review of numerical approach used in the …assisted mooring system [9]. moored system where...

International Journal of Engineering Technology and Scientific Innovation

ISSN: 2456-1851

Volume:03, Issue:05 "September-October 2018"

www.ijetsi.org Copyright © IJETSI 2018, All rights reserved Page 201

REVIEW OF NUMERICAL APPROACH USED IN THE OPTIMIZATION

OF MOORING SYSTEMS FOR FLOATING STRUCTURES.

Ben Uwihanganyea, Christiaan A. Adenyab, Hiram M. Ndirituc

aDepartment of Mechanical Engineering, Jomo Kenyatta University of Agriculture

and Technology, Main campus Juja, Kenya

bDepartment of Marine Engineering, Jomo Kenyatta University of Agriculture


cDepartment of Mechanical Engineering, Jomo Kenyatta University of Agriculture


ABSTRACT

This paper present a review on the technologies that are used in station-keeping of floating

platforms, the numerical methods used to model the mooring system dynamics with

environmental load of wind, current and wave force interaction. Furthermore the design and

optimization of the mooring system is reviewed. The lumped mass model found to be preferred

in commercial application over finite element and finite difference based on its simplicity and

ability to capture the same physics as of high order model. It was reviewed that Finite difference

would be better if its present nuances and numerical limitation are eliminated. It is notable that

the mooring line damping contribute about eighty percent of the total moored system damping,

hence its accurate prediction is critical during the design. The mooring line damping depends on

the drag force, therefore poor selection of the drag coefficient will lead to wrong prediction of

the amplitude of oscillation of the floater. During optimization of mooring system, it is seen that

the use of genetic algorithms have become popular. They account for environmental load

distribution, anchor holding capacity and mooring line properties such as materiel length and

tension. Some gaps are presented at the end of this review paper including unclear relationship

between mooring line damping and total tension and the surface roughness effect on drag

coefficient of mooring line.

Keywords: Mooring line, damping, drag coefficient and floater.


ISSN: 2456-1851


www.ijetsi.org Copyright © IJETSI 2018, All rights reserved 02

1. INTRODUCTION

The exploration of petroleum and gas in sea

or lake waters is going deeper to more than

2500m of depth [1]. In addition floating

wind turbine and wave energy converters

have shown to be among the potential

sources of renewable energy. This has

compelled many researchers to find an

optimum design, not only in terms of cost

but also safety of station-keeping of any

floating structure within water bodies.

Floating structures within water bodies

experience linear and rotational motions due

to environment loads such as wind, current

and waves. Station-keeping systems have to

respond effectively to these motions. As

shown in Figure 1, linear motions include

heave, sway and surge while rotational

motions include pitch, roll and yaw. Heave

motion is in vertical direction moving

upward or downward while yaw is the

turning rotation of a vessel about the same

vertical axis. The heave response should be

controlled and minimized for effective and

efficient working of floating offshore

platforms because this motion is primarily

responsible for causing damage to the risers

and mooring systems due to excessive

vertical motion of the vessel [2]. Surge is the

linear oscillation along x-axis while roll is

the rotation of a vessel about the same

longitudinal axis caused by maritime

conditions. In 1990, the mooring lines of a

semi-submersible located in North Sea were

damaged due to a severe storm [3]. Deng [4]

studied the wave group characteristics

effects on a semi-submersible in freak waves

and showed that the surge response greatly

increases due to the freak wave and the large

amplitude surge responses due to transient

freak waves. These displacements are

closely related to the maximum tension

forces of mooring lines. Therefore, the surge

motion response of a semi-submersible is a

key issue especially in the extreme sea state.

Sway motion moves laterally and is

generated directly either by the water and

wind currents exerting forces against the

vessel while pitch is the up or down rotation

of a vessel about the same lateral axis. In

numerical study of hydrodynamic response

of mooring lines for large floating structure

in South China Sea by Yipeng Pana in 2015

[5] showed that surge and sway become

larger in moored station keeping system

with longer mooring lines.

The floating vessel motions are also

classified as low frequency (LF) and wave

frequency motions (WF). The WF motions

is the vessel response to first order wave

loads while the LF is slow drift motion due

to second order waves, wind, or driven

motion due to vessel thrusters [6]. The

presence of both WF and LF in the same

direction is called superimposed wave

frequency.


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Figure 1: Linear & rotational motions of

the vessel

In any marine operations, an important

aspect is to ensure a precise position and

motion control of a floating structure. This is

desirable to maintain integrity of system

elements and to maintain safe distance to

other structures within the waters. The

station-keeping system is one of the major

components of a floating offshore unit. This

technology was invented due to the need of

offshore extraction of oil and gas from the

deep seas or lake waters, and then expanded

to renewable energy sector due to offshore

wind turbine and wave energy converters.

The design of station keeping for any

floating system must reflect the

environmental condition [7].

Different types of station keeping principles

are used in order to withstand the

environmental forces on the floating

structure arising from wind, waves and

current [8]. For a semi-submersible unit, the

station-keeping system can be a mooring

system only, a dynamic positioning (DP)

with thrusters and or a dynamic Positioning

assisted mooring system [9]. Moored system

where positioning uses the mooring lines,

thruster-assisted mooring system where

positioning uses both mooring lines,

thrusters and propellers and thruster assisted

mooring have been used in the design of

station-keeping systems for floating

production storage and offloading (FPSOs).

The thrusters are used for heading control

and for reducing the mooring load. One of

the principal reasons for using thruster

assisted mooring is that it can reduce overall

project costs by reducing the mooring

system in terms of either fewer mooring

lines or a lighter overall system, especially

for deep waters projects [10].

For the dynamic positioning system,

position is achieved by use of thrusters and

propellers. A propulsion system applied for

dynamic positioning of vessels must be able

to generate counter forces against

environmental forces such as wind, current,

and waves, as well as damping forces

resulting from the drag of a deployed array

of pipes and risers during station keeping

operations. Environmental forces are omni-

directional, therefore, propulsion systems or

devices must have the ability to generate

thrust in the full 360 degrees. In order to

move the vessel from location to location,

the propulsion system installed on DP

vessels needs to generate the conventional

propulsion forces in the longitudinal

direction of the vessel [11]. One of the main

disadvantages of dynamic positioning


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systems when compared to mooring systems

is the fuel costs consumed in operation [12].

These systems are used for different designs

and optimization, depending on cost and

safety requirements. This paper will keep its

focus on moored systems. It will review

numerical model developed to analyze the

dynamics of mooring lines, design and

optimization of mooring systems.

2. MOORING SYSTEM

A mooring system refers to any permanent

mechanism to which a floating object may

be secured by use of mooring lines. Mooring

systems are mainly composed of two

components: mooring line and anchor.

2.1. Mooring Line

Mooring lines may be made from chain,

wire rope, synthetic rope, or a combination

of these. Different combinations of line

material type [13], size, and location are

chosen in order to achieve given

requirements for the mooring performance

[14].

2.1.1. Chain

Chain is the most popular used for mooring

lines and is available in different size and

grades. The chains mooring lines utilize

their own weight to give good restoring

forces. These results to increase the top

tension of the lines and enlarge the vertical

loads on the vessel when the line is lifted

from the sea bottom [15]. Due to the lower

end of chain mooring line that is resting on

the water bed, the anchors only reacting to

the horizontal force. Furthermore chains

have good abrasion characteristics [16].

Figure 2: Studlink and Studless chain [17]

There are primarily two types of designs of

chain: studless and studlink chain as shown

in Figure 2. The studlink chain is commonly

used for floating structures that are moved

numerous times during their lifetime. The

stud provides stability to the link, resulting

in a chain that is strong, reliable and

relatively easy to handle. The studless chain

is commonly used for permanent moored

structures. Removing the stud reduces the

weight per unit of strength and increases the

chain fatigue life. However, this type of

chain is more expensive and less convenient

to handle [18].

2.1.2. Steel Wire Rope

The number of strands and wires in each

stand, core design and layout of strands is

critical for the required strength and bending

fatigue considerations of the wire rope [14].


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Figure 3 shows different type of wire rope

construction.

Single-strand ropes are commonly used in

permanent mooring systems. The wires are

wound as a helix with each layer rapped in a

different direction, providing torque

balancing which prevent the rope from

twisting as load is applied. This spiral strand

is more fatigue resistant than the multi-

strand wire rope. Sheathing with a

polyurethane coating, adding zinc filler

wires or using galvanized wires is a

common practice meant to enhance the

corrosion resistance. However, sheathing

provides the best performance, provided that

there is no damage to the sheath [18]. The

weight of the wire rope makes it suitable for

use [17].

The multi-strand wire ropes may contain

either a fiber or metallic core. This core

provides support to the outer wires,

especially in a drum, and may in some

applications absorb shock loading. Metallic

core ropes can be divided into two types:

independent wire rope core and wire-strand

core. Independent wire rope core is the most

common core for heavy marine applications.

The fiber core is used in lighter marine

applications [18].

Figure 3: Typical wire rope constructions

[17]

Steel wire rope has a lower weight than

chain, but approximately the same breaking

strength and higher elasticity. As a result it

does not result to increase the top tension of

the lines nor enlarge the vertical loads on the

vessel in case the line is lifted from the sea

bottom [8]. The wire rope constructions

consist of multiple wire strands wound in a

helical pattern around a center core to form a

rope. A six-strand wire rope is easy to

handle and is, along with studlink chain,

commonly used in temporary mooring. The

six-strand ropes are the most common type

of multistrand ropes used in the offshore

industry. To achieve higher strength the

wires have staggered sizes [18].


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2.1.3. Synthetic Fiber Ropes

The difference between a fiber rope system

and wire rope-chain systems is primarily the

non-linear stiffness. This is a nonlinear

minimum tension requirement and that the

location of the fiber rope segment needs to

be away from the fair-lead and the water-

floor. Fair-lead is where the mooring line

attaches the floater. In addition, unlike the

steel components the fiber rope stiffness

increases with mean load and decreases with

cyclic load range and with load relief over

time [14]. Fiber ropes for use in permanent

or temporary mooring systems normally

consist of polyester, aramid, high modulus

polyethylene (HMPE) or nylon. Polyester is

considered as a good candidate for mooring

applications due to its low cost, low stiffness

which induces less dynamic tension, good

fatigue properties, good strength to weight

ratio and good creep resistance [14]. Fiber

materials as HMPE and aramid are

considered suitable for applications where a

small rope diameter is required or for ultra-

deep water mooring applications. In shallow

water, nylon rope is often installed in the

mooring line to absorb energy from the

dynamics of the moored structure, due to its

high elasticity [14].

