optimizacion de estructuras

Escuela Superior Politécnica del Litoral Ship Design II

FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER

GROUP 2: STRUCTURAL OPTIMIZATION 1

FINAL DESIGN OPTIMIZATION OF 2,500 DWT

BULK CARRIER

GROUP N.-2

STRUCTURAL OPTIMIZATION

INDEX –

TUTOR:

ING. FRANKLIN JOHNNY DOMINGUEZ

AUTHOR:

ANGEL RUIZ GONZALEZ

CHRISTOPHER VILLALTA MIRANDA




1. INTRODUCTION ................................................................................................................. 4

2. GENERAL OBJECTIVE ...................................................................................................... 4

2.1. SPECIFIC OBJECTIVES ............................................................................................. 4

3. OBJECTIVE FUNCTION .................................................................................................... 5

4. METHODOLOGY ................................................................................................................ 7

5. PROCEDURE FOR THE OPTIMIZATION DEVELOPMENT OF GROUP 100 .............. 9

5.1. DESIGN VARIABLES ................................................................................................. 9

5.2. PRE-ASSIGNED VARIABLE ................................................................................... 11

5.2.1. Spacing validating of the pre-assigned variables ................................................ 11

5.3. ALGORITHM OPTIMIZATION. .............................................................................. 13

5.4. CONSTRAINTS ......................................................................................................... 14

5.5. CONSTRAINTS FORMULATION ........................................................................... 15

5.5.1. Plate thickness. .................................................................................................... 15

5.5.2. Sectional Modules. .............................................................................................. 16

5.5.3. Design Pressures ................................................................................................. 17

5.5.3.1. Bottom pressures ......................................................................................... 18

5.5.3.2. Side Pressures .............................................................................................. 18

5.5.3.3. Deck pressures ............................................................................................. 19

5.5.3.4. Inner bottom pressures ................................................................................ 19

5.5.3.5. Values of design pressures .......................................................................... 19

5.5.4. Analysis of stiffeners buckling ............................................................................ 20

5.5.5. Frequencies.......................................................................................................... 20

5.5.5.1. Natural frequency ........................................................................................ 22

5.5.5.2. Effect of the added mass ............................................................................. 24

5.6. DETERMINATION OF THE GAMMA FACTOR.................................................... 24

5.7. WEIGHT DETERMINATION. .................................................................................. 26

5.8. MAN HOUR. .............................................................................................................. 27

5.9. COST CALCULATION SUBROUTINE. .................................................................. 29

5.10. OUTPUT VARIABLES. ......................................................................................... 29

6. CALCULUS ........................................................................................................................ 30

6.1. Methodology to follow where the vessel to increase or decrease its dimensions. ...... 30

6.2. Comparison and validation of results and formulas. ................................................... 31

6.2.1. Analysis of the 3 -4 and 5th compartment with respect to the bottom and the

deck. 31




6.2.1.1. Double bottom analysis and Weather Deck ................................................ 33

6.2.1.1. Side Analysis ............................................................................................... 35

7. ANALISYS RESULTS ....................................................................................................... 42

8. REFERENCES .................................................................................................................... 43

9. ANNEX ............................................................................................................................... 44

9.1. Distribution factors for sea loads on ship’s shell and weather decks .......................... 44

9.2. SUBROUTINS PROGRAMMING ............................................................................ 45

9.3. Stability ....................................................................................................................... 45

9.4. Maneuverability .......................................................................................................... 45

9.5. Resistance and propulsion y Propulsión ...................................................................... 45

9.6. Cost ............................................................................................................................. 46

9.7. Man Hours ................................................................................................................... 46

9.8. Structurecubierta ......................................................................................................... 46

9.9. Structuredoublebottom ................................................................................................ 46

9.10. ANEX ...................................................................................................................... 47

9.11. ANEX ...................................................................................................................... 47

9.12. ANEX ...................................................................................................................... 47

9.13. ANEX ...................................................................................................................... 47




1. INTRODUCTION

When a vessel is built compliance with the structural requirements is crucial, as the vessel

must be extremely safely, getting support the loads to which it shall be subject.

In this booklet is intended that the minimum cost of construction provide us the strongest

structure as possible, this is part of the 100 technological group optimization, and this is

accomplished using the Germanischer Lloyd’s Society Classification rules [1] which

provide us a minimum parameters at the moment of design a structural element, these

parameters will be used as constraints.

The vessel in the midsection will have a longitudinal frame and at fore and aft will have

a transverse framing, the design variables and constraints are formed by the spacing

between stiffeners, sectional modules, Minimum frequency depending of the vessel

sector, and thicknesses plate.

2. GENERAL OBJECTIVE

Optimization of stiffeners and plates with the goal of decrease the vessel weigh, this

means a reduction in the construction cost and improvement of the structural arrangement.

2.1. SPECIFIC OBJECTIVES

Determining the objective function to minimize the cost of the ship structure.

Set restrictions based on classification societies.

Check the new dimensions using specialized software.




