regular head wave conditions,recommended by CFD workshop 2015.The length between
perpendiculars (LPP) of the model ship is 3.2m for which PIV
measurements have also been carried out at Osaka University.

Fig. 2 Heave motion amplitude.

The grid was generated using Gridgen. Then SUGGAR library
was used for the overset of grids. CFDShip-IOWA V4.5 (which isan overset, block structured, and incompressible URANS code
coupling with motion solver) has been used for numericalprediction. The k-ω SST turbulence model was employed using
no wall function. A single-phase level-set method has been used
to model the free surface and 2DOF (heave and pitch) ship
motions are considered. The computational domain and boundary
condition is shown in Fig. 1.

Fig. 3 Pitch motion amplitude.

Fig. 1 Computational domain and boundary conditions.

3.

Results

3.1 Ship motions and added resistance
CFD and EFD results of heave motion amplitude (z/A), pitch
motion amplitude (θ/Ak), and added resistance(σAW), shown in

Fig. 4 Added resistance coefficient.

the dummy boss although the secondary vortex is suppressed
under the boss. When t/Te = 0.425, the ship stern starts to move
upward and thus the low speed area under the boss outspreads
downward. The secondary vortex is clearly noticeable this time.
The bilge vortex is found just above the boss.

4.

Conclusions

Fig. 5 One period of wave at propeller plane, heave and pitch
motions (CFD results) for λ/L=1.15.

The predicted motions and added resistance show very good
agreement with EFD data which reveals that the CFDShip-IOWA
solver is good enough to make reliable prediction for high-speed
vessels. In addition, the CFD wake field at propeller plane shows
very good agreement with PIV measurement.
For future work, propeller will be included for more realistic
prediction and vortex behavior at the propeller plane will beanalyzed in details as well.

Fig. 6 Nominal wake velocity at the propeller plane (PIV).

Fig. 7 Nominal wake velocity at the propeller plane (CFD).

3.2 Nominal wake
The comparison between CFD and EFD (PIV) results ofnominal wake velocity at propeller plane has been done for
λ/L=0.65, 1.15 and 1.37 for one-quarter of period (Te). Fourtime instances (t/Te), for λ/L= 1.15, are shown in Fig. 5 withvertical lines. 0°, 90°, 180° and 270° are the wave phases at thewave gauge measured during PIV experiment. Results for only
λ/L=1.15 at two time instances have been shown in Fig. 6-7.
t/Te =0, when the wave crest is at bow (FP). When t/ Te~0.17,
the ship stern goes downward which can be easily understoodby the low speed area (in blue color shedding) above thedummy boss. The bilge vortex can be observed on the sides ofReferences
1) Hosseini, H., P. Wu, P. Carrica, H. Kim, Y. Toda, F. Stern: J
of Ocean Engineering, Vol. 59, pp. 240–273, 2013.
2) Wu, P., H. Sadat-Hosseini, F. Stern, Y. Toda: J of JASNAOE,
Vol. 24, pp. 13-19, 2017.
3) Wu, P., E. Tokgoz, H. Okawa, K. Tamaki, Y. Toda:
Computational and Experiment of Propeller Performance andFlow Field around Self-propelled Model Ship in Regular
Head Waves, Proc. of 31st SNH (California, USA), 2016.
4) http://www.t2015.nmri.go.jp/Instructions_KCS/Case_2.10/Ca
se_2-10.html

International Course of Maritime & Urban Engineering / Abstract of Master Thesis

July 28, 2017

Study on the Cloaking Phenomenon in Shallow Water Waves by
Designing the Geometry of Seabed
Ma Jianping

Ocean Space Development Subarea, Department of Naval Architecture and Ocean Engineering
Key Words: water wave cloaking, transformation media method, homogenization theory, anisotropic water depth

1. Introduction
In recent years, inspired by the pioneering idea of Pendry,
Schurig & Smith1), there are plenty of work concentrating on the
study of cloaking by constructing specific metamaterials in different research fields, such as electromagnetic waves and acoustic
waves. The core concept of this sort of cloaking is to shield objects by utilizing a coordinate transformation method to design
the material parameters, which can steer the waves in any desired
trajectory. Zareei & Alam2) extended the cloaking into shallow
water wave field by applying a nonlinear transformation that requires a spatially variable water depth.
Based on the previous research, this paper presents a rigorous
derivation of the water depth tensors for both the rectangle andcylinder shaped cloaks. The analytical solution and the implementation of water depth tensor for cylindrical cloaking are alsostudied. In addition, the distribution of plane wave and cylindricalwave cloaking are simulated. In this study, a linear potential flow
is assumed and FEM-based commercial software COMSOL Multiphysics is employed for numerical computations.

2. Governing Equation

where a and b are radii of inner and outer cloaking domains.
Then the coordinate system is distorted as shown in Fig.1. Applying this transformation into (2) yields the water depth tensor
expressed as rp2 − a 2

0 

2
2
−
 a  rp
(4)
h= 1 − 2  
h .
2
rp 
 b 
0
rp2 − a 2 Fig. 1

3.2 Square Cloak
The same idea as the cylindrical cloak can be used for designof a square-shaped cloak with inner square width 2a and outersquare width 2b. It can be seen that the coordinate transformation

a2
 x p =(1 − 2 ) xo2 + a 2 ,
b



a2
(1 − 2 ) xo2 + a 2b yp =yo .

xoAssuming the waves to be sinusoidal in time with radian frequency ω, the governing equation for the propagation of longwaves (i.e. kh ≪1, where k , h = h( x) are the wavenumber andwater depth respectively) is the shallow water equation, which is
written as∇ ⋅ (h∇h ) +ω2g

h =0 .

(1)

Here g denotes the gravitational acceleration and η means thewave elevation. A very important property of the shallow waterequation is form-invariant, therefore it will keep the same form in
any arbitrary coordinate system. In a new coordinate, keeping the
g as the real world gravitational acceleration, water depth is given by−(2)
h = FGO−1F T GP h ,where F is the Jacobian of transformation, and GO and GP
represent metric tensor of original and transformed physical coordinates, respectively.

Coordinate transformation for cylindrical cloak.