2.2. Anchor

Anchor is a device usually of metal or

reinforced concrete attached to a floater by a

marine cable to keep it in a particular

position by means of its weight or a fluke

that digs into water bottom. The choice of an

anchor is mainly dependent on water depth,

the soil behavior and the loads the anchor

needs to withstand, in addition to installation

method and cost. Figure 4 represents anchor

types ranged by water depth and soil type.

Figure 4: Typical anchor types ranged by

water depth and soil type [17]

1. Dead weight anchor: A dead weight

anchor typically consists of steel and

concrete. The horizontal and vertical load

capacity depends on the anchor submerged

weight and the friction between soil and

anchor, respectively. It may be used for

small mooring systems, but is normally not

used for deep water mooring systems [14].

2. Pile anchor: A pile anchor is a hollow

steel cylinder installed by use of a pile

hammer or vibrator. The anchor is able to

withstand both horizontal and vertical loads.

The capacity of this anchor is dependent on

the friction of the soil along the pile and the

lateral soil resistance [15].


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3. Drag embedment anchor: Drag

embedment anchors include both fluke

anchors and plate anchors. Installation is

performed by dragging the anchor into the

seabed. The anchor is well suited to

withstand horizontal loads. The capacity of

the anchor is dependent on size and angle of

the fluke or plate, the ability to penetrate and

the geotechnical conditions of the

installation area [15].

4. Suction anchor: The suction anchor also

consists of a hollow cylinder and is similar

to the pile anchor, although with a much

larger diameter. The anchor withstands both

horizontal and vertical loads, and the

capacity of it depends on the friction of the

soil along the cylinder wall and the lateral

soil resistance. These anchors can be

accurately positioned and are commonly

used for mooring at deep water [19].

5. Dynamically installed anchor: The

dynamically installed anchors include both

deep penetrating anchors and torpedo

anchors, and are designed to penetrate deep

into the seabed. There are no orientation

requirements on the loading for this anchor.

6. Vertical load anchor: Vertical load

anchors are installed in the same way as a

drag embedment anchor, but the penetration

depth is much larger. The anchor can

withstand both horizontal and vertical loads,

and is suited for deep water mooring

applications [15]. For more information on

Special anchors development for offshore

applications were reviewed by J. Atturio,

R.Taylor and P.Valent [20, 21, 22]. The

details on anchors sizing and pricing can

also were discussed by Baldt inc. and

Buttereld respectively [23, 24, 25].

2.3. Categories of mooring systems

2.3.1. Catenary mooring system

As shown on the Figure 5, the mooring line

is hanging freely and the whole cable profile

is suspended or part of its length rests on the

waterbed. A catenary line system usually

consists of chain links that relies on the

weight of links or clamp weight if used to

provide horizontal restoring force. If no

clump weight is attached, a very long

mooring line of chain links must be

considered to obtain adequate flexibility.

Hence, this concept might not be suitable in

shallow waters. Moreover, catenary line

systems will certainly induce vertically

downward loads [27]. Based only on the

motion responses of the floating structure,

the catenary mooring system is the most

suitable system because it exhibits the

smallest motion [28].

Figure 5: Catenary where mooring line

resting on the waterbed

2.3.2. Semi-Taut mooring system


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Figure 6 shows the semi-taut mooring

system where the lines are inclined and is

taut due to the pretension caused by the

platform excess buoyancy. The line does not

contact the waterbed and the anchor

experiences horizontal and vertical loads.

Most of the restoring loads are generated by

line elasticity. The mooring radius of the

semi-taut mooring system is smaller than

that of the centenary mooring system if

designed to support the same platform size

and weight. The semi-taut mooring system

come after the catenary system to have a

better response to the motion of the vessel as

water depth increases [28].

Figure 6: Semi-taut mooring line

2.3.3. Taut mooring system

The Figure 7 shows a taut line connected to

the anchor which is experiencing mainly a

vertical load. A taut-line system is

composed of wire or synthetic ropes and is

normally highly pretensioned. To investigate

the responses of taut mooring line against

hydrodynamic forces and external

excitation: Gottlieb and Yim [29] carried out

a stability analysis of a taut mooring system.

Umar and Siddiqui [30] carried out a

reliability analysis of taut mooring system

against yielding of taut moorings. As a

result, taut-line systems are usually quite

stiff both in horizontal and vertical

directions and can significantly reduce

vertical motions of the floating structure if

connected to the water bottom directly. Z.

Gao and T. Moan [27] found his feature is

certainly not acceptable for motion-

dependent structures like Wave energy

converters. In order to limit the influence of

mooring systems on vertical motions, the

top part of mooring lines, which is directly

attached to the floating, should be kept as

horizontal as possible. In such cases, buoys

can be attached.

Figure 7: Taut line

2.3.4. Taut mooring line with buoy

As Figure 8 shows, in this configuration the

buoy is attached to the sea bottom by a

vertical taut-line and connected to the

floating horizontally.

In 2011, Vicente et al.[32] investigated

different mooring configurations with slack

chain mooring lines of a floating point

absorber with or without additional sinkers

or floaters. It was found that the different

arrangement of the buoys and weights would


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bring significant differences in terms of

average and maximum tensions on the

mooring cables. In 2014, Zhi-Ming Yuan

and Atilla Incecik [31] studied the effects of

buoy position and its Volume with the

mooring system. They found that presence

of the subsurface buoy at half of the length

of the mooring cable in a single-line system

reduces the maximum static tension by

about 14 − 15% and by nearly 13% for

dynamic tension compared to the no buoy

condition. It was observed that the

displacement of the floating structure

increases as the buoy’s volume increases but

no optimal size or position of the buoy to

provide minimum displacement of the vessel

was studied [31]. It is necessary to establish

the relationship between buoy position and

size on one hand and the displacement of the

floater.

Figure 8: Mooring line with buoy [31]

2.4. Effects of water depth

The water depth has to be considered during

the selection and the design of the mooring

system. The water depth has different

impacts on the natural period and damping

ratio of the vessel motions moored by

catenary, semi-taut or taut mooring system.

From the numerical simulation, validated by

the experiment done in the Joint Laboratory

of Wind Tunnel and Wave Flume in Harbin

Institute of Technology, the global responses

of the semi-submersible platform attached

by mooring lines using catenary, semi-taut

and taut mooring systems in 500 m, 1000 m

and 1500 m water depth in the South China

Sea were compared[28]. It was seen that

there is an increase in surge and little

decrease of the pitch natural period with

water depth increase and the natural

damping ratios of the surge and pitch

decreases with increasing water depth. For

the most unloaded mooring line, the taut

mooring system is the most suitable due to

its small amplitude changes. For the most

loaded mooring line, the catenary mooring

system is the most suitable due to its small

peak value, followed by the semi-taut

mooring system. With increasing water

depth, the maximum tensions in lines

increase, indicating that when the length of

mooring lines becomes longer, the dynamic

forces in the mooring lines become more

significant [28].

2.5. Influence of Mooring line Damping

Damping is a characteristic of retaining the

equilibrium after a disturbance of the system

has occurred. The main sources of the total

damping for a moored structure are current

and viscous hull, radiation, wave drift force

and mooring line damping [34, 33]. The

dynamic responses of mooring line serve a

major role in the station keeping of any


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floating structure within water bodies. Thus

the accurate prediction of that response is

essential to have safe moored mechanism. It

is a useful parameter during the estimation

of the Low Frequency vessel motions for

moored offshore structures working in deep

water, whose nature frequency are close to

low frequency. When the LF becomes

similar to the natural frequency of the floater

will cause resonance, then the oscillation

amplitude of the floater will be magnified.

The mooring line induced damping

increases relative to other sources of

damping that are affecting the motion

response of the vessel considerably [33].

The work by Huse [36, 35] indicated that the

mooring line damping in surge for a floating

offshore oil and gas installation can

contribute as much as 80% of the total

damping. The increase of mooring line

damping can decrease the static tension by

reducing the LF motion amplitude, hence

the offset of the floater. It could also reduce

the dynamic tension in mooring line[38].

The problem is to find whether the increase

of the mooring line damping will increase or

decrease the total tension in the line. Thus

deep analysis of mooring line damping is

critical, particularly to satisfy the needs for a

safe station keeping of a floating platform. A

review of mooring line damping is presented

in the next section.

3. MOORING SYSTEM DAMPING

Mooring system damping is an important

parameter to analyze and optimize as much

as possible. This is indeed desirable because

if the mooring system damping increases it

will cause the system vibrations to die out

faster after an external disturbance. This can

be clearly seen in Figure 9.

Figure 9: Damping increases and system

vibrations die out quickly.

A moored floating platform system damping

is contributed by four components which are

the wave drift damping, the wind damping,

the current and viscous flow damping on the

hull, and the mooring line damping [33, 17].

Wave, wind and current damping are the

results of the environment forces on the

vessel here below shown in Figure 10.

Figure 10: Forces on a floating structure


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3.1. Wave drift and viscous damping

Moored vessels in water bodies are exposed

to large linear wave forces and moments,

which are linearly proportional to wave

amplitude and contain the same frequencies

as the waves. This linear component is also

known as first-order wave forces and it is

limited in the frequency scope of wave

spectrum [3].

In addition, floating structures are subjected

to nonlinear wave forces and moments

which are proportional to the square of the

wave amplitude. This is also known as

second-order wave force. The effects of

second-order wave forces are not often

considered since the magnitude of second-

order wave forces might be small relative to

the first-order force. However it may cause

resonance oscillations when its natural

frequency becomes similar to the natural

frequencies in surge, sway and yaw motions

of a semi-submersible positioned by

mooring or dynamic positioning system [39,

34] and [3]. The low frequency wave drift

force may excite the floater and mooring

system at their natural frequency, resulting

in resonant motions in both horizontal and

vertical planes. Therefore, the accurate

prediction of the wave drift forces exerted

on the structure is essential for safe and

optimum design of the mooring systems at

the initial stages.

The mean and slow drift forces on a moored

platform in water bodies could be calculated

by including difference frequency second-

order potential flow excitation [40].