3. OBJECTIVE FUNCTION

The objective function to be considered for optimization of this technology group is

focused primarily on reducing the cost of construction, below the objective function

described:

Minimize F(x) = PC ($)

PC =MC +LC *HC

Where:

PC Production cost ($),

MC Material cost ($),

LC Labor cost (man-hours),

HC Hourly cost ($/hour),

The ship is divided into compartments, and each of these is optimized, obtaining the

lowest possible weight per compartment which in turn will produce the lowest cost per

material. In the figure below shown the vessel divided by compartments, this partition is

made taking as reference the bulkheads.

Figure 1 Structural compartment division




For this, we have to determine the total weight of the ship, which is defined as follows:

WT = 𝛾 ∗ (WC1 + WC2 + WC3+WC4+…+WSUPERSTRUCTURE)

Where:

WT = The Total Weight of the structure to each ship on the iteration.

WSUPERSTRUCTURE = Weight of the Superstructure, this depend of the breadth of the ship.

WC1, WC2, etc. = Weight of each compartment. To do this we have to determinate the

previously volume of the material developed, and then multiply the specific weight of the

specific material. This weight will be found using the methodology presented below.

𝛾 = Gamma factor, this parameter is calculate in base to the preliminary weight of the

structure obtained before. And the calculus is explained later.

The next picture showing a typical compartment at mid-section of a bulk carrier vessel

that will be optimized:

Figure 2 Typical compartment at mid-section of a bulk carrier vessel




4. METHODOLOGY

This part of the project will be divided into three parts; the first is the theoretical part, the

second will be the calculation and development, the third analysis results. We do

reference [2] with the following flow chart to develop our process.

Figure 3 Flow chart after sub-module selection (constraints and cost data).

In the first block you will find the information of all restrictions for each design variable

defined for the development of this group 100 such as the separation between stiffeners,

also will be listed the pre allocated variables that help make this optimization does not

become so complicated for example the design pressure, dimensions of each

compartment, etc., the second block will be the calculation performed and obtained and

the third block is the analysis of the results expected in the project with those obtained in

the preliminary design.




In the first block will also prepare a flowchart to help us analyze the structure of the ship

for compartment, in order to obtain the weight of each and also get the cost of building

them. Cost will be affected in each compartment due to their level of difficulty at the time

of construction. Difficulty influences the cost of construction. This algorithm has the

following work methodology:

This analysis is performed for compartment such that when entering the pre

assigned variables such as the distances of the primary structure: web frame

bottom longitudinal beams, girders, stanchion and bulkheads, the program can

generate a separation stiffeners (design variable) into the compartment and

analyzed panel, then proceed to evaluate the restrictions according to the aspect

ratio of the panel, the plate thickness of the panel, the frequency generated by

these elements, the sectional module and the buckling of each element involved

in the panel; This analysis will be conducted around the compartment analyzed

waiting obtain acceptable size in accordance with ease of construction. Thus

obtaining as a result the ideal dimensions to fulfill with all restrictions by the

variables and the demands by the Classification Society used in this project.

In the second block, the programming of this algorithm is performed in software that

helps us evaluate quickly and repeatedly as provided in block 1. This shall be Matlab

software, which is easy when programming. Once programmed this process it will give a

confidence level to this programming, making this project have a better development and

form to evaluate the results. This program will be then executed on each vessel

dimensional matrix obtained in the workbook 1, to obtain the construction costs of each.

In the third block, the comparative study is made between preliminary results and those




obtained in this project, hoping that the preliminary weight is greater than that obtained

in this workbook. The results will be evaluated to meet the objectives and reach objective

conclusions about the application of this model of structural analysis in future

generations.

5. PROCEDURE FOR THE OPTIMIZATION DEVELOPMENT OF GROUP 100

5.1. DESIGN VARIABLES

Ranges must be set or fixed parameters including variables in order to obtain a

satisfactory optimization. Since it frame established it is longitudinal midsection,

frames and web frames, stiffeners and longitudinal beams, defining as design

variables the following parameters:

Figure 4 Compartment 3D and design variables. - Side and bottom view of midsection

SIDE

lbs

Plate floor

lss

BOTTOM

Spacing between

web frame

Web

Frame




Figure 5 Compartment 3D and design variables. - deck view from bottom of midsection

Longitudinal spacing of deck stiffeners (lds)

Spacing of deck transversal stiffeners (tds)

Longitudinal spacing of bottom stiffeners (lbs)

Spacing of bottom transversal stiffeners (tbs)

Longitudinal spacing of side stiffeners (lss)

Plate thickness (pt)

As we can see the spacing between stiffeners are an important design variables, these

are located within the boundaries they will be defined by the restrictions as detailed

in the following points.

lds

tds




5.2. PRE-ASSIGNED VARIABLE

The pre-assigned variables are those primary elements that their location were defined

in the preliminary design, with these fixed parameters the intention optimize the

separation between stiffeners and their respective dimensions, below shown the pre-

assigned design variables.

Bulkhead spacing (bs)

Deck girders spacing. (dgs)

Side girder spacing. (sgs)

Plate floor spacing. (pfs)

Girders spacing. (gs)

Web frame spacing. (wfs)

Engine seat. (es)

Main dimensions of the vessel.

5.2.1. Spacing validating of the pre-assigned variables

Once have been pre-defined variables assigned, what we want is to validate that

these are within the recommended range. Which mentions important aspects that

we must fulfill in the structural arrangement of a ship, such as:

Secondary reinforcement height should 2.5 times less than primary element.