(5)

mapped the right triangle in the original space into the right subdomain in the transformed physical space (as Fig. 2). Consequently the equivalent water depth tensor is obtained
a 2 2 xo2a2a2
y−(1 − 2 ) 2
 (1 − 2 ) 2
2 o
b
x
b
x
x
−
p
o
p


(6)
h=
h .
2
2
2
4
x
a
a
a
p
2
 −(1 − ) 2
yoyo + 2b 2 xo x 2p
xo4 x 2pxo 
The corresponding formulas for upper, left and bottom subdomains can be similarly obtained by applying rotation operatorswith rotation angles of π/2, π and 3π/2.

3. Coordinate Transformation
3.1 Cylindrical Cloak
In order to achieve the cylindrical cloak, the following nonlinear transformation is taken into accounta2
rp =(1 − 2 )ro2 + a 2bθ = θo p(3)

Fig. 2

Coordinate transformation for square cloak.

4. Cloaking Factor
For the purpose of measuring the efficiency of cloaking, we aresupposed to calculate the cloaking factor, which means the ratioof the total energy scattered by the object in the existence of the
cloak to the total energy scattered when seabed is flat, and it isdefined by Porter & Newman 3) as
Ω=

σ clk
.
σ flt

(7)

As can be seen from Fig.3, with the increase of ratio b/a, thecloaking factor can decrease to almost zero, a perfect cloaking.

Fig. 3a number of advantages. For instance, the presented cloak is omnidirectional and effective for all frequency water waves as longas it is under the assumption of shallow water wave. Meanwhile,
there are some drawbacks needed to be overcome. For the seabedtopography exhibited in Fig. 4, sedimentation or erosion will soon
make the cloak ineffective. Therefore, these issues are expected tobe solved appropriately in the future.

Fig. 5

Water pattern of cylinder-shaped cloaking for plane
wave.

Fig. 6

Water pattern of cylinder-shaped cloaking for cylindrical wave.

Fig. 7

Water pattern of square-shaped cloaking for plane
wave.

Fig. 8Water pattern of square-shaped cloaking for cylindrical wave.

Cloaking factor for the nonlinear mapping against
cloak size b/a with different value of ka.

5. Homogenization Theory
For the sake of realizing the anisotropic water depth describedin (4), we should apply the homogenization theory to design theequivalent topography of seabed. Considering a two-layered system, and each layer ought to be homogenous and isotropic. Here
we let the water depth h = h( r ) varies in the radial direction
between constant water depth h1 and h2 with the same width.
According to the homogenization theory, we obtainhh1 (rp )= hθ [1 + (1 − r )1/ 2 ] ,hθh2 (rp )= hθ [1 − (1 −hr 1/ 2
) ].
hθ

(8)

Keeping it in mind, we give an example for the geometry of water
depth consisting of 10 layers as shown in Fig. 4.

Fig. 4 Cross-sectional view of multi-layered water depth
structure.

6. Discussions and Conclusions
The results of numerical computations are demonstrated as Fig.
5-8. It is seen that the cloaking effect of cylinder-shaped cloak is
asymptotically perfect for both plane waves and cylindrical waves.
Concerning the square-shaped cloak, to some extent, it can perform well. However it is not good as the cylindrical cloak, overall.
The imperfection may be attributed to the unsmoothed coordinate
after transformation.
Here we show a scheme of designing a cloak for shallow water
waves via coordinate transformation method. Compared to someother techniques to realize the cloaking, this type of cloaking has

References
1) Pendry, J. B., Schurig, D., & Smith, D. R.: SCIENCE,
Vol.312, No.5781, pp.1780-1782, 2006.
2) Zareei, A. & Alam, M.-R.: J. Fluid Mech, Vol.778, pp.
273-287, 2015.
3) Porter, R. & Newman, J. N.: J. Fluid Mech, Vol.750,
pp.124-143, 2014.

International Course of Maritime & Urban Engineering / Abstract of Master Thesis

July 28, 2017

Role of Beach Morphology in a Tsunami Event – A Numerical Case
Study Based on 2004 and 2011 Tsunami Disasters
Akalanka Silva
Land Development and Management Engineering Laboratory, Department of Civil Engineering
Key Words: Tsunami, Beach Morphology, Inundation, Delft3D Flow, SWAN

1. Introduction
Tsunami is a series of ocean waves that occur often due tosubmarine earthquakes. These gigantic waves sends surges ofwater, sometimes reaching heights of over 30 meters on to land.
These wave trains can cause widespread destruction with in a very
short time frame when they strike ashore. Once generated,tsunamis race across the sea at up to 800 kilometers per an hour.
And their long wavelengths mean they lose very little energy along
the way. When it reaches shallow water, celerity will drop andwater will build up to several meters due to shoaling effect, keeping
energy conservation. When buildup reaches a critical level, wave
breaks or inundates as a surging front depending on the bed slope
and other morphological features of the coast line. A tsunami canrun up to several miles on a flat land or an unprotected beach until
it dissipate its energy.

displacements were calculated accounting USGS earthquake
parameters by Okada’s equations2). Up to this point calculations
were done in Matlab environment.
2.3 Tsunami Propagation
Wave propagation was simulated via Delft3D Flow module
applying water surface deformation resulted from earthquakes as
initial conditions (Fig. 1). Delft3D Flow is a multi-dimensionalhydrodynamic simulation program. The flow module is based onshallow water equations with bossinesq approximation applied(Equation 1 and 2)3).
𝑈𝑈 2
𝜕𝜕𝑡𝑡 𝑈𝑈 + ∇𝐻𝐻 � � + 𝑓𝑓𝑓𝑓𝑓𝑓 =ℎ−𝑔𝑔ℎ∇𝐻𝐻 (ℎ − 𝐻𝐻) + 𝜌𝜌𝑜𝑜−1 (𝜏𝜏𝑠𝑠 − 𝜏𝜏𝑏𝑏 ) + 𝑋𝑋𝜕𝜕𝑡𝑡 ℎ + ∇𝐻𝐻 𝑈𝑈 = 0(2)𝜂𝜂Where 𝑈𝑈 = ∫−𝐻𝐻 𝑢𝑢𝑢𝑢𝑢𝑢

1.1 Focus and Objectives
When a tsunami strikes, the damage it would cause is not only
depend on wave energy but also on morphological features of thecoastline. Disasters occurred in recent times left important
evidences that proves above fact as some affected areas weretotally destroyed while some showed very less damage. Therefore,
having an idea on this nature is important. The primary aim of thestudy is to identify the common morphological features of coastal
areas of which a tsunami will destructively impact. Objectives areachieved by a numerical recreation of 2004 and 2011 events.