Normally, it can be simplified by using

Newmans approximation and only including

quadratic terms from the first-order

potential. Pinkster [4] has made the first

attempt to estimate second-order wave drift

forces, where the wave forces were

calculated by means of quadratic transfer

functions. He calculated the quadratic

transfer functions for the low frequency

longitudinal force in head waves in regular

and irregular waves and compared them

with the experimental data. A reasonable

correlation was achieved considering the

complexity in both the test set-up and the

method of analysis. Stansberg et al. [41]

performed model tests with a moored semi-

submersible in irregular waves to evaluate

slow-drift wave forces and motions. The

experimental data were compared with

numerical predictions, based on traditional

potential flow theory as well as on empirical

drift coefficients. Large differences between

measurements and potential theory were

observed in high sea states, while the

empirical reconstruction compared well.

Hassan et al. [42] carried out a mode test in

scale 1:50 with a horizontally moored, large-

volume production semi-platform to study

slow-drift forces in currents and waves.

Berthelsen et al. [43] presented some main

results from the experiments and compared

them to time-domain numerical simulation

results where the slow-drift forces from both

the potential flow and the viscous drag

contribution were included. Moreover, many

researchers had studied about wave drift


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forces in the hydrodynamic response

analysis a moored semi-submersible

platform [44, 45, 28] and [46]. Schellin [47]

calculated and compared low-frequency

surge response of two moored floating

production platforms in waves using

numerical procedures based on time domain

simulations and frequency domain analysis.

They found that specifying a realistic

amount of wave drift damping is essential to

obtain reliable estimates of low-frequency

surge. Until now, to precisely predict the

drag coefficient for calculating viscous

damping is still a huge challenge to

researchers. The current study by Jian Hua

& Li Zhoub [3], a model test at the scale of

1:70 was used to measure the wave drift

force at low frequency for a semi-

submersible. The measured results were

presented and compared with numerical

diffraction analysis program based on

potential flow theory. In beam sea, wave

drift forces were predicted reasonably by

diffraction analysis within potential flow

theory for structures operating in both the

smaller and higher waves. In head sea, they

agreed well for the small wave, but there

was signicant difference for the higher

wave. One possible reason of that difference

yet to prove was that viscous effect on the

structure was neglected for the higher wave

in head sea. However, viscous drift forces

can be positive or negative. Therefore, cares

should be taken while adding viscous forces.

Study is needed on the viscous model to get

a better prediction.

3.2. Wind damping

The wind drag force is calculated based on

the formula as follow:

𝐹𝑤𝑖𝑛𝑑 =1

2𝜌𝑎𝑖𝑟𝐶𝑠𝐶𝐻𝑉10|𝑉10|𝑆

Where:

𝜌𝑎𝑖𝑟 : The density of air

𝐶𝑠: is the shape coefficient or drag

coefficient = 1 for large flat surface

𝐶𝐻: Height Coefficient, 𝐶𝐻 = 1 for FPSO:

Floating Production Storage and Offloading

𝑉10: Wind velocity at 10m above mean

water level

S: Project area of the exposed surface in the

vertical or the heeled condition

h: Vertical distance between center of wind

force and and center of resistance (by

mooring system).

3.3. Current damping

The current force is calculated using the

formula as follow,

𝐹𝑐𝑢𝑟𝑟𝑒𝑛𝑡 =1

2𝜌𝑤𝑎𝑡𝑒𝑟𝐶𝑑𝑈𝑓|𝑈𝑓|𝑆

Where:

𝜌𝑤𝑎𝑡𝑒𝑟: is the water density

𝐶𝑑: drag coefficient

𝑈𝑓: Current velocity

S: Project area of the exposed surface

3.4. Mooring line damping

The mooring-induced damping is one of the

main contributions to the low-frequency

damping, which further influences the

station keeping of floating structures. A


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reliable prediction of the mooring-induced

damping is essential for the estimation of the

low-frequency motion for floating structures

[48]. As discussed at the end of the previous

section, researchers have indicated that the

mooring line damping for a floating offshore

oil and gas installation can contribute

approximately 80% of the total system

damping. Thus what has been compelling

many researchers to develop different model

of estimating the mooring line damping to

insure safe and optimum design of the

mooring system.

3.4.1. Mooring induced damping

estimation

To estimate mooring induced damping,

Huse and Matsumoto [35, 37] and Huse [36]

applied the dissipated energy model.

Consider a moored floating body, its surge

motion is governed by the following

equation:

(𝑀 + 𝑚𝑎)𝑑2𝑋

𝑑𝑡2+ 𝛽

𝑑𝑋

𝑑𝑡+ 𝐾(𝑥)𝑋 = 𝐹(𝑡)

where: M is the floating barge mass, ma is

the floating barge additional mass by water,

X is the motion response of the floating

barge, β is the system damping

coefficienssst, K is the mooring line

stiffness and F(t) is the environmental load

which is causing motion to the floating

structure. The system damping is in the form

of an equivalent linear surge damping

coefficient β. The dissipated energy E

during one LF oscillation of period τ is

related to the linear coefficient β by the

formula.

𝐸 = ∫ 𝛽 (𝑑𝑋

𝑑𝑡)

𝜏

𝑂

2

𝑑𝑡

The linear damping coefficient β can be

obtained as:

𝛽 =𝐸

𝜋𝑋02𝜔𝑜

Where X0 is the amplitude of oscillation and

𝜔0 is the angular velocity.

3.4.2. Quasi-static method assumptions

The alternative for dissipation energy

method was to adopt a quasi-static method

where the following assumptions had been

made[49]:Firstly, inertia forces in the

mooring line were neglected compared to

drag. Secondly, line profile at any time

during the harmonic surge oscillation was

reasonably well described by the quasi-static

centenary equations. Thirdly, friction effects

of the seabed and internal damping of the

mooring line are not considered here.

Consequently, the mooring line damping is

due to drag forces acting on the mooring line

only. Drag forces acting perpendicular to the

line are considered while drag forces parallel

to the line are neglected. fourthly, The

transverse drag force on an element of the

mooring line is described by the Morison

formulation only.

Liu and Bergdahl [50, 51] then after

Bauduin and Naciri [52] whose model is


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called B&N model proposed improvements

on Huses quasi-static model for mooring

line-induced damping by approximating the

deformation of the line shape and the

transverse velocity of the line in more

accurate ways, respectively. Researchers,

Johanning et al., 2007; Sarkar and Eatock

Taylor, 2000; Webster, 1995 [48] had tried

to obtain the efficient and accurate

estimation of the damping, which can be

represented by the energy dissipation. In

2008, Tang et al. reviewed the studies on

mooring dynamic and concluded that it was

still lack of efficient approaches to predict

mooring-induced damping. Yuan et al. 2010

revealed the energy state of the mooring

lines and further predicted the dissipated

energy due to mooring line damping. In

2014 Dongsheng Qiao and Jinping Ou [53]

in their paper of mooring line damping

estimation for a floating wind turbine(FWT),

had used the energy absorption by a

mooring line resulting from the FWT motion

to derive the numerical estimation method.

They analyzed effects of excitation

amplitude, excitation period and drag

coefficient on the mooring line damping. It

indicated that With increase of drag

coefficient, the non-dimensional damping

almost linearly increases. This means that

the drag coefficient should be prudently

analyzed during the design. In brief, many

scholars prefer dissipated energy model to

estimate the mooring induced damping. The

accurate mooring system damping

prediction may depend also on the floating

structure viscous. So, it should be

considered for better prediction during the

optimum design of moored system.

3.5. Drag Coefficient

In the previous studies the researchers were

omitting the contribution of the mooring line

damping when predicting the motion of the

moored floater. This is due to the small drag

area of the mooring line. However referring

to what we have seen in some literature, the

mooring line damping contributes about

80% of the total mooring system damping.

Considering the result of the Marinteks

experimental study [54], surge amplitude

decrease of by 20 - 25% have been obtained

when mooring lines damping are included.

The amplitude of oscillation of the moored

floater is overestimated if the damping of

mooring line is omitted [55]. Thus, for

obtaining the accurate estimation of the

moored floater motion, the inclusion of the

mooring line damping which is dependent to

the drag force is crucial. Thus the study and

proper selection of drag coefficient(CD) is

important. A sufficiently exact

determination of drag force is required for

accurate prediction of mooring performance

and for selection of appropriate mooring

configuration [78]. Although, errors of

selecting drag coefficients on the mooring

components are less important due to small

drag area(A), they may well lead to

significant errors in predicting the moorings

dynamics[73]. With reasonable choice of

mooring line and buoyancy, it has to be

accepted that drag forces will cause non-


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negligible inclination of mooring line[114].

The drag force can be written as:

𝐹𝑑 =1

2𝐶𝑑𝜌𝐴𝑉2

Where Fd is the drag force, Cd is the drag

coefficient, ρ is the fluid mass density, A is

the cross sectional area and V is flow

relative velocity. The drag coefficient for

mooring components is normally considered

to be those of the corresponding bodies

shape for the appropriate range of Reynolds

numbers. Their data can be found in

engineering handbooks [76] [77] and [72].

3.5.1. Influential factors of drag

coefficient

The drag coefficient depends on Reynolds

(Re) and Keulegan Carpenter (KC) numbers.

The poor analysis of drag coefficient could

cause the large difference between

numerical and experimental studies of the

mooring system damping. In 1989, the study

by Huse and Matsumoto [62] show that

under superimposed WF motion, without

considering CD variations based on Re and

KC numbers, there is a large discrepancy

between numerical estimation of the

moorings damping and experimental results.

The numerical estimation over-predict the

damping of the mooring line by a factor

varying between 1.2 - 2 for different sea-

water conditions. Recently, the Phd

dissertation by Zhengqiang Xu [6]

concluded that the low Re number (lesser

than 106) has less effects on the CD

variation but KC number has meaningful

effects. The same case when the Re number

is high, the KC effects on the drag

coefficient is negligible but Re number has a

meaningful influence.