The spacing of web frames in topside tanks is generally to be not greater than 5

frame spaces.

The spacing of adjacent girders is generally to be not greater than 4.6 m or 5 times

the spacing of bottom or inner, bottom ordinary stiffeners, whichever.

The spacing of floors is generally to be not greater than 3.5 m or 4 frame spaces

as specified by the designer, whichever is the smaller.

The spacing of solid floors is not to be greater than 3.5m or four transverse frame

spaces.




In case of transverse framing, the spacing of bottom girders is not to exceed 2.5m.

In case of longitudinal framing, the spacing of bottom girders is not to exceed

3.5m.




5.3. ALGORITHM OPTIMIZATION.

The algorithm used to optimize the structures for the vessel shown below:

Data input, Pression

design, Compartment dimensions

Location of

stiffeners and

primary elements,

transversals and

longitudinals

Verification

of the

aspect ratio

Minimun

tickness

calculation

Calculation of

SM required

Select from library

a sectional module

available

Buckling analysis

of the selected

stiffener

Analysis of

both

frequencies

Weight and

stiffeners

dimensions of each

compartmentdimen

Pass

No Pass




5.4. CONSTRAINTS

These restrictions or limitations will be established either by the Classification

Society or by the owner needs, maximum or minimum values will be taken by

certified references in order to obtain the best possible optimization for our vessel.

The restrictions to be evaluated in this project have been separated part as follows:

Spacing stiffeners.

300 mm is taken as the initial value, due to issues of solder structure. Also be

taken as the final value the formulation by Lloyd's Register [4] for separation

between stiffeners.

S = (0.47+(0.97*L/1000)/0.6) [mm]

Aspect ratio.

Here we suggest take into consideration the aspect ratio for each compartment

before to do the calculation of the plate thickness. As follows:

Table 1 Values suggested of aspect ratios

Aspect Ratio (l/s) After Peak Midsection Fore Peak

Bottom 1 2 - 1 1 - 2

Side 2 - 1 2 - 1 2 - 1

Deck 4 - 3 4 - 3 4 - 3

Plate thickness.

After setting the aspect ratio for each section of the plate (bottom, side and

deck), we proceed to determine the plate thickness with formulations used by

Classification Society Germanisher Lloyd’s [1], doing it to each compartment

and section.




Sectional Modules.

We proceed to determine by formulations of Classification Societies

Germanisher Lloyd’s [1] the sectional module of each primary and secondary

stiffener, making this for each section and compartment.

Buckling.

Here the dimensions of the secondary and primary stiffeners be analyzed with

a buckling criteria presented by RINA [5], such that the web of the stiffener

has a length such that there is no presence of buckling in the same due to the

design load considered in this. This analysis was developed in the library used

to this project.

Frequency.

For vessels with a single propeller, plate fields and stiffeners should fulfil the

following frequency criteria given by [6]. To fulfil the criteria the lowest

natural frequencies of plate fields and stiffeners are to be higher than the

denoted propeller blade passage excitation frequencies.

5.5. CONSTRAINTS FORMULATION

Of the information presented by the Classification Society Germanisher Lloyd’s [1],

which shows formulations that will be defined as constraints, we have formulations

to:

5.5.1. Plate thickness.

Table 2 Formulations to determinate the plate thickness of the panel.

Thickness (mm)

Bottom Deck Side

Minimum Plate thickness (mm) 𝑡 = 5 + 0.04𝐿 + 𝑡𝑘 𝑡 = 5 + 0.02𝐿 + 𝑡𝑘 𝑡 = 5 + 𝑘𝐿 + 𝑡𝑘

Plate thickness (mm) 𝑡 = 1.9𝑛𝑓𝑠√𝑃𝑘 + 𝑡𝑘 𝑡 = 1.9𝑛𝑓𝑠√𝑃𝑘 + 𝑡𝑘 𝑡 = 1.9𝑛𝑓𝑠√𝑃𝑘 + 𝑡𝑘




Plate thickness (mm)

Inner bottom 𝑡 = 1.1𝑠√𝑝𝑘 + 𝑡𝑘

Floor plates 𝑡 = 𝑡𝑚 − 2√𝐾

Side Girder 𝑡 =ℎ2

120ℎ𝑎

Center Girder 𝑡𝑚 =ℎ

ℎ𝑎(

ℎ

100+ 1) √𝐾

ℎ = Depth of the centre girder according [mm].

ℎ𝑎 = Depth [mm] of centre girder as built.

p = Design Loads according to the analyze area.

L = rule length in m.

tk = 1.5 mm, corrosion addition

5.5.2. Sectional Modules.

Table 3 Formulations to determinate the plate thickness of the panel.

