Variation Of Stress Created By Waves And Marine Engineering Essay

Abstraction: The offshore platform have normally leg for prolonging on sea deep. The concretion of the legs is really complicated because of the fluctuation of the tonss in clip. In this paper is present the numerical consequences for bear downing of a leg with forces caused by moving ridges and marine currents. The package for computation of force induced by H2O usage Airy theory ( for regular moving ridges ) . The construction has been analyzed numerically utilizing the plan Solid Works-COSMOS/M ( emphasis and supplantings ) , and FORHID ( tonss ) .

Keywords: emphasis, moving ridge, FEM, offshore platform

1. Introduction

The offshore constructions have been divided into following classs [ 1 ] :

1. Fixed Platforms: steel templet constructions and concrete gravitation constructions. These platforms are built on concrete or steel legs, or both, anchored straight onto the ocean floor, back uping a deck with infinite for boring rigs, production installations and crew quarters.

2. Compliant tower: compliant tower, guyed tower, articulated tower, tenseness leg platform. These platforms consist of slender flexible towers and a pile foundation back uping a conventional deck for boring and production operations.

3. Floating Structures: drifting production system ; drifting production, storage and offloading system

2. Types of Loads

Tonss on offshore constructions are gravity tonss and environmental tonss. Gravity tonss are originating from deadweight of construction and installations either lasting or impermanent. Environmental tonss regulating the design of seaward constructions. Assorted environmental tonss moving on the offshore platform are [ 1 ] :

1. Gravity Loads: structural dead tonss, installation dead tonss, fluid tonss, unrecorded tonss, boring tonss

2. Environmental Tonss: air current tonss, wave tonss, current tonss, perkiness tonss, ice tonss, clay tonss

3. Seismic Loads

2.1. Environmental Loads on Offshore Structures

The Environmental tonss include: air current, wave, current, temblor, ice and snow, temperature, sea bed motion, marine growing and tide generated tonss. Tonss due to weave, moving ridges and temblor are discussed in item.

1.2.1 Wind tonss

Wind loads act on the part of a platform above the H2O degree, every bit good as on any equipment, lodging, derrick, etc. located on the deck [ 2 ] . Wind induced tonss moving on offshore platforms on a derrick is defined by cardinal equation of aerodynamic forces:

( 1 )

The footings are fallowing meaning:

I? – air denseness

– retarding force coefficient of retarding force

A – projection country of a construction

U ( T ) – air current velocity

1.2.2 Wave tonss

The moving ridges are assumed to be long-crested. They can be described by a planar flow field, and are characterized by the parametric quantities: moving ridge tallness ( H ) , period ( T ) and H2O deepness ( vitamin D ) as shown in Figure 1.

Fig.1.A moving ridge construction

A moving ridge is defined by the undermentioned feature:

i?¬ – is wave length is the horizontal distance ( in metres ) between two consecutive crests,

– moving ridge tallness, is the difference in surface lift between the moving ridge crest and the old moving ridge trough. For a simple sinusoidal moving ridge

– the amplitude, is the magnitude of the maximal supplanting from average sea-level. This is normally indicated in metres ( or pess )

T – the period is the clip interval ( in seconds ) between the transitions of consecutive crests passed a fixed point.

f – the frequence is the figure of crests which pass a fixed point in 1 2nd. It is normally measured in Numberss per second ( Hertz ) and is the same as 1/T, which is the reciprocal of the period

c=i?¬/T – the rate of extension which represents the extension velocity of the moving ridge crest

i?·=2i?°/T – pulsation moving ridge and

k=2i?°/i?¬ -wave figure.