(1)

η is surface deviation, H is equilibrium depth, f = 2Ωsinϕ, Ω is
Earth’s rotation rate, ϕ is latitude, ρ0 is reference density, h = η+H,
u is velocity vector in x, τs,τb are turbulent vertical momentum
fluxes at top and bottom, X denotes integrated horizontal
momentum fluxes.

2. Methodology
2.1 Literature Review and Data Collection
The energy dissipation of tsunami and wind wave are different
due to the characteristics of the two kinds of waves. Tsunami is ashallow water wave, even in Deep Ocean, with very longwavelength and relatively high especially near shore. It does notbreak when attacking the shore rather composed of run-up and rundown1). From this fact, and as coastal morphology directly governs
wind wave energy dissipation, it could be suggested that the roleof beach morphology in a tsunami event is different than the
behavior ahead of wind waves.
To assess the role, various data was collected focusing 2004 and2011 tsunami events. Bathymetry data was extracted from freely
available GEBCO data set. Earthquake parameters were acquired
from USGS online data base and water level observations of 2011
tsunami in several locations were downloaded from NOWPHAS.
2.2 Bathymetry Preparation and Tsunami Generation
Firstly, two main regional domains were made to cover the areaof 2004 and 2011 tsunamis. WGS84 spherical coordinate system
was used and bathymetries were fitted in to rectangular grids
having resolution of 0.020 (approximately 1.7 x 2.2 km). Initial

Fig. 1 Simulations of 2004 and 2011 tsunami events.

a
b
c

e
d
2004

2011

Fig. 2 Distribution of local models inside main domains.
2.3 Coastal Interaction
Five separate local domains were built in higher resolution of
0.0020 (approximately 170 x 220 m) inside main two domains (Fig.
2) to assess the coastal interaction of the upcoming tsunami. Wave
conditions extracted from calibrated regional models were fed in to
local models from open boundaries as time series.
2.4 Assessment of Some Common Features in a Coastline
In addition to local domains mentioned above, a common
bathymetry was prepared that consists of general morphologicalfeatures to further investigate the behavior of tsunami striking on a
bay and headlands (Fig. 3). This is inspired by the results of above
mentioned simulations.
(MSL- Mean Sea Level)

Blue-B, Red-b, Green-H, Gray-hb (2.5m above MSL, ~150m from shoreline)
B (5m below MSL, ~400m from shoreline)h (3m above MSL, ~150m from shoreline)
H (4m below MSL, ~150m from shoreline)

Fig. 6 Water level variations at one set of focus points.
Fig. 3 Common bathymetry with focus points.

3.2 Results of the Common Model

2.5 Assessment of Wind Wave vs Tsunami
The common domain is then subjected to an irregular wind wave
condition (Hs=1m, Tp=6s, Wind speed=10m/s from East) toinvestigate the differences of energy dissipation compared totsunami. Wind wave field is calculated via SWAN. SWAN is afully spectral third generation wave model which is based on thediscrete spectral action balance equation. It also uses fully implicit
schemes thus become unconditionally stable.

Hydrodynamic parameters explained above were extracted
similarly from simulation of common domain. In addition to thatwind wave field was extracted from the wave model and results areshown in Figures 7 and 8 respectively.

Blue-B, Red-b, Green-H, Gray-h

3. Results and Discussion
3.1 Results of Regional Models
Tsunami propagation from source to shallow water is focused inregional model stage. Calibration is done by comparing water levelvariations at numerous locations of 2011 Japan tsunami event withmeasured data. Figure 4 shows the calibration plot at Southern
Iwate (N39015’31’’ E142005’29’’)

Water Level (m)8.00

Fig. 7 Water level variations at focus points in common domain.

Measured data
Simulated data

3.00

-2.00

Fig 8. Wind wave field at steady state.

Time

-7.00

Fig.4 Comparison of measured and simulated data (2011 event).
3.1 Results of Local Models
Water level variations, Current velocities and bed shear stresses
were extracted from each local model at numerous focus points. A
sample focus area and parameter extraction points are illustrated in
Figure 5. Figure 6 gives the comparison of water level variations at
different focus points.

b (1.5m above MSL)
B (14m below MSL)h (5m above MSL)

Alike behavior to local models that explained above wasobserved in tsunami simulation while wind wave is dissipating its
energy in a conventional manner which is higher wave heights nearheadlands and comparatively lower energy concentration inside thebay.

4. Conclusions
The behavior of a tsunami at a coastline directly depend on beachmorphology. The relation is comparatively different from that ofwind waves as higher energy concentration observed in partiallyclosed areas such as bays. Results and findings will be useful forplanners and designers of tsunami protection measures in the future.

H (40m below MSL)

References(MSL- Mean Sea Level)
All points are ~100m from shoreline

Fig. 5 A set of focus points of local model “a”.
Both events in 2004 and 2011 acted similarly from the view pointof coastal interaction. Water level heights, current velocities andbed stresses at partially closed bays showed significantly higher
values than those in front of headlands or flat beaches.

1) Pal, B. Panda, K. Comparison of erosional features by tsunami
and wind waves, ICRAGEESD, San Diego, May 2010.
2) Okada, Y. Surface deformation due to shear and tensile faults
in a half-space, Bulletin of SSA, Vol. 75, No. 4, pp.1135-1154,
August 1985.
3) Dutykh, D. Mathematical modelling of tsunami waves,
Mathematics Ecole normale superieure de Cachan - ENS
Cachan, January 2008.

International Course of Maritime & Urban Engineering / Abstract of Master Thesis

July 28, 2017

Water-on-Deck Effects on Roll Motions of an Offshore Supply Vessel inRegular Stern Quartering Waves
Su Sandy Htun
Ship Design Subarea, Department of Naval Architecture and Ocean Engineering
Key Words: offshore supply vessel, water on deck, pure loss of stability, roll damping, second generation intact stability criteria

The second generation intact stability criteria are currently
under development at the International Maritime Organization;(IMO). These criteria are physic-based, consisting of two-leveled
vulnerability criteria and direct stability assessment. One of theremaining issues is the applicability of the criteria for preventing
pure loss of stability in astern waves to offshore supply vessels(OSV). OSVs show an inconsistency problem in the first andsecond level criteria.
OSVs have extended low weather decks about half of the ship
length which is surrounded by bulwarks with freeing ports. But
they often have no bulwark at stern end because of operational
purpose. Thus, in heavy seas, large amount of water can betrapped on the weather deck.
Dillingham1) performed numerical simulation of 2D flow ofwater on deck (WOD) of a fishing vessel in beam seas andFalzarano et al2) improved this method to apply to 3D flow ofwater on deck of an OSV in beam seas. Both approved bynumerical simulation that the water on deck reduces the roll but
not always. Umeda, Aqmil et al3) performed a model experimentof an OSV in regular stern quartering waves and compared it withnumerical model proposed by Kubo et al4). They found that there
were no severe roll at high speed but there was the large heel at
low speed. These results cannot be explained by the simulation
which does not take into account of the water on deck.
In this research, the effect of low weather deck length and theeffect of water on deck on the behavior of OSVs are investigated.
Free running model experiments of the OSVs are performed withmodels having the same hull form but different low weather deck
lengths. Also, the experiment results are compared withnumerical simulation which considers the water on deck effect.