Sectional module 𝑐𝑚3

sectional module 𝑐𝑚3

Transversal Stiff. 𝑍 = 0.63𝑙2𝑠𝑝𝑤𝑘 𝑍 =83𝑙2𝑠𝑝𝑤𝑘

𝜎 𝑍 = 0.5𝑙2𝑠𝑝𝑤𝑘

Longitudinal Stiff. 𝑍 =83𝑙2𝑠𝑝𝑤𝑘

𝜎 𝑍 =

83𝑙2𝑠𝑝𝑤𝑘

𝜎 𝑍 =

83𝑙2𝑠𝑝𝑤𝑘

𝜎

sectional module 𝑐𝑚3

Main frame 𝑍 =100𝑙2𝑠𝑝𝑤𝑘

𝜎 𝑍 = 0.63𝑙2𝑠𝑝𝑤𝑘

𝑍 = 0.5𝑙2𝑠𝑝𝑤𝑘

𝑍 = 6.5√𝐿

Girder 𝑍 =100𝑙2𝑠𝑝𝑤𝑘

𝜎 𝑍 =

100𝑆2𝑏𝑝𝑤𝑘

𝜎 𝑍 =

100𝑆2𝑏𝑝𝑤𝑘

𝜎

Where:

l = stiffener span in m

𝑍𝐵 = 1.549 𝑚3 𝑍𝐷 = 0.842 𝑚3 𝑍𝑅 = 0.674 𝑚3

s = stiffener spacing in m.

P = Design Loads according to the analyze area.

𝑛𝑓 = 0.83, depend of the framing system.

𝑘= 1, for 𝑅𝑒𝐻 = 235𝑁

𝑚𝑚2

ka = correction factor for aspect ratio of plate field




= (1,1 – 0,25 s/l )2

= maximum 1, 0 for s/l = 0,4

= minimum 0, 72 for s/l = 1,0

𝜎 = allowable local stress in N/mm2 for mild steel

wk = section modulus corrosion factor in tanks

b = loading breadth in m

S = girder span in m.

The following image shows a typical stiffener T with associated plate, the purpose of this

image is could visualizer the variables which will indicate each element that component

the stiffener.

ℎ𝑤= web height, mm

𝑡𝑤= web thickness, mm

𝑡𝑝= plate thickness, mm

𝑡𝑓= flange thickness, mm

𝑏𝑓= flange breadth, mm

Figure 6 typical T stiffener.

5.5.3. Design Pressures

The design pressures where determinate using the formulas presented by

Germanisher Lloyd’s (Lloyd, 2015). This calculus is required to calculate the

sectional module of each stiffener.

This formulation going to help us to determinate the pressures according to the

section of the compartment at analyze, have to be careful due to the sides pressures

changes a lot depending of the vessel draft.




5.5.3.1. Bottom pressures

The pressure on the bottom shell is determinate by the following formula:

𝑝𝑩 = 10𝑇 + 𝑝0𝑐𝐹 [𝐾𝑁

𝑚2]

Where:

T= draught [m]

P0 =Basic external dynamic load [kN / mm2] for wave directions with or

against the ship's heading, define as: 2.1(CB + 0.7)c0cLf

CB= Block coefficient

c0 = wave coefficient

c0 = [L

25+ 4.1] cRW

cRW = 1; For unlimited service range

L= rule length

cL = Length coefficient, defined as: √L

90

f = 1.00; or plate panels of the outer hull (shell plating, weather decks)

cF = Distribution factors according with the table shown in annex [1]

5.5.3.2. Side Pressures

5.5.3.2.1. Pressure below the waterline

𝑃𝑆 = 10(𝑇 − 𝑧) + 𝑃0𝑐𝐹 (1 +𝑧

𝑇) [

𝐾𝑁

𝑚2]

z: vertical distance [m] between load center of element and base line.

5.5.3.2.2. Pressure above the waterline

𝑃𝑆 = 𝑃0𝑐𝐹

20

10 + 𝑧 − 𝑇 [

𝐾𝑁

𝑚2]




5.5.3.3. Deck pressures

𝑝𝐷 = 𝑝0

20𝑇

(10 + 𝑧 − 𝑇)𝐻𝑐𝐷 [

𝐾𝑁

𝑚2]

𝐻 = Depth [m]

5.5.3.4. Inner bottom pressures

𝑃𝐼 = 9.81𝐺

𝑉ℎ(1 + 𝑎𝑣) [

𝐾𝑁

𝑚2]

Where:

𝐺 =mass [t] of cargo in the hold

𝑉 = Volume [m3] of the hold (hatchways excluded)

ℎ = Height [m] of the highest point of the cargo above the inner bottom,

assuming hold to be completely filled

𝑎𝑣 = Acceleration addition

5.5.3.5. Values of design pressures

When evaluating these formulations with each ship of tri-dimensional matrix,

for each of them a library is created. So, taking as an example the preliminary

vessel dimensions, the following library was obtained.

Table 4 Design pressure vessel for compartment

Stern Mid-section Bow

Compartment 1 Compartment 2 to 4 Compartment 5 Compartment 6

Bottom pressure [𝐾𝑁

𝑚2] 83.355 69.028 78.02 95.46

Side pressure [𝐾𝑁

𝑚2] Below water line 79.07 61.16 70.28 99.07

above water line 60.84 34.53 47.9 90.21

Deck pressure [𝐾𝑁

𝑚2] 25.93 23.58 24.88 26.5

Inner bottom pressure [𝐾𝑁

𝑚2] 64.45 55.8




This table describes the values of design Pressures Depending the section of

the compartment.