The challenge is to estimate the influence of

the surface roughness, transverse

oscillations and flow regimes (patterns) on

drag coefficient variation. In reality there is

a wide variety of surface roughness, from

small protrusions existing in the texture of

the surface itself to large roughness in the

form of marine growth. The roughness will

not only increase the projected area, but also

affect various aspects of the flow, such as

the separation angle, the turbulence level

and vortex shedding [6]. Therefore, the

effect of the surface roughness upon the

drag coefficients normally cannot be

neglected. The transverse oscillation can

have an effect of increasing the drag force,

which can be explained by two popular and

pragmatic approaches [38].

3.5.2. Mooring line response with

variation of drag coefficient

Many researchers have been changing the

CD of moorings to examine the effects of

mooring damping on floaters motion. In

2003 Luo and Baudic [63] reported that the

CD variations have negligible effect on the

floaters motion. Contrary, in 2001 Wichers

and Devlin [64] had found that effect of CD

variations on floaters motion is significant.

In 2002, the drag coefficient importance to

enlarge the mooring line damping was also

studied by Sarkar and Taylor [65]. The


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moorings damping could be very important

in reducing amplitudes of LF motions.

However, the mean drag of the moorings

due to current/wave force could also

increase the mean offset of floaters.

Depending on the contributions of these two

components, the final impact of the CD

variations could be case-dependent [63].

Indeed, the mooring line damping effects on

LF motion depend on its proportion in the

system damping and magnitude of the

system damping which is challenging to be

precisely determined.

4. DYNAMIC MODELING OF

MOORING LINE

In the moored platform, mooring lines are

important elements to care about. Its good

response to the environment drag forces will

lead to a meaningful stability of the floating

vessel. It is previously seen that the mooring

line contributes up to 80% of the mooring

system damping [36, 35]. Since 1960,

mooring line models were being studied to

predict the behavior of moored surface

vessels to extreme surface wave excitation

[66]. The researchers have been modeling

and analyzing mooring line dynamic using

three techniques which are lumped mass,

finite element and finite difference models

[67, 68]. Before that, it is better to

understand the limitations of static analysis

that was used before.

Quasi-static method is simple useful and

convenient for finding maximum mooring

lines tension due to environment load of

wind, current and waves. It is often used in

the preliminary design stage of mooring

systems [69]. It assumes the identical and

linear motion of the mooring system

between two static positions, during a given

time step for which the loads on the systems

are assumed constant [77]. With Quasi-static

analysis, the top end tension is determined

with respect to the displacement caused the

WF and LF motions.

However, the quasi-static method can result

in large errors when the dynamic response

of the mooring line is dominant, which has

been verified by experimental investigation

[71]. In Quasi-static analysis, the dynamic

effects associated with mass, fluid

acceleration, water bed friction and damping

on the mooring line are ignored [72]. In

quasi-static analysis the drag forces acting

on the mooring line perpendicularly are

considered to be responsible of mooring line

damping only and the forces parallel to the

line are neglected. It is obvious that Quasi-

static method is not considering mass

inertia, internal damping and hydrodynamic

drag loading [73], bending and stiffness

effects though there are some advanced

analytical techniques that try to account such

limitation of vibration[75,74]. Further

review on development and implementation

of quasi static approach can be found in

Bauduin et al.[52], Wang et al.[76], Chai et

al.[77] and Masciola et al. [78]. Because of

the above discussed limitations associated

with quasi-static analysis, a dynamic

mooring analysis is viewed as a rigorous

approach for measuring ultimate and fatigue


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loads in floating offshore structures

moorings. Dynamic mooring models also

feature the ability to easily model

cable/seabed contact with irregularly

contoured seafloors [79] and impact with the

seafloor, as well as the capacity to capture

fluid drag loading and vortex-induced

vibrations[80]. The severity of the sea state

also implies the importance of using a

dynamic mooring model in the simulation as

demonstrated in the DeepCwind

semisubmersible tank test campaign [81]

and [82].

4.1. lumped mass model

A lumped mass model(LM) consider the

continuum mooring line by a series of short

straight line elements. Furthermore, it

assumes that a considered length of the

mooring line can be approximated by a LM

that represents the motion of the line. Then

the hydrodynamic forces lumped on the

concentrated mass are calculated [83]. A

model can be defined as an LM system if the

corresponding mass matrix is strictly

diagonal. There are different variations of

LM model [84, 85, 87, 89, 90, 91]. The first

numerical analyses of the non-linear

dynamics of undersea cables was

represented by Walton and Polacheck [92].

It was based on a heuristic spatial

discretization of the mooring line in two

dimensions.

Figure 11: The lumped model as applied

to the simulation of a single point [66]

The Figure 11 shows the model graphically,

where the mooring line is considered to be a

series of mass less and inextensible finite

segments joined by frictionless pin at

specified positions which made the

representation to be flexible and no bending

or torsional stiffness was considered. Walton

and Polacheck obtained a series of ordinary

differential equations governing the motion

of each node point using Newtons second

law by look at the gravitational,

hydrodynamic and buoyant forces and the

mass of the line at the node points. The

Newton-Raphson approach was then used

solve these equation. This model has

continued to be popular regarding dynamic

analysis of mooring line. Many researchers

have been applying this approach to estimate

waves and gravitational forces on mooring

line in different perspectives. Hicks and


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Clark [93], Nath and Felix [94] and

Merchant and Kelf [95] applied lumped

mass model to analyze the dynamics of

single point moorings. Later Kelf and

Merchant [96] applied it for mooring line

with buoy dynamic analysis. Matsubara et

al. have used the lumped mass model to

simulate the two dimensional motion of a

buoy-cable system for aquaculture

applications [97]. During the assessment of

the importance of composite mooring line

dynamic response in station keeping by

Khan and Ansari [98], the LM had shown

flexibility to simulate the assembly of chain,

cable and synthetic rope that composed each

mooring line. Such flexibility makes the LM

popular in many offshore engineering

practices [99]. Recently, the investigation

done by the national renewable energy

laboratory, lumped mass model was

preferred for implementation in mooring

analysis program over other models based

on its simplicity, low computational cost,

and ability to provide physics similar to

those captured by higher-order models [67].

However for applications where knowledge

of the bending and torsional moments is of

consequence, linear elements are not

adequate since they do not exhibit any

curvature or twist [17]. Bending effects of

cable are important in low-tension towing

maneuvers[85] and for fatigue analysis in

taut mooring systems [86], but bending also

augments the stability of the numerical

model[87, 88]. The use of lumped mass

models requires to provide cable length as

input data and when the mooring line

contact the waterbed it will be hard to find

out the location of the point [100]. The LM

representation traditionally has been derived

heuristically using Newton-Euler methods,

but it can also be obtained based on

Lagrange and Hamiltonian mechanics [101].

Further uncovered description of LM model

on mooring line can be found in [102, 103,

104].

4.2. Finite element analysis

The Finite Element Analysis(FEA) method

is a numerical method by which the

mechanism, structure or continuum is

divided into interconnected small finite

segments. The physical characteristics

within and around a considered segment are

similar to that of its nodes. The marine cable

elements are commonly assumed to be

straight lines. Its accuracy is then dependent

on the number of elements. However,

curved cable elements have been shown to

be more accurate than the straight line

element when continuity of slope across

nodal points is enforced [67] FEA models

have been applicable over many years ago

[105, 106, 107, 108] to capture advanced

features to include improved numerical

integration, hence increases stability [110].

Comparing FEA to LM, FEA model is able

to achieve good results with lower

discretization [92, 108]. Ketchman and Lou

[111] demonstrated that the LM

methodology converges into the same

results with FEA representations when the

discretization size is sufficiently small. Yang

and Teng [112] used FEA approach to


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analyze the static and dynamics of mooring

line. Garett [105, 88] and Ran[113]

developed a specific FEA model that

includes bending stiffness. The derivation

process initiated in[105, 114, 113] is similar

to the comprehensive high order LM

approach in [115]. Besides the method

developed in [105, 88, 113] that is based on

Galerkins method of weighted residuals, a

different basis function can be used to obtain

the equation of motion for the discretized

cable system[116].

Further detailed description of finite element

modeling for mooring lines can be found in

[117, 118, 119, 120].

4.3. Finite difference

The above two models have shown to not

account elasticity and bending stiffness of

the mooring line as the cable is studied as a

series of divided linear elements. The

inclusion of bending stiffness is achievable

with Finite difference approach based on the

demonstration done by Howell and

Triantafyllou for low-tension cable or chain

numerical simulation [121]. The Finite

difference model (FD) differs from FEA by

replacing piecewise gradients with first

order difference functions. In other words,

FEA computes derivatives of the basis

function exactly while FD estimates the

gradients. Thomas and Hearn [122]

developed a time-domain finite-difference

technique that accounts the seabed friction

effects as well as the lifting and grounding

of the seabed-lying portion of the cable.

Huang [123] used finite difference method

to analyze the dynamic behavior of marine

cable in three dimensions. Hover et al.[124]

used finite difference scheme in the

Calculation of dynamic motions and

tensions of towed underwater cables. In

2006 Gobat and Grosenbaugh [125]

investigated the numerical limitations of FD

model, and their effort gave out a clear

understanding of how the method of

integration leads to stability. Even if FD

model has limitations of numerical

implementation, it is easier implemented

into a computer code than LM or FEA. It

will be of advantage if the numerical

challenges of it are addressed. FD models

gives high fidelity modeling capabilities

compare with FEA model. In 2008 Matuela

et al. [126] developed mathematical model

and a matching numerical approach based

on finite differences to predict the static

configuration of mooring or towing

compound cables. Further detailed

descriptions of implementing finite

differences for mooring line, cable and/or

riser models are given in [127, 128, 129,

130]. To summarize, FD model is not

popularly used in commercial applications

because of its numerical limitation, and

more research is needed to improve and

simplify the approach [67].

4.4. Finite Segment

Even if the lumped mass, finite differences

and FEA are the most popular discretisation

schemes for mooring lines. Researchers like

Winget and Huston [131] and Kamman and


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Huston [132] utilised a finite segment

scheme consisting of a series of ball-and-

socket connected rigid rods, to discretize a

mooring line. Nichol et al. [133] developed

a finite segment model for the mooring

system of floating tidal energy devices.

Garrett [114] utilizes a similar scheme

consisting of elastic rods. Filipich and

Rosales [134] model a chain mooring line,

by discretizing the chain into its individual

links.