2. Model Experiment
2.1 Ship Model
The ship model used is the same one as in Umeda, Aqmil et al3).
Principal particulars of the OSV are shown in Table 1. But, in thecurrent experiment, the original model was modified into four
different models based on low weather deck length and GM asshown in Table 2.
Table 1 Principal particulars of the OSV.
Length, Lpp
60.00mBreadth, B
16.40mmDepth, D
7.20m
Molded draught, d6.00m
Metacentric height, GM
1.45m

The experiment was conducted for regular waves of two wave
cases (the wavelength to ship length ratio, /L = 1.0, and thewave steepness, H/ = 0.1, /L = 1.5 and H/ = 0.1). The heading
angle was 30 degrees from the wave direction and the tested
Froude numbers range from 0.15 to 0.37.
Table 2 Length of low weather decks of the used models.
Length of lowl/LppGMweather deck, lOriginal OSV
39.94 m0.67
1.45m
Case 10m
0.0
1.45m
Case 2
10.48 m
0.17
1.45m
Case 325.21 m0.42
1.45m
Case 3 with reduced GM
25.21 m0.42
1.053mThe cases of 1, 2, and 3 are also checked with the draft pure
loss level 2 criteria. Case 1 and Case 2 pass the Level 2 but Case
3 fails. This indicates that model in Case 3 can be vulnerable topure loss of stability according to the level 2 criteria.
2.2 Experiment Results
The results from model experiment for the wave case of /L =1.5 and H/ = 0.1 are shown in Fig. 1. For a comparison sake, theexperiment result of original model3) is also included.
60

Max. Roll Angle (degrees)

1. Introduction

50

Case 140

Case 230
20

Case 3

10

Case 3 with reduced GM

0
0.1

0.2

0.3

0.4

Original Model

Froude Number

Fig. 1 Experimental results of all four model cases comparedwith original model result.
For Case 1, Case 2 and Case 3 models, the roll angles are notso large and also no tendency of pure loss of stability. However,as stated before, Case 3 is judged as vulnerable to pure loss by thelevel 2 criteria check. Thus, some contradictions exist between
the level 2 criteria result and experiment result.
For Case 3 model with reduced GM, large roll angles are foundfor low speed (Fn<0.25). During the experiment, it was found thata large amount of water entered from the stern for this case anddespite the egress through the freeing ports, the ingress from sternis much larger. Thus, this large roll angles can be considered dueto the static heeling moment of large volume of water trapped ondeck.

3. Numerical Simulation
3.1 Simulation model
Numerical simulation using a coupled surge-sway-yaw-roll
model developed by Kubo4) which is based on the maneuveringmodel for ships in calm water by Hirano and Takashima5) isapplied. The linear wave-induced forces and moments arecalculated by slender body theory with low encounter frequency
assumption, (Umeda6)). The maneuvering coefficients were
estimated empirically and the roll damping coefficient, thecalm-water resistance and propeller open characteristics wereobtained by model experiments.

agreements between the experiment and the simulation can berealized within the feasible range of the water amount on deck.
The roll amplitudes in the numerical simulation for Case 2 and 3
are reduced because of roll damping effect due to water on deck.
Here, the used water depth on deck is around 0.3m while thebulwark height is 2.7m. The mean roll angle in the simulation forCase 3 with reduced GM increases because of hydrostatic heeling
moment due to water on deck. Here, the used water depth on deckis 0.5m while the bulwark height is 2.7m. The mutual importanceof these two different effects of WOD could depend on themagnitude of hull restoring moment.

3.2 Simulation Results
The simulation results for all model cases are shown in Fig. 2.
Not so good agreement between experiment and simulation isfound except for Case 1, (which has no low weather deck so that
also no WOD).

Fig. 3Time series of simulation with WOD for regularwaves of /L=1.5 and H/=0.1. Here, the Froudenumber is 0.29 for Case 2 and Case 3 and 0.15 forCase 3 with reduced GM.

4. Conclusions
Fig. 2

An example of time series of each case in regularwaves of /L=1.5 and H/=0.1. Here, the Froudenumber is 0.15 for Case 1, 0.29 for Case 2 and Case
3 and 0.15 for Case 3 with reduced GM.

3.3 Water on Deck
For Case 2 and Case 3, having low weather deck, a certain
amount of water can enter and be trapped. If some phase lag
exists between the natural roll frequency of trapped water and theship roll frequency, the water on deck may act as anti-rollingdevice. Since the 4DOF model does not take into account of this,I attempt to use the ITTC recommended estimation formula7) forthe equivalent linear roll damping due to flooded water, which isbased on the database obtained from a systematic modelexperiment by Katayama et al8). The formula is a function of thelength and breadth of the flooded compartment and its water
depth, the motion frequency and the roll amplitude.
For Case 3 with reduced GM, the static heeling arm due toaccumulated water is calculated using normal hydrostatics. The
freeing ports are assumed to be closed and the flow of water isconsidered only over the bulwark.
The numerical simulation model is extended to take account of
the above roll damping effect and the heel moment effect of the
WOD and then applied to the experiment cases. The results areshown in Fig 3. Here, the amount of water on deck, which was
not measured in the experiments, is systematically changed forrealizing reasonably good agreements in the numerical simulation.
The results shown in Fig 3 indicate the reasonably good

It is confirmed experimentally that the Pure Loss Level 2
Criteria cannot be applied to ships with low weather deck length
which is greater than 0.4Lpp and which is not completely
surrounded by bulwarks.
The presence of WOD is important for the stability of the OSV.
For high metacentric height, the presence of WOD reduces theroll oscillation. In contrast, when GM is reduced, the heeling
moment due to accumulated water becomes more relevant.
This work was partly carried out as a research activity ofGoal-based Stability Criteria Project of Japan Ship Technology
Research Association in the fiscal years of 2016 funded by the
Nippon Foundation.