5.5.4. Analysis of stiffeners buckling

When the stiffener were selected, it must perform a buckling analysis to see if the

elements selected from the database do not fail, so for this analysis the Society

Classification RINA [5] shown us a table with maximum parameters where we

have to fulfill some aspect ratios of the dimensions stiffener:

Table 5 Criteria to evaluated the buckling in a stiffener

/

5.5.5. Frequencies

After obtaining the dimensions of the plate (thickness, length and width of the

panel) and stiffener. It will proceed to evaluate the natural frequency of the

same, and these frequencies will be compared with that obtained in the

propulsion system (Blade frequency) by recommendations given by




Germanischer Lloyd´s and thus establish whether the dimensions of the panel

and stiffeners are suited to adopt these criteria.

Now we have to be careful that our natural frequencies of plates and stiffeners

don't be near to the blade frequency in engine room area, at the next table we

can see the minimum critical frequencies that could exist in areas nearest to

the propeller:

Table 6 Frequency criteria by Germanischer Lloyd’s

Where:

𝛼 = ratio, defined as: 𝛼 =𝑃

∆

P = nominal main engine output [kW]

∆ = ship's design displacement [t]

𝑓𝑝𝑙𝑎𝑡𝑒 = lowest natural frequency [Hz] of isotropic plate field under

consideration of additional outfitting and hydrodynamic masses

𝑓𝑠𝑡𝑖𝑓𝑓 : Lowest natural frequency [Hz] of stiffener under consideration of

additional outfitting and hydrodynamic masses.

𝑑𝑟 : Ratio, defined as, 𝛼 =𝑟

𝑑𝑝; 𝑑𝑟 ≥ 1

r = distance [m] of plate field or stiffener to 12 o'clock propeller blade tip

position.

𝑑𝑝 = propeller diameter [m]

𝑓𝑏𝑙𝑎𝑑𝑒 =: Propeller blade passage excitation frequency [Hz] at n, defined as:

𝑓𝑏𝑙𝑎𝑑𝑒 =1

60𝑛𝑧




n: maximum propeller shaft revolution rate [1 / min]

z : number of propeller blades

Then in out areas of engine room like mid-section and superstructure we have

to fulfill the follow restrictions:

Table 7 Natural frequencies in mid-section and

superstructure by Germanischer Lloyd’s

𝑓𝑛(𝑝𝑙𝑎𝑡𝑒 𝑜𝑟 𝑠𝑡𝑖𝑓𝑓) > 1.2*4𝑓𝑏𝑙𝑎𝑑𝑒 Bottom

𝑓𝑛(𝑝𝑙𝑎𝑡𝑒 𝑜𝑟 𝑠𝑡𝑖𝑓𝑓) > 1.1*2𝑓𝑏𝑙𝑎𝑑𝑒 Side

𝑓𝑛(𝑝𝑙𝑎𝑡𝑒 𝑜𝑟 𝑠𝑡𝑖𝑓𝑓) > 1.1𝑓𝑏𝑙𝑎𝑑𝑒 Deck

Thus, depending on the location of the panel analyzed in the vessel, the

dimensions of this panel shall be to accepted whether it fulfill the criteria

presented in table 2 or 3 of this section.

To calculate the natural frequency of the plate and the stiffener we use the

following equations.

5.5.5.1. Natural frequency

The natural frequency is a factor to be careful as this will also depend on the

dimensions analyzed, which to calculate it is used the formulations presented

by Lloyd's Register [5].

In the case of plate’s frequency the natural frequency is calculated by:

𝑓𝑛 = 5.5375𝑡

𝑎𝑏√(

𝑏

𝑎)

2

+ (𝑎

𝑏)

2

+ 0.6045




Where:

a panel length (meters)

b panel breadth (meters)

t panel thickness (mm)

In the case of stiffener with associated plate, the same reference indicates that

the natural frequency of this can be approximated by the following

formulation:

𝑓𝑖 =𝐾𝑖

2𝜋𝐿2 √

𝐸𝐼

𝑚 (1 +𝜋2𝐸𝐼𝐿2𝐺𝐴

) [𝐻𝑧]

Table 8 Mode of vibration

Where:

𝐾𝑖: Constant where i refers to the mode of vibration.

EI = Flexural rigidity of plate stiffener combination

L= Beam length

GA = Shear rigidity of the plate stiffener combination

A: sectional area of the associated plate.

m = Mass per unit length of the stiffener and associated plating

Mode Ki Mode Ki

1 22.40

2 61.70

3 121.0

4 200.0

5 299.0




5.5.5.2. Effect of the added mass

The effect of the added mass is vital, as this factor makes our calculated

frequency drops too therefore does not meet the minimum values of

frequencies.

To consider this phenomenon is implemented the following formula:

𝑓𝑤𝑎𝑡𝑒𝑟 = 𝑓𝑖Ψ

Where:

Ψ =√

𝑝

𝑝 +𝜌1

𝜌𝑝

; 𝑝 = 𝜋𝑡√(1

𝑎2+

1

𝑏2)

𝜌1= density of the liquid

𝜌𝑝= density of the plate

t = plate panel thickness

When to obtain the value of the technological group for the propulsion, where the

reduction ratio and propeller will be determined, these data help us to determine the

blade frequency, determined by the following formula:

𝑓𝑏𝑙𝑎𝑑𝑒 = 𝑅𝑃𝑀𝑒𝑛𝑔𝑖𝑛𝑒 [𝑟𝑒𝑣

𝑚𝑖𝑛] ∗

𝑍

𝑟𝑎𝑡𝑖𝑜 ∗ 60[𝑠𝑒𝑐]= [𝐻𝑧]

Where:

𝑍= number of blades.