1.2.2.1 Speed and length moving ridge

Based on look pulsing i?· ensuing velocity and wave length [ 3 ] , [ 4 ] :

( 2 )

Where cg extension velocity wave whith same length and amplitude is:

( 3 )

1.2.2.2 Pressure moving ridge

The hydrodynamic extra force per unit area ensuing from moving ridge is:

( 4 )

1.3 Morison ‘s Equation

The inactiveness and added mass consequence and the muffling consequence of the retarding force force on the slow impetus gesture, for the slender cylindrical natation construction, can be evaluated by utilizing Morison ‘s equation. Morison et Al. ( 1950 ) proposed that the entire force is the amount of drag force and inertia force. The entire force is result from the moving ridge and current burden can be calculated by Morison equation [ 5 ] .

Morison equation per unit length is:

( 5 )

Where is the entire force,

– is the denseness of the sea H2O,

– is the added mass coefficient,

– is the retarding force ( opposition ) coefficient,

u – is the H2O atom speed relative to the member normal to the member axis,

D – is diameter of the member exposed to the sea.

The first term in the equation is inertia constituent and the 2nd term is the drag constituent. This can be expressed as:

( 6 )

Fig. 2. Diffraction Model ( Wu & A ; Eatock-Taylor, 1999 ) [ 6 ]

2. Loads computation

2.1Hydrodynamic forces generated by wave action

In this sentence are mentioned theoretical consequences obtained with the plan “ FORHID ” . “ FORHID ” plan solved the computation of hydrodynamic forces and minutes given by marine currents and wave action on constructions composed of saloon webs. Using the Morison-O’Brien equation consequence the minutes and of forces and from the BASIC of fixed construction ( see figure 3 ) .

The necessary day of the months for to run the plan is defined in table 1 [ 7 ] .

Table 1 Data entry

Symbol

Explanation

Value

Nitrogen

Number of curves ;

303

I?

Density of the sea H2O

1.013 [ t/m3 ]

Centimeter

Added mass coefficient.

2

Cadmium

Resistance coefficient.

1

DELTD

Diameter growing due to the deposition phenomenon

0 [ m ]

ANIU

Cinematic viscousness

0.00000101 [ m2*s ]

CR1

Current speed to the ocean floor

0.6 [ m/s ]

CR2

Current speed at free surface

1.2 [ m/s ]

eleven, Lolo, zi

Node coordinates saloon

[ m ]

Calciferol

Diameter of the beam exposed to the sea

[ m ]

PERT

Wave period

10.2 [ s ]

HVAL

Wave tallness

14.3 [ m ]

ADINC

Water deepness

33 [ m ]

ZBAZA

Distance from the base construction

0 [ m ]

UMIU1

Wave angle

0 [ grades ]

The plan delivers consequences, table 2:

Table 2 Consequences aˆzFORHID ”

Symbol

Explanation

Hydrodynamic burden for saloon, ,i ”

FXI, FYI, FZI

hydrodynamic force constituents on the saloon aˆzi ”

XFI, YFI, ZFI

co-ordinates of the point of application of hydrodynamic force calculated on the saloon aˆzi ”

FI1

hydrodynamic force of the saloon aˆzi ” ; of a node 1

FXI1, FYI1, FZI1

hydrodynamic force constituents of the node “ 1 ” of the saloon “ I ”

, ,

entire hydrodynamic force constituents construction

F

the entire hydrodynamic force construction

,

minutes of entire forces, and in relation to the basic program construction

2.2 Loading. Structural analysis consequences

Were adopted ensuing hydrodynamic forces and minutes ensuing on the plan “ FORHID ” . Forces and minutes given by summed of moving ridge and Marine currents action are the consequences for each node. Tonss were imposed for each node individually.

3. Numeric analysis

The Finite Element Method ( FEM ) knew a speedy development in tandem with the addition of the computational capacities and it has enforced as a general numerical method of work outing technology jobs from different countries, inclusively the naval sphere [ 8 ] .

The structural analysis through the finite component method requires utilizing the same equations of the snap theory. MEF cardinal equation is:

( 12 )

Where – is the vector of nodal forces, [ K ] – is the rigidness matrix and is displacement vector.

In this paper is presented an numerical ( utilizing FEM ) trial for the theoretical account to see the distribution of emphasis. To find by computation the emphasis was used the Solid Works-COSMOS/M package.