References
1) Dillingham, J: Marine Technology, Vol.18, No.1, 1981.
2) Falzarano, J.M., Laranjinha, M., Soares, C.G.: ISSW, 2002.
3) Umeda, N., Aqmil, A. et al: ISSW, 2016.
4) Kubo, H., Umeda, N. et al: Proceedings of APHydro, 2012.
5) Hirano, M., Takashima, J.: Transactions of the West-Japan
Society of Naval Architects, Vol.59, 1979.
6) Umeda, N., Yamakoshi, Y. et al: Proceedings of Sevastianov
Symposium, 1995.
7) ITTC : Recommended Procedures, Numerical Estimation ofRoll Damping, 7.5-02-07-04.5, 20118) Katayama, T.: Journal of JASNAOE, 2009.

International Course of Maritime & Urban Engineering / Abstract of Master Thesis

July 28, 2017

A Study on Socio-spatial Structure of Informal Settlements byAnalyzing Relationships between Physical Environment and Human
Behaviors in the Inner-city Kampung, Jakarta.
Nugroho Sumanto
3rd Laboratory, Department of Architectural Engineering
Key Words: Urbanization, Kampong, Socio-spatial structure, Physical Environment, Human behaviors.

1. Introduction
Indonesia, in similar vein as other countries within the Southeast Asian region, is experiencing rapid urbanization and urban
growth. Within the Indonesian Archipelago, more than half of the
population (around 52%) resides in urban areas, a figure estimatedto rise to 57.2 percent in 2020 (UN-Habitat, 2015). This trend ismore pronounced in the Jakarta urban region, currently a mega citywith more than 10 million inhabitants. With an urban population
growth rate of 3.7 percent, the city is experiencing immense interurban and rural-migrant migration without significant supply inaffordable housing and basic infrastructure facilities for most of its
urban population.
The effect of this, has been the predominant distribution of
kampong in Jakarta. Kampong, which refers to a settlement in rural
surroundings that comes into being within urban conglomerations(Budiarto, 2003), is usually defined by characteristics such as poor
either planning or housing conditions, and lack of basic
infrastructure such as drainage, water, and sanitation. Even thoughthese areas are marginalized and faced the threat of eviction, they
have also provided a cheap housing solution and livelihood formany urban residents (low-income earners) since the Dutchcolonial period. There have been several attempts to address thechallenge of kampong include the KIP (1960s), public and private
housing interventions and most recently million houses national
program. Yet, the challenge of kampong persists without
sustainable solutions that works for the urban poor.
This study, situated within the context of the above-mentioned
challenges seeks to contribute to efforts in improving kampong
through spatial analysis and bottom-up settlement improvement
strategies. The first step, this study argues, is to obtain a better
understanding in the existing socio-spatial structure of kampong
within Jakarta, in terms of spatial and behavioral aspects to informbetter planning, design and policy strategies.
The objective of the study was therefore (i) to analyze theexisting spatial structure of kampong, (ii) to understandrelationship between human behaviors and informal open space.
Kebon Kacang, which is one of the inner-city kampongs within theCentral Business District (CBD) of Jakarta was selected as the casestudy area. It is located centrally within the Tanah Abang subdistrict, Central Jakarta. This area is surrounded by the city’s mostimportant and prestigious commercial, business and service areas
such as Plaza Indonesia Shopping Mall, Grand Hyatt Hotel, theJapanese Embassy, and the UN local headquarters.
Research methodology adopted for the study included house-tohouse field survey in two different communities: RW3 and RW8of Kebon Kacang (see Fig. 1). The process included literature
review, field observation, questionnaire based interviews with 110

heads of households (35 from RW3 and 75 from RW8) andinstitutional interviews, and mapping of human behavior. Since thetwo community are divided into neighborhood units, five houses
were randomly selected in all the neighborhood units. In eachhouse, the head of household was selected for the interview. For
the purposes of understanding human behavior, open spaces wereselected and human behaviors (activity, age, time and gender) weredirectly observed and mapped.

Fig. 1 Map of studied areas in Kebon Kacang, Central Jakarta.

2. Findings
The findings from this field survey, using the methodology
described above, are presented below.
In terms of land tenure, the survey revealed that main mode ofland acquisition was family inheritance. However, land status,
which refers to the right to use land, was ‘Hak Girik’ (Land Tribal
Right): a Dutch colonial era practice which granted holding title toresidents for cultivation. However, it appears residents over theyears have interpreted holding right as ‘building and use right’,leading individual house construction and claim of land andproperty ownership.
The study also identified several evidences of housemodification among residents in the study areas. In both of thestudy areas, house modifications included parts of the house suchas roof, walls, floors or extension of number of rooms. Change infunction of rooms, for example conversion of living rooms into
bedrooms for rental purposes. They are several reasons behindthese practices, including improving house condition after disaster(e.g. fire or flooding) or generating income from rent to improvehouse conditions. However, owners were more likely to modify thehouse than tenants.
Another important finding was the significance in location in
determining access to facilities and services such as water andsanitation. The field survey revealed houses located along local
access roads were better served with facilities such as waterwhereas those around cul-de-sacs were poorly served. This is dueto the cost of extending services to inner parts of the study
communities, according to interviews. Additionally, even thoughboth toilet and bathroom facilities were available in the study areas,
there was no septic tank. Consequently, one-fifth of the residents’deposit waste water into gutters. This is a major problem forchoked gutters, which cause flooding problems during heavy rains.
Informal economic activity remains the dominant sector in termsof labor and employment in the study areas. In both RW3 and RW8,
the main activities included food vending, tailoring, motorcycle
drivers, and kiosk-style grocery stores. In RW8, which is closer tothe CBD, most of the residents engaged in mobile food vending,street markets, tailoring and many others. The reason behind thiswas the concentration of commercial activities and population
around the CBD provided customer base for those involved in
informal economic activities.
In term of spatial network, the study categorized a 5-level
hierarchy based on function. The typology of the spatial networks
is categorized into four groups based on an order of openness: I, U,
T, and Z. Thus, I and U are more open (linking the studied areas
externally to other parts of the sub-district) and had wider width(not less than 2.5 meters) while T and Z, are typically irregular,
spontaneous and connecting houses and isolated spaces (width lessthan 2.5 meters).
In view of human behavior in informal open spaces, the study
revealed a relationship between the typology of open space and thecategory of human behavior. This was also influenced by the
openness of the different typology of the spatial networks. For
instance, I type, in both RW3 and RW8 more economic oriented
behaviors such as street vending, mobile food vending, kiosk-style
shops (see Fig. 2). The reason for this is due to the openness of the
I typology. Also, social activities such as chatting, gathering andlingering were observed around the spots where economic
activities were organized. For T type, the study observed moresocial and stationary activities such as chatting, gathering, sitting
or lingering. The Z, which is less open in comparison with I and T,
had no significant activities—passive space. This is because of thenarrowness (less than 1.2 meters) its connection with other open
spaces is limited.
Generally, open spaces that had seating facilities, trees or tents
had more social activities since it provided comfortable situation
for residents. The study also revealed that the presence of free WiFi in open spaces affected the social human behavior as moreyoung people gathered to use internet and chat. Residents have also