5.6. DETERMINATION OF THE GAMMA FACTOR

This parameter will help us later for the calculation of the total weight of each vessel

of the tri-dimensional matrix, since the weight obtained by the algorithm does not

include the weight of welding, brackets, etc.




Weight which in reality should be include in parametrically form and is calculated in

the following way.

1. The weight obtained by programming will be compared with the estimated weight

obtained in the preliminary design [3], this relationship 𝑊𝑝𝑟𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑟𝑦 𝑑𝑒𝑠𝑖𝑔𝑛−𝑠𝑡𝑒𝑒𝑙

𝑊𝑝𝑟𝑜𝑔𝑟𝑎𝑚𝑖𝑛𝑔 will

call it the gamma factor (𝛾).

𝛾 =𝑊𝑝𝑟𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑟𝑦 𝑑𝑒𝑠𝑖𝑔𝑛−𝑠𝑡𝑒𝑒𝑙

𝑊𝑝𝑟𝑜𝑔𝑟𝑎𝑚𝑖𝑛𝑔 ;

Where:

𝑊𝑝𝑟𝑒𝑙𝑖𝑚𝑖𝑛𝑎𝑟𝑦 𝑑𝑒𝑠𝑖𝑔𝑛−𝑠𝑡𝑒𝑒𝑙= 663.83 Ton

2. 𝑊𝑝𝑟𝑜𝑔𝑟𝑎𝑚𝑖𝑛𝑔 will be the total weight of the structure of the ship calculated in the

following way:

2.1. Once the code is programmed, will enter the necessary data corresponding to


2.2. List the thickness of each plate involved in the compartment.

2.3. Obtained the weight of the plates involved in the compartment depending on

its thickness. 𝑊𝑖.

2.4. The sum of all the weights found would be the total weight of the

compartment. 𝑊𝐶𝑖 = ∑ 𝑊𝑖

2.5. And the sum of the weight of each compartment including superstructure will

be the total structure weight of the ship.

𝑊𝑇𝑜𝑡𝑎𝑙 = ∑ 𝑊𝐶𝑖 + 𝑊𝑆𝑢𝑝𝑒𝑟𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒




5.7. WEIGHT DETERMINATION.

Once it has generated the appropriate dimensions of stiffener, such that fulfill

with the restrictions said previously to the analyzed panel, proceed to

performance this same analysis along the same compartment (bow to stern),

so matching the dimensions found lengthwise along the compartment, doing

this same procedure to change section (side, deck, or Bottom).

That said, proceed to product algorithm weight per compartment in the

following form:

1. List the thickness of each plate involved in the compartment.

2. Obtained the weight of the plates involved in the compartment

depending on its thickness. 𝑊𝑖.

3. Using parametrically the gamma factor. 𝛾

4. Determination of real weight using gamma factor. 𝑊𝑟𝑒𝑎𝑙𝑖= 𝛾 ∗ 𝑊𝑖.

5. The sum of all the weights found would be the total weight of the

compartment. 𝑊𝐶𝑖 = ∑ 𝑊𝑟𝑒𝑎𝑙𝑖

6. And the sum of the weight of each compartment including

superstructure will be the total structure weight of the ship.

𝑊𝑇𝑜𝑡𝑎𝑙 = ∑ 𝑊𝐶𝑖 + 𝑊𝑆𝑢𝑝𝑒𝑟𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒

So we follow the next format to find the weight per compartment:

Compartment k; k = 1,2,3,4,5,6,7

i t 𝑊𝑖 𝑊𝑟𝑒𝑎𝑙𝑖= 𝛾 ∗ 𝑊𝑖

1 mm ton ton




5.8. MAN HOUR.

Repair guide book for ship, the values that are presented have been decreased 15%,

due to that the price of man hour for a repair is more expensive than making a new

vessel. The table of values used are shown as follows.

Table 9 initial value of H-H according to thickness work

Table 10 Real value – decreased 15% by construction

Plate (mm) HH/ton

6 175

8 171,5

10 168

12,5 161

16 154

20 140




Table 11 increase factor (IF)

To bind the weight thickness of the plate involved calculated in section 5.8 of this booklet

with its corresponding man hour, follow the following format in the algorithm.

Compartment k; k = 1,2,3,4,5,6,7

i t 𝑊𝑖 𝑊𝑟𝑒𝑎𝑙𝑖= 𝛾 ∗ 𝑊𝑖 HH/ton HH IF 𝐻𝐻𝑟𝑒𝑎𝑙𝑖

1 mm ton ton adimensional 𝑊𝑟𝑒𝑎𝑙𝑖∗

𝐻𝐻

𝑡𝑜𝑛 adimensional 𝐻𝐻 ∗ 𝐹𝐼

Obtaining the real total man hours of the vessel j; j = 1, 2, 3…, 27.

∑ 𝐻𝐻𝑟𝑒𝑎𝑙 𝑖

𝑛

𝑖=1

= 𝐻𝐻𝑟𝑒𝑎𝑙 𝑘

𝐻𝐻𝑟𝑒𝑎𝑙 𝑗 = ∑ 𝐻𝐻𝑟𝑒𝑎𝑙 𝑘

5

𝑘 =1

Then binds this man hour of each vessel and its respective dimensions with the

subroutine for calculation of production cost.