Most steel offshore support constructions are 3-dimensional frames fabricated from cannular steel members. This gives the best via media in fulfilling the demands of low retarding force coefficient, high perkiness and high strength to burden ratio [ 3 ] . The most common used seaward construction is a jacket construction, which comprises a prefabricated steel support construction ( jacket ) extended from the sea bed ( connected with hemorrhoids at the sea bed ) to some height above the H2O surface degree, and a steel deck ( topside ) on the top of the jacket.

The chief leg tonss are given by: ain weight, organic structure platform weight, wave tonss moving on leg construction and air current tonss moving on sidelong surface of platform organic structure.

The platform considered in this survey is the “ Gloria ” platform. The infrastructure is a piled steel jacket. The Gloria infrastructure has four legs supported by perpendicular steel hemorrhoids grouped symmetrically around each corner leg. The jacket ‘s lower portion is 47.68 m high and is connected to the heap foundation. At the underside, to imitate connexion leg – underside H2O has built a really stiff construction that simulates fastness. Discredited theoretical account is constructed of 156 nodes and 303 curves.

Fig. 3. Leg ‘s construction theoretical account

The diameter and thickness beam of which is build the jacket construction is present in table 3

.

Table 3 The diameter and thickness of beam

Diameter [ m ]

Thickness

[ m ]

0.914

0.050

0.460

0.032

0.340

0.016

0.220

0.008

Was considerate for tonss:

Case I – merely ain weight ;

Case II – ain weight and moving ridges

The supplanting and emphasis distribution for initial theoretical account construction charged with ain weight and organic structure platform weight is present in figure 4 and figure 5.

Fig. 4. Stress distribution for construction leg theoretical account

Fig. 5. Supplanting for construction leg theoretical account

In following tabular array is presented emphasis and supplantings fluctuation on node figure 160 at z=47,68.m.

Table 4. Stress fluctuation

Time

[ s ]

Stress fluctuation

[ MPa ]

Case I

Case II

0

7,39E+01

1,43E+02

0,851

1,00E+02

1,702

9,71E+01

2,552

9,24E+01

3,403

8,80E+01

4,254

9,22E+01

5,105

8,77E+01

5,956

9,21E+01

6,806

9,74E+01

7,657

9,89E+01

8,508

1,17E+02

9,359

1,26E+02

10,21

1,43E+02

Table 5. Displacement fluctuation

Time

[ s ]

Dispalcement fluctuation

[ millimeter ]

Case I

Case II

0

0,805

1,1

0,851

2,7

1,702

2,5

2,552

2,5

3,403

2,5

4,254

2,5

5,105

2,5

5,956

2,5

6,806

2,5

7,657

2,5

8,508

2,5

9,359

2,5

10,21

2,5

In following diagram is presented normal emphasis fluctuation which appear on the leg from wave action at an angle of incidence 0 grades.

Fig. 6 Variation emphasis

4. CONCLUSIONS

After numerical survey made can pull the undermentioned decisions:

1. As can be seen from Table 2, wave influence on normal emphasis is 41,2 % compared with his ain weight. Maximal emphasis from node considered value of 1.43e+02 MPa is with 58 % smaller than the the admissible stuff which is made aˆ‹aˆ‹leg ( 360 MPa ) .

2. As can be seen from Table 2, wave influence on supplanting is 70 % compared merely with his ain weight.

3. From points 1 and 2 consequences that the moving ridge and sea currents have a major influence on the emphasiss and supplantings which appear in the construction leg of an seaward platform. From this we can reason that it is necessary to see these influences on the dimensioning of such constructions.

Recognition

The writers appreciatively acknowledge POSDRU undertaking – ” Bettering the concern rhythm pupils in doctorial surveies ” – 61445 ID 88/1.5/S acronym EFFICIENT for fiscal support, grant of the University “ Dunarea de Jos ” of Galati, 2011