5. DESIGN & OPTIMIZATION OF

MOORING SYSTEM

The need of offshore exploration of oil and

gas in deep sea waters is increasing and now

can reach beyond 2500m.The use of

mooring system to station-keeping position

of any floating platform in deep water has

proved to be efficient over other means. This

has been compelling researchers to find out

an optimum design of mooring system for

different sea-state.

5.1. Design consideration

The mooring design must be an integral part

of the overall floating structure design,

because the mooring system not only

influence the capital costs, but also the

system performance in both operational and

survival sea-states. The objective is to find

design solutions to mitigate peak mooring

loads, while avoiding the costly overdesign

or compromising the performance of the

floater[135]. The design consideration

associated with a mooring system here

discussed includes design criteria, design

loads, design life, operation and

maintenance considerations. In the

following, the design criteria with respect to

the design limit states and the design loads

with respect to the environmental criteria are

described.

5.1.1. Design Limit States

The design criteria are formulated in terms

of three limit states: Ultimate limit state

(ULS), Accidental limit state (ALS) and

Fatigue limit state (FLS). DNV Offshore

Standard [136] defines the limit states as

following.

• An ultimate limit state to ensure that the

individual mooring lines have adequate

strength to withstand the load effects

imposed by extreme environmental actions.

The ULS requires that the mooring lines

shall resist all known loads with a sufficient

margin, and states that a design against

overload of an intact mooring system in

extreme weather shall be conducted.

• An accidental limit state to ensure that the

mooring system has adequate capacity to

withstand the failure of one mooring line,

failure of one thruster or one failure in the

thrusters control or power systems for

unknown reasons. A single failure in the

control or power systems may cause that

several thrusters are not working. The ALS

requires that an accidental event shall not

develop into progressive collapse, hence a

design against overload for a damaged

system in extreme weather conditions shall

be performed. A damaged system is


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considered as a system where one or two

line failures have occurred.

• A fatigue limits state has to be analyzed to

ensure that the individual mooring lines

have adequate capacity to withstand cyclic

loading. Analysis of the mooring system

shall be performed in accordance with these

three limit states.

The mooring line design for permanent

mooring must satisfy all three limit states.

The FLS requires that the safety margin

against fatigue failure shall be acceptable.

The mooring system shall thus be designed

against fatigue failure, taking all possible

sea states into account [136]. In order to

consider the FLS, a wide range of

environmental conditions is needed. The

following description of the properties,

analysis and fatigue safety factor is based on

offshore standard [136]. The fatigue

damage, D, in mooring line components are

accumulated by cyclic loading, and summed

up from the fatigue damage arising from

Environmental states combined to simulate

the long term environment that the mooring

system is exposed to

𝐷 = ∑ 𝑑𝑖

𝑛

𝑖=1

Where di is the fatigue damage to the

component arising in sea state i and defined

as

𝑑𝑖 = 𝑛𝑖 ∫𝑓𝑠𝑖(𝑠)

𝑛𝑐(𝑠)

∞

0

𝑑𝑠

Where ni is the number of stress cycles

encountered in sea state i, f S i(s) is the

probability density of stress cycles in sea

state I and nc(s) is the number of stress

cycles leading to failure. The number of

stress cycles in sea state i is defined as:

𝑛𝑖 = 𝑁𝑃𝑖

Where N is the total number of stress cycles

during the entire lifetime and Pi is the

probability of occurrence of sea state i. The

capacity of a component is described by the

S-N curve

𝑛𝑐 = 𝑎𝐷𝑆−𝑚

Where aD and m are parameters of the S-N

curve dependent on the mooring line

composition.

Figure 12 presents S-N curves for different

mooring line compositions

Figure 12: Design S-N curves [136]

Fatigue analysis is generally performed by

frequency domain method, where both wave

frequency tension cycles and low frequency


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www.ijetsi.org Copyright © IJETSI 2018, All rights reserved 2

tension cycles are taken into account. The

fatigue damage in the environmental state i

is determined by:

𝑑𝑖 =𝑛𝑖

𝑎𝐷𝐸[𝑆𝑖

𝑚]

Where 𝐸[𝑆𝑖𝑚] is the expected value of the

nominal stress ranges raised to the power m

in environmental state i. If the low

frequency content of the stress process is

neglectable, a narrow-banded assumption

can be applied. Fatigue damage in

environmental state i then becomes:

𝑑𝑖 =𝑉𝑜𝑖 𝑇𝑖

𝑎𝐷

(2√2𝜎𝑠𝑖)𝑚

𝛤 (𝑚

2+ 1)

Where 𝜎𝑠𝑖 is the standard deviation of the

stress process, Γ() is the gamma function,

V0i is the mean up crossing rate of the

tension process and 𝑇𝑖 is the duration of the

environmental condition. The intent of the

fatigue limit state is to ensure sustainable

resistance to fatigue failure of each type of

Component in an individual mooring line.

The design equation for FLS is given as:

1 − 𝑑𝑐 𝛾𝐹 ≥ 0

Where 𝑑𝑐 the characteristic fatigue damage

is accumulated as a result of cyclic loading

during the design life time, and 𝛾𝐹 is the

single safety factor for the fatigue limit state.

In the fatigue analysis, the fatigue safety

factor shall cover a range of uncertainties.

For mooring lines that are not regularly

inspected, the safety factor is thus given as:

𝛾𝐹 = 5 𝑖𝑓 𝑑𝑓 ≤ 0.8

𝛾𝐹 = 5 + 3 (𝑑𝐹 − 0.8

0.2) 𝑖𝑓 𝑑𝑓 > 0.8

Where 𝑑𝑓 is the adjacent fatigue damage

ratio. The ratio between the characteristic

fatigue damage dc in two adjacent lines

taken as the lesser damage divided by the

greater damage. Further description of

different techniques useful to analyze the

fatigue of moorings and risers in floating

production systems for offshore oil and gas

exploration can be found in [137, 138, 139,

140, 141]. Also Snap loads on moorings

were found to significantly influence

damage in several experiments [139, 142,

143]. Thus considering the effect of snap

loads is crucial for assessing the fatigue of

mooring lines. Palm et al.[144] developed a

model that captures the real amplitude and

duration of snap loads in mooring lines.

5.1.2. Environmental Criteria

There are mainly two classifications of

environmental conditions when evaluating a

mooring system; maxi-mum design

condition and maximum operation

condition.

1. Maximum Design Condition: The

maximum design condition is described by

the combination of waves, wind and current

for which the mooring system is designed.

This condition is defined as extreme

combinations of wind, waves and current

causing an extreme load in the design

environment [14]. The environmental effects


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applied for the calculations of design limit

states above discussed in section, should

include the most severe combinations of

waves, wind and current with a return period

of no less than 100 years for the

combination. The most severe conditions are

those leading to the most extreme mooring

loads. In order to determine the most

unfavorable conditions, both intensity and

directions of the environmental effect are of

importance [136]. The environmental loads

are specified in terms of:

Significant wave height (Hs )

Peak wave period (Tp )

Wave spectrum

Wave energy distribution

Main wave direction

Mean wind speed, over a 1 hour

averaging period 10m above sea

level (U 1hour, 10m)

Wind spectrum function

Wind direction

Surface current speed (Vc )

Current profile over depth

Current direction

2. Maximum Operation Condition: The

maximum operating condition is defined as

the combination of waves, wind and current

in which the unit is capable of continue to

work, including for instance to drill,

produce, offload or maintain gangway

connection. This condition shall not exceed

the maximum design condition [14]. In

order to obtain a 100-year design

environment, different sets of conditions are

investigated. In accordance with [145],

waves of a sea state with return period of

100 years should normally be used. These

wave conditions shall include different

combinations of significant wave heights

and peak periods. In addition, the mean

wind speed 10 m above the water surface

with a 100-year return period and a surface

current speed with a 10-year return period

should be applied. Both wind and current

should be based on the marginal distribution

of the wind and current speeds at the

specific location respectively [136].

5.2. Optimization

In engineering many optimization problems

are naturally very complex and hard to find

their solution by conventional optimization

techniques [146,147]. To address such

challenge, in 1960s researchers started an

new techniques named evolutionary

algorithms where they had imitated living

beings by simulating the process of natural

evolution of human beings [148, 150, 149].

Today the use of genetic algorithms (GAs)

has become popular among evolutionary


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algorithm types. In 2014 Tianhui Fan [151,

152] used it to optimize his design of

truncated mooring system based on static

and damping equivalent. In 2006, M.

Shafieefar and A. Rezvani [1] used the same

techniques of GAs to optimize the design of

moorings for floating structures. They

mentioned the aspect to be considered

during the mooring system optimization.

Firstly the platform heading, this accounts

the environmental forces directional

distribution function. Secondly the mooring

pattern which consider the mooring system

holding capacity factor like anchor position,

Thirdly, the mooring line tension or length,.

Fourthly the mooring line materials and

sizes and finally automation to minimize

time taken during design. They have

presented a codes to optimize the design of

moored floating structures which determine

floating structures offset and handles design

constraint like safety factor of the lines. The

code implementation has shown good results

to mooring design optimization cases.

However, it was noticed that, they had

considered safety factor constraint of

mooring lines only. It means that they were

able to control the tension limit of lines but

there was no information of anchor tension.

The anchor tension could be considered as

constraint of mooring system design as its

weight practically matter and that is why it

is needed to take it into consideration as a

design constraint by further researchers.

6. CONCLUSION

Mooring system is mechanism used to

control the position of floating structures in

water by means of marine cables.

Researchers have been studying mooring

line statically and were unable to analyze the

effects of friction and bending strength. In

summary, this review found that the

mooring line motion can cause resonance

when its natural frequency becomes similar

to that of the floater. The mooring line

motion is due to the drag force and depends

on drag coefficient. In the analysis of the

floater motion with respect moored system

and to drag forces. The selection of drag

coefficient should involve the Re and KC

numbers otherwise it will results a large

discrepancy between numerical and

experimental results.

Among the gaps found during this review

are the unclear relationship between

mooring line damping and mooring line total

tension. It is seen that the increase of the

mooring line damping will decrease the

amplitude of low frequency motion, hence

static tension. It could also increase the

dynamic tension, however it was not seen

whether it will increase or decrease the total

line tension. It has been seen that the finite

difference approach of mooring line

dynamics would lead to stability, give high

fidelity modeling capabilities. However it

has limitation of numerical implementation.