5.9. COST CALCULATION SUBROUTINE.

5.10. OUTPUT VARIABLES.

Scantling of primary and secondary elements.

Structural weight

Ship production cost

Ship Construction cost

Initial –

Subroutine cost

Cost Calculate:

Work Group

Group 100

Group 200

Group 500

Group 600

HH Ship,

Matrix A, B, C

Final –

Subroutine cost

Ship Construction

and Production Cost




6. CALCULUS

6.1. Methodology to follow where the vessel to increase or decrease its dimensions.

Is known in advance that time optimize the vessel this can increase or decrease its

dimensions, is why that has been established a mapping for compartment ̈ the new vessel¨

according to the dimensions of the preliminary design

Compartment 3 to 6

All cargo is transported in this sector, and is the double bottom and double skin side skin,

then when the dimensions of the vessel optimize either increase or decrease, this

difference with respect to the dimensions of the preliminary design will be assigned to

the increase or decrease of the hull, having fixed the double bottom and double side skin,

this intends to load is not disturbed.

The following example demonstrates graphically what was explained in the previous

paragraph

Figure 7 methodology to perform where breath increase

Compartment 1 and 2

These correspond to the aft sector, since this sector is wide expected that the difference

occurs in a small percentage which will be assigned with reference to the model made in





Compartment 7

These compartments are critical, because it is in this sector where increase or decrease

the length of the vessel as required, also this sector is no longer has the double hull, this

will be the allocation of dimensions as a percentage in relation to the preliminary design

could be more delicate, however we know that this sector or corresponding to the sleeve

to be thinner not will be a high value

6.2. Comparison and validation of results and formulas.

The data corresponding to the preliminary design [3], were used for the validation of the

program, scantling results obtained through the use of the software Poseidon will be

compared with the results achieved by programming in Matlab the formulations presented

by Societies Classifications [1] and [4].

6.2.1. Analysis of the 3 -4 and 5th compartment with respect to the bottom and

the deck.

What is meant to do at this point is run the program in Matlab, and compare the results of

the preliminary design, these being, aspect ratios, sectional modules, thickness, etc.

Figure 8 compartment number 4th




Para el desarrollo de la estructura de fondo y la cubierta en el barco se há implementado

una biblioteca de perfiles en L, la cual fue obtenida desde el Software Poseidon.

A esta biblioteca se le hizo el análisis del buckling, y luego se la ordenó de tal manera

que tenda un módulo seccional decresiente. Como se ve en la siguiente tabla.

hw tw bf tf tpf Lpef Z[cm3]

FILA 1 55 5 35 5 4 150 12,03

FILA 2 55 5 35 5 5 150 12,52

FILA 3 55 5 35 5 6 150 12,94

FILA 4 60 5 35 5 4 150 13,27

FILA 5 55 5 40 5 4 150 13,29

FILA 6 55 5 40 5 5 150 13,82

FILA 7 60 5 35 5 5 150 13,82

FILA 8 55 5 40 5 6 150 14,27

FILA 9 60 5 35 5 6 150 14,28

FILA 10 60 5 40 5 4 150 14,63

FILA 11 55 6 35 6 5 180 14,94

FILA 12 60 5 40 5 5 150 15,22




La biblioteca completa se la presentará en los Anéxos.

6.2.1.1. Double bottom analysis and Weather Deck

Analysis is being developed by compartment both to bottom and deck, for each generated

s.

Deck

The analysis for the cover in compartment 3, 4, 5 and 6. It is developing in such way that

the cross beams are those who support the longitudinal reinforcements.

Bottom

When evaluating the first longitudinal s will give as a result the structure of the double

bottom. How will it look in the code of this structure (structuredoublebottom.m) in

annexes and also the development of the same.

Then since the code generates a weight for each s (the letter f is used for this variation of

s), the following equation is used to calculate the total weight of the double bottom (Wdb)

through the compartments.

Wdb(f,Ncomp) = 2*Wsg(f,Ncomp) + Wcg(f,Ncomp) + 2*Wpf(f,Ncomp) +

2*Wib(f,Ncomp) + 2*Wb(f,Ncomp) + 2*Wrsib(f,Ncomp) + 2*Wrsb(f,Ncomp)

1 2 3

2

4 5 6 7




Multiplied coefficients are due to that it is calculating the weight of the double bottom on

either side of the centerline.

This is ha compared with the Poseidon sectional modules and are very close. So we sa

confidence to continue advancing to other compartments such as 1, 2, and 7. In addition

this code eliminating the s that do not meet the restrictions of the frequency in relation to

the blade frequency by in ensures that the values presented below pass these restrictions.

The following results and comparisons to present, as referred to in the title belong to the

calculation of the vessel double bottom, corresponding to the compartment number 3, 4,

5 and 6 (see Annex).

Variables to Weather Deck

The total weight to the structure of the Weather is calculate according to the following

equation.