introduced speed bumps on some roads to reduce motor traffic andencourage children to play on these roads.

3. Conclusions
Jakarta’s dual city status, in terms of daily intersections offormal and informal socio-spatial and economic aspects, exert
significant implications on the urban planning and design of thismega city. The study has attempted to provide a field based
analysis of an inner-city kampong, at the heart of the Jakarta. The
aim has been to comprehend the socio-spatial aspects of existing
conditions and human behavior aspects of open spaces.
This thesis has contributed to locally based understanding of
kampong in Indonesia. The study has affirmed the findings inprevious studies about Kampong (and informal settlements
generally), such as the residents’ occasional housing modification
to deal with declining physical conditions, and to take advantage
of income opportunities (rent or commerce). Additionally, how thespatial structure, openness and typology of open spaces directly
influence human behaviors such as gathering, chatting, selling oreven sitting.
Based on the findings from the study, a couple ofrecommendations have been made to improve current conditions.
Firstly, improve the condition of open spaces to enhance theirusability and comfortably for residents, especially children.
Secondly, redesign the spatial networks of roads and alleys toimprove accessibility, social liveliness, and the opportunity forresidents to continue informal economic activities such as foodvending. In terms of community planning, supporting residents toorganize (through bottom-up processes) and initiate interventionsin their neighborhoods (participatory community planning anddevelopment).
Future research could take into consideration comparative sociospatial analysis of different kampong to identify potentials, positive
aspects and model for improvement.

References
1) Budiarto, L. Dwellers and strangers: Socio-cultural entity,
space-use, and spatial configuration in kampung settlement of
Jakarta, Indonesia. Proceedings of the 4th International Space
Syntax Symposium, London. 2003.
2) The State of Asian and Pacific Cities. Urban transformations:
Shifting from quantity to quality. United Nations Commissionfor Human settlements, UN Habitat. Nairobi: Kenya 2015.

Fig. 2 Observed human behavior in the inner-city kampong in Kebon Kacang, Central Jakarta, Indonesia.

International Course of Maritime & Urban Engineering / Abstract of Master Thesis

July 28, 2017

Flow Field Measurement Around Self-Propelled
KRISO Container Ship Model in Head Waves
Htike Aung Kyaw
Hull Form Design Sub-Area, Department of Naval Architecture and Ocean Engineering
Key Words: KRISO Container Ship (KCS), Particle Image Velocimetry (PIV), EFD, Flow Field Measurement, Head Waves

1. Introduction
During designing process of a ship, one of the main and mostcommon problems which the Naval Architects face is thenecessity to ensure that the combination of hull form and the
propulsion arrangements are at the most efficient state in sense ofhydrodynamics and within the design requirements. The mostimportant task would be that the ship shall perform at thedesignated speed with the minimum power while having thehighest propulsive efficiency without endangering the ship and its
crew in any circumstances. Generally speaking, this can beachieved only by proper matching of the hull and the propeller.
Thus, Propeller-Hull interaction is a conspicuous topic indesigning a sustainable ship. Another issue worth mentioning
would be the global warming. Reduction of greenhouse gas
emissions is underway around the world so as to prevent global
warming. The performance of propulsion of ships in waves isimportant for reduction of CO2 emission in actual voyages.
Studies are being made on fluctuations of the inflow velocity topropeller and change of velocities before and after the propellers
and rudders in a way to develop feasible energy saving devices
and achieve higher propeller efficiencies. CFD (Computational
Fluid Dynamics) is also rapidly improving nowadays and detailed
simulation of flow field around ships in waves are also
progressing very fast. Various CFD softwares are being
developed and widely used in research, development and design
steps. However, the detailed measurement data around ships inwaves are not yet enough to validate the accuracies of the CFD.
Here, the flow field is measured in waves using a stereo PIV(Particle Image Velocimetry) at the downstream section of therudder of a self-propelled KCS ship model. Self-propulsion
experiments in waves have been conducted and the test conditions
for this PIV measurement had been determined.

2. Outline of Experimenttemperature was about 16C and average water temperature wasaround 13C.
Table 1 Principal Particulars of KCS Model Used.
Length (B.P)
LBP (m)3.200
Breadth
B (m)
0.448
Depth
D (m)
0.264
Draft
T (m)
0.150
Displaced Volume0.140
 (m3)

Fig. 1 KCS Model in Towing Tank.
2.2 Experimental Conditions
Pitch and roll free gimbal under the load cell attached on thebottom end of the heaving rod was mounted at the center ofgravity the model and this heaving rod was installed in a lightweight carriage. A servo-type wave meter was installed 3.24 m infront of FP, to acquire incident wave data. The ship was free tosurge, heave and pitch. Motor and dynamometer were installed
for self-propulsion tests. Forces on longitudinal (x)-direction (Fx)were measured using a load cell attached to the heaving rod where
positive Fx was taken towards the aft of the ship. Wave elevation,
Fx, heave, pitch, surge, thrust and torque were measured andlogged for each experiment condition. From this, we could plot atimes series data of aforementioned data and calculate terms suchas effective inflow velocity, surge velocity, surge acceleration,hydrodynamic force etc. as shown in Fig. 2.