There is a need to investigate and simplify

the implementation of finite difference

model by overcoming its numerical

limitations. It was reviewed that the mooring

line damping plays major part to the total


ISSN: 2456-1851



mooring system damping. This depend to

the hydrodynamic forces on the line which

is relative to the drag coefficient. The

surface roughness effect on CD values

variation of mooring line is not considered

in any analysis reviewed. Actually, the

impact of surface roughness could

considerably influence the variation of CD.

So it might be important to carry out the

investigation of this effect.

It has been seen that both the position and

volume increase of the buoy affect the

mooring line tension hence the floater offset.

However there is no code has been

generated to automatically predict the

optimum position and volume of the buoy

with maximum allowable floater offset

desired.

REFERENCES

[1] Mehdi S. Aidin R., Mooring

optimization of floating platforms using

agenetic algorithm

www.researchgate.net/publication/23590819

6; 2006.

[2] Philip, Nallayarasu, & Bhattacharyya.,

Experimental investigation and CFD

simulation of heave damping effects due to

circular plates attached to spar hull Nimmy,

Ships and Offshore Structures,

http://dx.doi.org/10.1080/17445302.2013.83

5146, 2013.

[3] Jian Hua and Li Zhoub., Experimental

and numerical study on wave drift forces on

a semi- submersible platform in waves

College of Shipbuilding Engineering, Harbin

Engineering University, Harbin, P.R. China

& Aker Solutions, Fornebu, Norway, 2015

[4] Pinkster JA. Low frequency second order

wave exciting forces on oating structures.

Delft (the Netherlands): Delft University of

Technology, 1980

[5] Yipeng Pana, Prasanta Kumar Sahooa &

Lin Lub Numerical study of hydrodynamic

response of mooring lines for large floating

structure in South China Sea, Taylor &

Francis, 2015.

[6] Zhengqiang Xu Phd thesis: Drag

Coefficient and Damping of Moorings and

their Effect on FPSOs Response University

of Strathclyde, Glasgow Department of

Naval Architecture, Ocean and Marine,

2014.

[7] Ioannis K. Chatjigeorgiou, Ioannis

Thanos, Paraskevi Bourma, Thomas

Mazarakos and Spyros A. Mavrakos;

Mooring system & motion response analysis

of a gas import terminal in operating and

survival conditions, National Technical

University of Athens, School of Naval

Architecture and Marine Engineering

Laboratory of Floating Structures and

Mooring Systems 9 Heroon Polytechniou

Ave, GR157-73, Greece, 2005

[8] O.M. Faltinsen, Book: Sea loads on ships

and offshore structures, Cambridge

university press, 1990.

[9] Sue Wang, On the Assessment of

Thruster Assisted Mooring, American


ISSN: 2456-1851



Bureau of Shipping Houston, Texas, USA,

2012.

[10] S. Ryu, Hull/Mooring/Riser Coupled

Motion Simulations of Thruster-Assisted

Mooring Platforms, Texas A&M University,

2003.

[11] Dietmer Deter, Conference of Dynamic

Positioning, Marine Technology Society,

1997.

[12] Aalbers, B. Albert, de Vries, Leo; van

Vugt, Hans, Dynamic Positioning,.

Conference, Fuel consumption and emission

predictions: application to a DPFPSO

concept. Houston, October 2006.

[13] Ramberg, S. E. and Gri n, O. M., Free

Vibrations of Taut and Slack Marine Cables

Journal. of Struct. Div., ASCE, Nov. 1977.

Also, see discussion in the June 1978 issue.

[14] API Recommended Practice, Design and

Analysis of Station keeping Systems for

Floating Structures., 2005.

[15] Vryhof, Anchor Manual, 2015.

[16] DR. IR. Gerad Van OORTMERSSEN,

The motions of a moored ship in waves,

Publication no. 510 Netherlands ship model

basin Wageningen, the netherlands, 2008.

[17] K. E. Klingan, Automated optimization

and design of mooring systems for deep

water, M.thesis, Norwegian University of

Science and Technology, 2016.

[18] SUBRATA K. Chakrabarti, Handbook of

offshore Engineering Offshore Structure

Analysis, Inc, Elsevier Ltd,2005

[19] G.T. Houlsby and B.W. Byrne, Design

Procedures for Installation of Suction

Caissons in Clay and Other Soils. OUEL

2268/04,2004 [20] Atturio, J. M., Valent, P. J.,

and Taylor, R J.,”Preliminary Selection of

Anchor Systems for OTEC,’” Ocean

Engineering, Vol. 6, Nos. 1/2, 1979

[21] Taylor, R. J., Jones, D. and Beard, R. M.,

Uplift-Resisting Anchors, Ocean Engineering,

Vol. 6, Nos. 1/2, 1979

[22] Valent, P. J., Taylor, R. J., Atturio, J.

M., and Beard, R. M., Single Anchor Holding

Capacities for OTEC in Typical Deep Sea

Sediments Ocean Engineering, Vol. 6, Nos. 1/2,

1979.

[23] Baldt Inc. Baldt Anchor Catalogue.

Chester (PA): Baldt.1990a

[24] Baldt Inc. Baldt chain catalogue. Chester

(PA): Baldt. 1990b.

[25] Musial W, Buttered S. Future for

offshore wind energy in the United States,

Energy Ocean 2004 Conference; June 2829;

Palm Beach, Florida.

[26] Mohammed Khair Al-Solihat and Meyer

Nahon; Stiffness of slack and taut moorings,

Francis and Taylors, 2015.

[27] Z. Gao and T. Moan; Mooring system

analysis of multiple wave energy converters in

a farm configuration, Proceedings of the 8th


ISSN: 2456-1851



European Wave and Tidal Energy Conference,

Uppsala, Sweden, Centre for Ships and Ocean

Structures, Norwegian University of Science

and Technology, Otto Nielsens vei 10, NO-

7491, Trondheim, Norway, 2009

[28] Dongsheng Qiao and Jinping Ou,

Global responses analysis of a semi-

submersible platform with different

mooring models in South China Sea, Deep-

water Engineering Research Center, Dalian

University of Technology, Dalian, China /

Taylor & Francis, 2012.

[29] Gottlieb, O. and Yim, S. C. S., Nonlinear

oscillations, bifurcations and chaos in a multi-

point mooring system with a geometric

nonlinearity, Appl. Ocean Res; 1992

[30] Umar, A. and Siddiqui, N. A., Reliability

analysis of a moored vessel, Journal of

Structural Engineering, SERC, India, 2002

[31] Zhi-Ming Yuan & Atilla Incecik

Numerical study on an hybrid mooring

system with clump weights and buoys;

Ocean Engineering, 2014

[32] Vicente P.C., Falc£o A.F., Justino P. J

Slack-chain mooring configuration analysis of a

floating wave energy converter. 26th

International Workshop on Water Waves and

Floating Bodies, Athens, Greece.2011

[33] Yang, W.S., Phd thesis: Hydrodynamic

Analysis of Mooring Lines Based on Optical

Tracking Experiments. Texas A & M

University, December 2007.

[34] Lars Johanning, George H. Smith,

Julian Wolfram; Measurements of static and

dynamic mooring line damping and their

importance for floating and underwater

WEC devices, Elsevier ltd, 2007

[35] E. Huse, Influence of mooring line

damping upon rig motions, In: Proceedings

of the 18th Offshore Technology Conference;

1986 May 58 Houston, TX. p.433438.

[36] Huse E. New developments in prediction

of mooring system damping in; Proceedings of

the 23rd Offshore Technology Conference;

1991 May 69; Houston, TX. p. 291298.

[37] E. Huse, Matsumoto K. Practical

estimation of mooring line damping,

Proceedings of the 20th Offshore

Technology, 1988.

[38] JOURNE, J. M. J. & MASSIE, W. W.

Offshore Hydromechanics, Delft University

of Technology, 2001.

[39] Bayati, Jonkman J, Robertson A. The

effects of second-order hydrodynamics on a

semi-submersible floating offshore wind turbine.

Journal of Physics, 2014.

[40] Faltinsen OM., Sea loads on ships and

ocean structures. Cambridge: Cambridge

University Press, 1990

[41] Stansberg C, Yttervik R, Nilsen F. Wave

drift forces and response in storm waves.

Proceedings of the Seventh International

Symposium on Practical Design of Ships and

Mobile Units;1998.


ISSN: 2456-1851



[42] Hassan A, Downie M, Incecik A,

Baarholm R, Berthelsen P, Pakozdi C,

Stansberg C. Contribution of the mooring

system to the low-frequency motions of a

semisubmersible in combined wave and current.

Proceedings of the ASME 2009 28th

International Conference on Ocean, O shore and

Arctic Engineering; 2009 May 31Jun 5;

Honolulu (HI): ASME, 2009.

[43] Berthelsen P, Baarholm R, Pakozdi

C, Stansberg C, Hassan A Downie M,

Incecik A. Viscous drift forces and

responses on a semisubmersible platform in

high wave, Proceedings of the ASME 2009;

28th International Conference on ocean Off

shore and Arctic Engineering; 2009 May

31Jun 5; Honolulu (HI): ASME, 2009

[44] Nallayarasu S, Siva Prasad P.

Hydrodynamic response of spar and semi-

submersible interlinked by a rigid yole part I:

regular waves. Ships Offshore Struct.

7(2):133141,2012.

[45] Nallayarasu S, Siva Prasad P.

Hydrodynamic response of spar and semi-

submersible interlinked by a rigid yole part II:

random waves, Ships Offshore Struct.

7(2):133141,2012.

[46] Ye Q, Jin W, He Y, Bai Y. System

reliability of a semi-submersible drilling rig.

Ships Offshore Structures. 2013

[47] Schellin, T. E., Jiang, T.and Sharma S.

Numerical prediction of low-frequency

surge of two moored floating production

platforms; Proceedings of Tenth

International Symposium and Exhibit on

Offshore; Mechanics and Arctic Eng., Vol.

1-A, Offshore Technology, Houston,

pp.165174

[48] Lingzhi Xiong, Wenhua Zhao, Study on

global performances and mooring- induced

damping of a semi-submersible, Article in

China, Ocean Engineering October 2016.

[49] Tianhui Fan, Dongsheng Qiao &

Jinping Ou, Innovative approach to design


and damping equivalent, Taylor & Francis,

Ships and Offshore Structures, 9:6, 557-568,

DOI: 10.1080/17445302.2013.867631,2014.

[50] Liu, Y. Dynamics and Extreme Value

Problems for Moored Floating Platforms.

Ph.D. Thesis, Chalmers University of

Technology, Gothenburg, Sweden, 1998.

[51] Liu, Y.; Bergdahl, L. Frequency-

domain dynamic analysis of cables. Eng.

Struct. 1997, 19, 499506

[52] Christian Bauduin & Mamoun Naciri,

A Contribution on Quasi-Static Mooring

Line Damping, Journal of Offshore

Mechanics and Arctic Engineering, 2000.

[53] Qiao, D. & Ou, J., Mooring line

damping estimation for a floating wind

turbine., The American Naturalist Scientific

World Journal, 2014, 840283.

https://doi.org/10.1155/2014/840283, 2014

[54] HUSE,E. Influence of mooring line

damping upon rig motions, Offshore


ISSN: 2456-1851



Technology Conference. Houston, Texas,

1986.

[55] NAKAMURA, M., KOTERAYAMA,

W. & KYOZUKA, Y. Slow drift damping

due to drag forces acting on mooring lines,

Ocean Engineering, 18, 283296. 1991.

[56] Casarella M.J. and M. Parsons Cable

systems under hydrodynamic loading, J.Mar

Technol Soc. 1970

[57] M. Finker and G. Siedler, Drag

coefficients of oceanographic mooring

components, Kiel University, 1985.

[58] Fofonoff N.P. Buoy-system motions,

Hand book of ocean and underwater

engineering, McGraw Hill, 9-109 to 9-115,

1969.

[59] Sass F. & Ch. Bouche, Handbook of

ocean engineering, Dubbel Taschenbuch fur

Maschinenbau, Springer-Verlag,884 pp;

1956.

[60] Hoerner, S.F. Fluid Dynamics Drag

Publ. by the Author New Jersey, 1965.

[61] Myers, D.A., Holm C. H. & R.F.

McAllister, Handbook of ocean and

underwater engineering, McGraw Hill 1-2

to 12-112pp, 1969.

[62] HUSE, E. & MATSUMOTO, K.

Mooring line damping due to first and

second order vessel motion, Offshore

Technology Conference. Houston, Texas,

1989.

[63] LUO, Y. & BAUDIC, S. Predicting

FPSO responses using model tests and

numerical analysis, 13th International

Offshore and Polar Engineering. Conference

(ISOPE-2003), Honolulu, Hi. 167-174,

2003.

[64] WICHERS, J. E. W. & DEVLIN, P. V.

Effect of coupling of mooring lines and

risers on the design values for a turret

moored FPSO in deep water of the Gulf of

Mexico, 11th International Offshore and

Polar Engineering Conference

(ISOPE2001), Stavanger, Norway. 480-487,

2001.

[65] Sarkar, A., Taylor, R.E., Dynamics of

mooring cables in random seas, J. Fluids

Struct. 16 (2), 193212, 2002.

[66] Bradley J. Buckham, Dynamics

Modelling of Low-Tension Tethers for

Submerged Remotely Operated Vehicles.

University of victoria, 1997.

[67] J. J. Marco Masciola and A. Robertson,

Extending the capabilities of the mooring

analysis program: A survey of dynamic

mooring line theories for integration into

fast, National Renewable Energy

Laboratory, 2014

[68] Chatjigeorgiou, I. K. and Mavrakos, S.

A. Comparative evaluation of numerical

schemes for 2D mooring dynamics, Int. J.

OffshorePolar Eng;2000.

[69] Y.Inoue, H.Miyabe, X.Weiyi and

M.Nakamura, Comparative Study on the

Quasi-Static Analysisand Dynamic


ISSN: 2456-1851



Simulations for Estimating the Maximum

Tensions of Mooring Lines, International

Offshore and Polar Engineering

Conference, 1991.

[70] Vickers, A. Improve the Understanding

of Uncertainties in Numerical Analysis of

Moored Floating Wave Energy Converters.

Ph.D. Thesis, University of Exeter, Exeter,

UK, 2012.

[71] PAPAZOGLOU, V. J., MAVRAKOS,

S. A. & TRIANTAFYLLOU, M. S.

Nonlinear cable response and model testing

in water. Journal of Sound and Vibration,

140, 103-115,1990

[72] Johanning, L.; Smith, G.H.; Wolfram,

J. Towards design standards for WEC

moorings. In Proceedings of the 6th

European,Wave and Tidal Energy

Conference, Glasgow, UK, 29 August 2

September 2005.

[73] Hall, M.; Goupee, A. Validation of a

lumped-mass mooring line model with

DeepCwind semi-submersible model test

data. Ocean Eng. 2015, 104, 590603

[74] Griffin, O. M. and Rosenthal, F., The

Dynamic Of Slack Marine Cables, J.

Offshore Mech. Arct. Eng., 11(4), pp.

298302, 1989.

[75] Starossek, U. Cable Dynamics a

Review, J. Structural Eng. Int., 4, pp.

171176, 1994.

[76] Wang, L.Z.; Guo, Z.; Yuan, F. Quasi-

static three-dimensional analysis of suction

anchor mooring system. Ocean Eng. 2010,

37, 11271138.

[77] Chai, Y.; Varyani, K.; Barltrop, N.

Semi-analytical quasi-static Formulation for

three-dimensional partially grounded

mooring system problems. Ocean Eng. 2002,

29, 627649

[78] Masciola, M.; Jonkman, J.; Robertson,

A. Implementation of a Multi segmented,

Quasi-Static Cable Model. In Proceedings of

the 23rd International Offshore and Polar

Engineering Conference, Anchorage, AK,

USA, 30 June5 July 2013.

[79] Gatti-Bono, C., and Perkins, N. C;

Numerical Simulations of Cable/Seabed

Interactions, J. Int. Soc. Offshore and Polar

Eng., 14(2);2004

[80] Nicoll, R. A; Dynamic Simulation of

Marine Risers with Vortex Induced

Vibrations, Masters Thesis, University of

Victoria, British Columbia, Canada; 2004.

[81] Masciola, M., Nahon, M., and Driscoll,

F., Preliminary Assessment of the

Importance of Platform Tendon Coupling in

a Tension Leg Platform, J. Offshore Mech.

Arct. Eng., 135(3), 2012.

[82] Masciola, M., Jonkman, J., Robertson,

A., Coulling, A., and Goupee, A.

Assessment of the Importance of Mooring

Dynamics on the Global Response of the

DeepCwind Floating Semisubmersible

Offshore Wind Turbine, 23rd International

Offshore and Polar Engineering (ISOPE)


ISSN: 2456-1851



Conference, Anchorage, AK, June 30 July

2013.

[83] R. Chiou, PhD thesis: Nonlinear

Hydrodynamic Response of Curved Singly

Connected cable., Oregon State University,

2004

[84] Chai Y. Varyani K. and Barltrop N.

Semi-analytical Quasi-Static Formulation

for three Dimensional Partially Grounded

Mooring System Problems, Ocean Eng., 29,

pp. 627649, 2002.

[85] Buckham B. Driscoll F. R. and Nahon

M. Development of a Finite Element Cable

Model for Use in Low-Tension Dynamics

Simulation J. Applied Mech., 71(4), pp.

476485. 2004.

[86] Dalane, J. I., Fatigue Reliability

Measured Response of the Heidrun TLP

Tethers, Marine Structures pp. 611628;

1997.

[87] Buckham B. Nahon M. Seto M. Zhao

X. and Lambert C. Dynamic of a Towed

Underwater Vehicle System: Part 1: Model

Development Ocean Eng., 30(4), pp.

453470. 2003

[88] Powell, G., and Simons, J., Improved

Iteration Strategy for Nonlinear Structures

Journal of. Numerical Methods 1981.

[89] Lambert C. Nahon M. and Chalmers D.

2007 Implementation of an Aerial

Positioning System with Cable Control

IEEE/ASME Transactions on Mechatronics,

12(1), pp. 3240.

[90] Nahon M. 1999 Dynamics and Control

of a Novel Radio Telescope Antenna AIAA

Modeling and Simulation Technologies

Conference and Exhibit, pp. 214222.

[91] Williams P. Trivaila P. 2007 Dynamics

of Circularly Towered Cable Systems, Part

1: Optimal Configurations and their

Stability J. Guidance, Control and

Dynamics, 30(2), pp. 753765

[92] Walton, T. S. and Polacheck, H.,

Calculation of Transient Motion of

Submerged Cables, Mathematics of

Computation, Vol. 14, No. 69, 1960, pp. 27-

46.

[93] Hicks, J. B. and Clark, L. G., On the

Dynamic Response of Buoy-Supported

Cables and Pipes to Currents and Waves,

Offshore Technology Conference, Vol.

OTC-1556, 1972, pp. 453-462

[94] Nath, J. H. and Felix, M. P., Dynamics

of a Single Point Mooring in Deep Water,

ASCE Journal of Water Ways, Harbour and

Coastal Engineering Division, Vol. 96,

1970, pp. 815-833.

[95] Merchant, H. C. and Kelf, M. A. Non-

Linear Analysis of Submerged Ocean Buoy

Systems, Proceedings of MTS/IEEE

OCEANS 73, Vol. 1, 1973, pp. 390-395.

[96] Kelf, M. A. and Merchant, H. C.

Analysis of a Multiple Buoy Instrument

Platform; A Non-Linear Model Proceedings

of MTS/IEEE OCEANS 74, Vol.1, 1974,

(pp.44-48)


ISSN: 2456-1851



[97] Matsubara, Y., Hideaki, N., and Hirao,

A.Dynamic Behaviour of the Submerged

Buoy-Cable System by Ocean Waves

Coastal Engineering in Japan, Vol. 28,

1985, (pp. 235-241.)

[98] Khan, N. U. and Ansari, K. A. On the

Dynamics of a Multicomponent Mooring

Line, Computers and Structures, Vol. 22,

No. 3, 1986, pp. 311-334.

[99] Herbich, J. B. and Ansari, K. A.

Developments in Offshore Engineering.

Wave Phenomena and Offshore Topics, Gulf

Publishing Co.: Houston, TX, 1999, pp.

195- 233.