2.1 Overview of Experiment
A 3.2 m KRISO Container Ship (KCS) model has been used
for this experiment. Various experiments were conducted in thetowing tank of Osaka University by our team. This experiment
was conducted to measure the flow field at the downstream
section of the rudder using the PIV systems for the self-propelledship model in head waves. Principal Particulars of the model are
as shown in Table.1. A 5-blade propeller was installed at a
position 56mm forward of AP. This propeller has a diameter of
0.1099m, pitch ratio (P/D) of 0.95, expended area ratio (AE/AO)
of 0.8002 and a hub ratio of 0.18. Open-Water Test had been
conducted for this propeller beforehand. PIV experiment for flow
field measurement was conducted in mid-April where average air

Fig. 2 Time Series of Logged and Calculated Data for /LBP = 1.15.

3. Stereoscopic PIV Measurements in Waves

0 deg

90 deg180 deg

270 deg

PIV Measurements were made for head waves of /LBP = 0.65,
1.15 and 1.37 with the ship speed of 1.456 m/sec, i.e. Froude
Number 0.26. The PIV measurement plane is located at 80 mm
aft of AP. PIV laser and cameras were triggered by delaying the
calculated time period for each wave condition using thezero-crossing signals from the wave meter.
In this PIV measurement, the flow field at a plane behind therudders was measured around the self-propelled ship model inwaves. In Fig. 3, the velocity distribution is shown for wave
condition (/LBP = 1.15). The zero degree phase shown here is themoment when average value of the wave elevation at wave meterchanges from minus to plus. The other phases are shifted every ¼
period. The flow velocity and the coordinates shown here are
non-dimensional. For each /LBP, PIV images were taken at 3
different water depths to ensure the coverage of the whole flow
field for each wave condition and to overcome the vertical limitsof the PIV system. The number of data used for time averaging ofeach depth was about 100 images per phase.

Hydraulic Research (IIHR)’s free-running 2.7 m model data havebeen compared. The results of comparisons were foundacceptable as in Fig.4 graphs.

Fig. 4Comparison of non-dimensionalized wave and ship
motions among other institutions.

5. Conclusions
Fig. 3 Phase-Averaged Velocity Distribution in Waves.

4. ComparisonsThis experiment focused mainly on flow field measurement at
aft of rudder for a self-propelled KCS model in head waves but it
is not just limited to visualizing the flow field at the point ofinterest. Comparisons of the ship motions corresponding to waves
with other tests facilities were carried out so that the accuracy ofthe experiment itself can be confirmed. Not to mention, we also
compared the trend of graphs for thrust and torque, resistance andpowering as well as the propeller revolutions for calm water andeach wave conditions with the data received from FORCE
Technology. FORCE Technology used a 6.0702 m KCS modeland conducted with Heave and Pitch being free. During our
experiment, 3 DOF (degree of freedom) ship motion wasconsidered, namely, heave, pitch and surge using a weak springarrangement whilst keeping the ship in an average position withregards to the towing carriage.
Furthermore, non-dimensionalized wave elevation, heave andpitch with FORCE Technology’s model and Iowa Institute ofShip motions such as heave and pitch had been confirmed withvarious test facilities and were found agreeable although the test
methods in each facilities were different: FORCE Technology
having only 2 DOF, IIHR conducting as free-running model.
More accurate flow field measurements can be done using the
PIV systems if the number of runs increases so as to obtain more
images or if PIV system can have larger vertical field of view sothat we could run less number of vertical depths whilst having
more images for the same number of test runs.
Flow-field calculated by CFD for the self-propelled KCS inhead wave conditions will be conducted in the future. With theexperimental data and flow-field measurement provided by thepresent work, CFD result will be validated and modified to
explain the phenomena in this experiment.

References
1) Tamaki, K (2017): Study on Fluctuating Flow Field aroundContainer Ship Stern in Waves, Osaka University.
2) FORCE Technology, Claus D. Simonsen (2017): Added
Powering in Regular Head Seas.
3) IIHR Test Summary: T2015 Case (Updated: February 2017)

International Course of Maritime & Urban Engineering / Abstract of Master Thesis

July 28, 2017

Numerical Study on Determination Technique for EquivalentDistributed Stress
Ahmad Zakky

Ocean Material Engineering, Department of Naval Architecture and Ocean Engineering
Key Words: Equivalent distributed stress, Crack cohesive force model, Crack opening displacement, Stress intensity factor,
Finite element method

1. Introduction
In this study, a new EDS determination method based on left
opening right closing integral capable of avoiding the singularity1)
is proposed. In this method, EDS is approximated by 3rd order
spline interpolation without singularity. When EDS’s spline knots
are arranged at SIF’s evaluation positions in the a-K relation, thespline coefficients are determined by using the SIF at a point
nearby to notch bottom. When the spline knots are arranged
irrelevantly to the a-K relation, the coefficients are determined byleast square method (LSM). The validity of proposed methods are
examined by comparing the estimated fracture mechanics
parameters (SIF and COD) with those derived from the strict
solution or elastic-plastic finite element (EPFE) analyses.

2. New approach for the EDS evaluation
The EDS for an ICC panel subject to uniform remote loading(Dugdale model) should be uniform and equal to the remote stress.
Let us consider an ICC panel with a crack half-length of c. The
position on the crack face is specified by the x-coordinates in
Fig.1. Let Nξ be the number of division for spline interpolation,ξi(i=1,…, Nξ) x-coordinates of the right end for the i-th divisionsection, and ξ0=x0 at the notch bottom(a=0). EDS in the i-th
section fi(x) is approximated by 3rd order spline interpolation by
the equation below:fi ( x=) α i x3 + βi x 2 + γ i x + δ i (xi −1 < x ≤ xi ) ; =i 1,..., Nx(1)where, αi, βi, γi, δi are cubic spline interpolation coefficients. {ξi(i=0,…,Nξ)} are spline knots. Let Na be the number of SIF
evaluation point, and aj (j=1… Na) be the x-coordinates of the j-thevaluation point. Na is chosen so that Na ≥ Nξ. Let Kj be the SIF at
x=aj. Superposition principle leads to the equation of Kj below:
Kjfi ( x)2
a j ≤xi min ( ai ,xi )=dx ; j 1,..., N a∑i =1 ∫x =xi −1
π aj
1 − ( x / a j )2(2)

where, fi(x) is given by Eq. (1).
The spline’s continuum conditions at knots for 0th-2nd
derivatives and the natural spline’s endpoint conditions are given.
Then this conditions are the governing equations that relate thespline coefficients to the requirements of spline EDS model (a-K
relation, spline’s continuum conditions and natural spline’s
conditions). Let m be the number of governing equations and n thenumber of spline coefficients. The m and n are given by equations
below:
m = N a + 3 ( Nξ − 1) + 2, n = 4 N a(3)When the spline knots are arranged irrelevantly to the a-K
relation and Nξ<<Na, m becomes larger than n. The governing
equations can be written as Eq. (4). This system of linear equations
is over determined, and the spline coefficients can be determinedby linear least square method. In this case, the a-K relation is notstrictly established, but EDS’s spatial instability can besuppressed.
 A11  A1n 
 