[100] B. V. . C. Barbu, A novel numerical

approach to the dynamics analysis of marine

cables, International Journal of Applied

Science and Technology, 2014

[101] Rupe R. C. and Thresher R. W. 1975,

The Anchor-Last Deployment Problem for

Inextensible Mooring Lines; Transactions of

the ASME, (74-WA), pp. 10461052.

[102] Low, Y.; Langley, R. Time and

frequency domain coupled analysis of deep-

water floating production systems. Appl.

Ocean Res. 2006, 28, 371385

[103] Van den Boom, H. Dynamic behavior

of mooring lines. In Proceedings of the

BOSS Conference, Delft, The Netherlands,

15 July 1985.

[104] Chai, Y.; Varyani, K.; Barltrop, N.

Three-dimensional Lump-Mass formulation

of a catenary riser with bending, torsion and

irregular seabed interaction effect. Ocean

Eng. 2002, 29, 15031525.

[105] Garret, D. L. Dynamic Analysis of

Slender Rods, J. Energy Resource

Technology, 104, pp. 302306, 1982.

[106] Kennedy, R. M., Crosstrack Dynamics

of a Long Cable Towed in the Ocean, IEEE

OCEANS81, Boston, MA, September 1618,

pp. 966970, 1981.

[107] Lo, A., and Leonard, J. W., Dynamic

Analysis of Underwater Cables, J.Eng.

Mechanics Division, 108(4), pp.

605621,1982.

[108] Leonard, J. W., and Nath, J. H.,

Comparison of Finite Element and Lumped

Parameter Method for Oceanic Cables, Eng.

Structures, 3(3), pp.153167, 1981.

[109] Bathe, K. J., Finite element procedure,

Englewood Cliffs, N. J. Prentice-hall, 1996.

[110] Chung, J., and Hulbert, G. M., A Time

Integration Algorithm for Structural

Dynamic with Improved Numerical

Dissipation: the Generalize Method, J. App.

Mech. (pp. 371375); 1993.

[111] Ketchman J. J. and Lou Y. K;

Application of the Finite Element Method to

Towed Cable Dynamics, Proc. MTS/IEEE

Oceans, 1975.

[112] Yang Min-Dong and Teng Bin; Static

and dynamic analysis of nonlinear finite

element, Chinese, Ocean Engineering

Society, 2010.


ISSN: 2456-1851



[113] Ran, Z. Coupled Dynamic Analysis of

Floating Structures in Waves and Currents

Ph.D. Thesis, Texas A & M University,

College Station, TX, 2000.

[114] D. L. Garrett, Coupled Analysis of

Floating Production Systems; Ocean Eng.,

32, pp. 802816, 2005

[115] Buckham, B. J. Dynamics Modeling of

Low Tension Tethers for Submerged

Remotely Operated Vehicles Ph.D. Thesis,

University of Victoria, British Columbia,

2003.

[116] Kaczmarczyk, S., and Ostachowicz,

W. Transient Vibration Phenomena in Deep

Mine Hoisting Cables: Part 1:

Mathematical Model, Journal of Sound and

Vibration, 2003.

[117] Aamo, O.M.; Fossen, T.I. Finite

element modelling of mooring lines. Math.

Comput. Simul. 2000 , 53, 415422.

[118] Aamo, O.; Fossen, T. Finite element

modelling of moored vessels. Math. Comput.

Model. Dyn. Syst. 2001 , 7, 4775

[119] Palm, J.; Paredes, G.M.; Eskilsson, C.;

Pinto, F.T.; Bergdahl, L. Simulation of

mooring cable dynamics using a

discontinuous Galerkin method. In

Proceedings of the 5th International

Conference on Computational Methods in

Marine Engineering, Hamburg, Germany,

2931 May 2013

[120] Montano, A. Restelli, M. Sacco, R.

Numerical simulation of tethered buoy

dynamics using mixed finite elements.

Comput. Methods Appl. Mech. Eng. 2007,

196, 41174129

[121] Howell, C. T. and Triantafyllou, M.

S., Investigation of Large Amplitude

Nonlinear Dynamics of Hanging Chains,

International Journal of Offshore and Polar

Engineering, Vol. 3, No. 3, 1993, pp. 162-

167

[122] Thomas D. O. and Hearn G. E. Deep

water mooring line dynamics with emphasis

on sea-bed interference effects, Offshore

Technology Conference, OTC 7488, Vol. 3,

203 241; 1994.

[123] Huang, S., Dynamic analysis of three -

dimensional marine cables, Ocean Eng;

1994.

[124] Hover, F. S., Grosenbaugh, M. A. and

Triantafyllou, M. S., Calculation of dynamic

motions and tensions in towed underwater

cables, IEEE J. Ocean. Eng; 1994.

[125] Gobat, J., and Grosenbaugh, M., Time-

Domain Numerical Simulation of Ocean

Cable Structures, Ocean Eng., 33(10), pp.

13731400, 2006.

[126] Matulea, I. C., N stase, A., T lmaciu,

N., Sl mnoiu, G. and Goncalves Coelho, A.

M., On the equilibrium configuration of

mooring and towing cables, Appl. Ocean

Res; 2008.

[127] Chatjigeorgiou, I.; Mavrakos, S.

Assessment of bottom-cable interaction

effects on mooring line dynamics. In


ISSN: 2456-1851



Proceedings of the 17th International

Conference on Offshore Mechanics and

Arctic Engineering, Lisbon, Portugal, 56

July 1998.

[128] Ablow, C.; Schechter, S. Numerical

simulation of undersea cable dynamics.

Ocean Eng. 1983, 10, 443457.

[129] Howell, C.T. Investigation of the

Dynamics of Low-Tension Cables.

Ph.D.Thesis, Woods Hole Oceanographic

Institution, Massachusetts Institute of

Technology, Cambridge, MA, USA, 1992.

[130] Chatjigeorgiou, I.K. A finite

differences formulation for the linear and

nonlinear dynamics of 2D catenary risers.

Ocean Eng. 2008, 35, 616636.

[131] Winget, J.; Huston, R. Cable

dynamics, A finite segment approach.

Comput. Struct. 1976, 6, 475480.

[132] Kamman, J.W.; Huston, R.L.

Modelling of submerged cable dynamics.

Comput. Struct. 1985, 20, 623629.

[133] Nichol, T.; DuBuque, G.; Fabien, B.;

Dynamic Modelling of Compliant-Moored

Submerged Systems with Applications to

Marine Energy Converters. In Proceedings

of the 2nd Marine Energy Technology

Symposium, Seattle, WA, USA, 1517 April

2014.

[134] Filipich, C.; Rosales, M. Dynamic

Analysis of plane mooring chains of

inextensible links. Mec. Comput. 2007 , 26,

24792495.

[135] Josh Davidson and John V. Ringwood

Mathematical Modelling of Mooring

Systems for Wave Energy Converters. A

Review, Centre for Ocean Energy Research,

Maynooth University, 2017.

[136] DNV-OS-E301 Offshore Standard,

DNV GL, 2013.

[137] Saidee, M.H. Fatigue Analysis and

Design of Mooring Systems. Assessment and

Comparison of Different Methods. Masters

Thesis, NTNU, Trondheim, Norway, 2015.

[138] Low, Y.M.; Cheung, S.H. On the

long-term fatigue assessment of mooring

and riser systems. Ocean Eng.2012, 53,

6071

[139] Thies, P.R.; Johanning, L.; Smith,

G.H. Lifecycle fatigue load spectrum

estimation for mooring lines of a floating

marine energy converter. In Proceedings of

the ASME 2012 31st International

Conference on Ocean, Offshore and Arctic

Engineering, Rio de Janeiro, Brazil, 16 July

2012; pp.667676.

[140] Thies, P.R.; Johanning, L.; Harnois,

V.; Smith, H.C.; Parish, D.N. Mooring line

fatigue damage evaluation for floating

marine energy converters: Field

measurements and prediction. Renew.

Energy 2014, 63, 133144.

[141] Christiansen, N.H.; Voie, P.E.T.;

Hgsberg, J.; Sdahl, N. Efficient mooring line

fatigue analysis using a hybrid method time

domain simulation scheme. In Proceedings

of the ASME 2013 32nd International


ISSN: 2456-1851



Conference on Ocean, Offshore and Arctic

Engineering, Nantes, France, 914 June 2013;

p.V001T01A035.

[142] Harnois, V. Analysis of Highly

Dynamic Mooring Systems: Peak Mooring

Loads in Realistic Sea Conditions. Ph.D.

Thesis, University of Exeter, Exeter, UK,

2014

[143] Savin, A.; Svensson, O.; Leijon, M.

Azimuth-inclination angles and snatch load

on a tight mooring system. Ocean Eng.

2012, 40, 4049

[144] Palm, J.; Eskilsson, C.; Bergdahl, L.

Mooring cable simulations with snap load

capturing for wave energy applications. In

Proceedings of the 2nd International

Conference on Renewable Energies

Offshore, Lisbon, Portugal, 2428 October

2016

[145] ISO 19901-7: Specific Requirements

for Offshore Structures, Petroleum and

Natural Gas Industries, 2013.

[146] Singh, N. Systems Approach to

Computer-Integrated Design and

Manufacturing. Wiley, New York, 1996.

[147] Su YH, Yang JM, Xiao LF, Li X.

Multi-objective optimization design of

truncated mooring system based on

equivalent static characteristics. China

Offshore Platform. 23(1):14 19, 2008.

[148] Michalewicz Z. Genetic algorithms +

data structures = evolution programs. New

York (NY): Springer-Verlag, 1994.

[149] Michalewicz, Z., Schoenauer, M.,

Evolutionary computation for constrained

parameter optimization problems.

Evolutionary Computation 4 (1), 132. 1996.

[150] Lagaros N.D., Papadrakakis M.,

Kokossalakis G. Structural optimization

using evolutionary algorithms. Computers

and Structures 80, 539571, 2002.

[151] Tianhui Fan, Dongsheng Qiao &

Jinping Ou; Innovative approach to design


and damping equivalent; Ships and Offshore

Structures/ Francis taylor, 2014.

[152] Tianhui Fan, Dongsheng Qiao, Jun

Yan, Chaohe Chen & Jinping Ou

Experimental verification of a semi-

submersible platform with truncated

mooring system based on static and

damping equivalence ,Ships and Offshore

Structures , 2017.

review of numerical approach used in the …assisted mooring system [9]. moored system where...

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