 

 a1      β1    γ 1  =[ A=]{U }     δ1       δ N   ξ  A m1  Amn  K1 
K 
 2
  


 K Na RHS }  0 
{=
  


 0 


 0 
 0 

(4)

When spline knots are arranged at SIF evaluation positions in
the a-K relation, Nξ =Na, and m=n -1. This makes the system Eq.
(4) to be underdetermined, and there is no unique solution. In thiscase, the equation of the SIF at a point nearby to notch bottom,
shown below, is appended to the governing Eq. (5).

K sx1 =2∫
π ( sx )1

f1 ( x)sx1

x = x01 − ( x ( sx1 ) )

2

dx

(5)

where, Ksx1 is the SIF at x = sx1 (0<s<1). This point nearby tonotch bottom is within the 1st (the closest to the notch bottom)
spline section, and the right hand side of Eq. (5) becomes a linear
equation of {α1, β1, γ1, δ1}. In this case, n=m=4Na, and thegoverning equations can be written as: A11′′]{U }  [ A= An′1 a1 β 1
 A1′n    γ 1 

 =
δ 
1
′   
 Ann
  
 
δ Nξ  K1 
K 
 2  .

 K Na RHS }  0 
{=
  


 0 


 0 
 0 

(6)

This system of linear equations is a full-rank system, and thesolution is unique. In this case, the a-K relation is strictly
established, but the system becomes ill-conditioned, and EDS’s
spatial instability due to over fitting may occur. Hereafter, thepoint at x=sx1 is called ‘NBP (nearby point)’. Hereafter, EDS

determination in which spline knots are arranged at SIF evaluation
points and utilize the SIF at NBP is called ‘NBP’ determination.
For LSM determination, the approximated solution of Eq. (6)can be calculated by adopting least square method (LSM) as
shown below:

{U }

=
A+  { RHS } ;  A+ ( [ A] [ A] ) [ A]
T

−1

T

needed to adopt spline knots intervals smaller than 0.5mm underconditions chosen.

(7)

where, A+ is the Moore-Penrose pseudo inverse. The strict solutionof Eq. (4) is calculated by solving the linear equation system.

3. Development of strip yield model based on EDS
From a-K relationship subject to an external load and that
subject to a uniform cohesive stress equivalent to yield stress,
Crack opening displacement (COD) derived from each stress canbe calculated, then, COD in strip yield model is obtained asfollow,=
V (b) V P (b) − λσ YV Y (b)(8)

Fig.1 The comparison of EDS’s of an out-of-gusset welded joint

where, VP(b) is COD derived from an external load, and VY(b) is
COD derived from cohesive stress. λ is plastic constraint factor,
σY is yield stress.

4. Numerical example
In order to examine the applicability of proposed EDS
determination techniques, FM parameters of a semi-circularsurface crack in an out-of-gusset welded joint studied by
Kajimoto2), are calculated by EDS-based crack cohesive force(CCF) model. The crack depth is 5 mm and external force 100
MPa is applied. σY is 392 MPa. Young’s modules is 20,600 MPa,and Poisson’s ratio is 0.3. a-K relations are prepared by
performing linear finite element FCP (LFEFCP) analysis, and thereference solutions of EPFM parameters (COD and γp) arecalculated by performing elastic-plastic finite element (EPFE)
fracture mechanics analyses.
As the result in Fig. 2 shows the comparison of fP determinedby the proposed EDS determination techniques. This figure showsthat a large numerical instability appears near the notch bottom(c<0.5mm) (3D_NBP). fP becomes negative at the notch bottom.
This cannot be logical, and FM parameters calculation based on
this EDS is meaningless. It is considered that this is due to theextremely large amount of unbalance in segment length, and thepoor accuracy of the SIF at NBP estimated by the extrapolation.
Fig. 10 shows that this numerical instability is well suppressed incases 3D_LSM0.5 and 3D_LSM0.25, and the fP’s stability
becomes better with the increase in spline segment length.
Fig. 11 also shows that the EPFE’s COD (VFE) approximately
agrees with CCF model’s CODs when a finite quantity of VFE iscalculated. On the real crack face (c<5mm), the COD for case
3D_NBP shows a strange decline in the 1st spline segment (c <0.205mm, adjacent to the notch bottom), while those for LSM
cases it shows smooth and monotonic changes. It is consideredthat the strange COD in case 3D_NBP is due to the EDS’s
numerical instability (Fig. 10). The difference in CODs for LSM
cases is negligibly small when the spline knots interval is larger
than 0.25. These results show that it is essential to adopt
LSM-based EDS determination technique for the cases withouthighly precise SIF for infinitely small cracks, and there is noFig.2 The comparison of COD’s of an out-of-gusset welded joint

5. Conclusions
In this study, an EDS determination method based on left
opening right closing integral capable of avoiding EDS’s
singularity has been proposed with high prediction accuracy toestimate various elastic-plastic FM parameters for infinite centercracked panels. This demonstrates the effectiveness of the FM
parameter calculation techniques based on a left opening rightclosing integral, which is capable of avoiding EDS’s singularity. It
is essential to adopt LSM-based EDS determination technique forthe cases without highly precise SIF for infinitely small cracks(such as a surface crack in a three-dimensional welded joint), andthere is no needed to adopt spline knots intervals smaller than
0.5mm under conditions chosen. In other hand, it is needed to
examine the plastic constraint factor λ, which is used in
CCF-model analysis, for various three-dimensional cracks byperforming EPFE and crack cohesive force (CCF) analyses.

References
1)
2)

Osawa Naoki et.al.: Papers on Japan Maritime Ocean
Engineering Lecture, 2015 A - GS 8 – 3
Kajimoto Katsuya: Doctoral thesis, Hiroshima University,
1985.