Wwd(f,Ncomp)=2*Wrslwd(f,Ncomp)+2*Wpwd(f,Ncomp)+3*Wrplwd(f,Ncomp)+2*Wrp

twd(f,Ncomp);

Where Wsg is the weight of the side girder, Wcg the weight of the

center girder, Wpf is the weight of the plate floor, Wib is the weight

of the plate of the inner bottom, Wb is the weight of the plate of the

bottom, Wrsb is the weight of the longitudinl stiffeners in the

bottom and Wrsib is the weight of the longitudinl stiffeners in the

inner bottom.

Weight of the structure analysis.




6.2.1.1. Side Analysis

Using the matlab software was programmed structures and plates, in order to determine the weight

of the vessel.

Secondary elements – longitudinal Stiffeners

Weight of each compartment, specifying relevant within each spacing:




After these results, analyses the total weight per compartment generated by each separation,

obtain the following results;

Identification of the minimum weight and its corresponding separation

Secondary elements – transversal Stiffeners




As the analysis carried out for the weight of the longitudinal elements, applies this process to

the calculation of weight with their corresponding separation.

Selection of the weight based on the separation of reinforcements in the longitudinal analysis




Weight obtained for primary transversals elements in compartment 3, 4, 5, and 6

Weight of primary transversals elements per comparment compartment 1, 2 and 7

Weight of longitudinal primary in compartment 3, 4, 5, 6




Weight of longitudinal primary in compartment 1 and 2

Total weight of plates per compartment

Total weight of side, whereas primary and secondary stiffeners in addition to the plates.

Finally the following table presents a comparison of findings with regard to profiles

stiffeners, obtained by programming in Matlab and those obtained with the software

Poseidon are:




compartment 1 (mm) compartment 2 (mm)

compartment 3

(mm)

compartment 4

(mm)

compartment 5

(mm)

compartment 6

(mm) compartment 7 (mm)

SIDE

Long Stiff L 130*10,0*80*10,0 L 105*11,0*75*11,0 L 160*10,0*75*10 L 160*10,0*75*10 L 160*10,0*75*10 L 160*10,0*75*10 L 160*10,0*75*10

POSEIDON L 130*10,0*90*10,0 L 130*10,0*90*10,0 L 120*10,0*80*10 L 120*10,0*80*10 L 120*10,0*80*10 L 120*10,0*80*10 L 120*10,0*80*10

Trans stiff L 180*10,0*85*10,0 L 245*9*85*13 L 200*10,0*95*10,0

POSEIDON L 200*11*90*11 L 300*10*90*10

Trans Bea, PL 10 PL 10 PL 10 PL 10

POSEIDON PL 8 PL 8 PL 8 PL 8

Vigas trans L 345*10,5*120*16 L 325*10,5*120*14,0 L 380*10,5*120*18

POSEIDON L 330*12*115*12 L 330*12*115*12

Vigas long PL 10 PL 10 PL 10 PL 10

POSEIDON PL 5 PL 5 PL 5 PL 5

Vigas long L 530*20*140*20 L 530*20*140*20

POSEIDON T 400*14*120*20 T 400*14*120*20




As you can see in the table results they do not differ much, with this we can conclude

that with respect to the formulations used in the Matlab, these are indicated for the

analysis of our boat.

In addition, a check is performed on Poseidon of stiffeners obtained by programming

in Matlab, the sky blue indicates that elements approve the scantling:

In annexes (9,13 y 9,14) detailed the stiffeners admitted to the poseidon software and

verification of its approval.

7. ANALISYS RESULTS

Elements are compared, in the bottom of the vessel we have similar results, taking

into account the accuracy of the software may be better in comparison with the




programming in Matlab, in spite of this, the values are very close, with this we can

say that the programming made for the development of the optimization of the ship

can be deployed.

8. REFERENCES

[1] DNV. (2001). Hull Structural Design Ships With Length Less Than 100 metres. 94.

[2] Philippe Rigo, 'A module - oriented tool for optimum design of stiffened structures -Part I',

ANAST, 20013

[3] Christopher, Angel,' Preliminary Design of 2500 Dwt Bulk carrier', ESPOL, 2015

[4] Lloyd, G. (2015). Rules for Classification and Construction. Hamburg: DNV GL SE.

[5] RINA. 1861. Rules for the Classification of Ships. Genova: RINA S.p.A.

[6] Lloyd'sRegister. (2014). Sloshing Loads and Scantling Assessment. Lloyd’s Register

Marine, 110.




9. ANNEX

9.1. Distribution factors for sea loads on ship’s shell and weather decks




9.2. SUBROUTINS PROGRAMMING

9.3. Stability

These features will help to evaluate the stability criteria and in addition to obtain the

acceleration of the roll of the ship.

Curvegz.m

Criterios_estabilidad.m

RollingAceleration.m

9.4. Maneuverability

This function will help us determine the tactical diameter, turning diameter and also

qualify them through ABS formulations.

Maniobrabilidad.m

9.5. Resistance and propulsion y Propulsión

These functions will serve us to from the dimensions of the ship and the propeller

obtain KtKq curves of the same and also with data from selected reducer to obtain the

power that would in fact provide us this prop.

KtKq.m

Estim_propEfic.m (this function determine the best dimensions of the propeller

to minimize the total cost of the propulsion system)

ResisKtKq.m

Resistance84.m

Resistance82.m




9.6. Cost

Function that helps us calculate payment of used working group roles being this

calculation in function of the dimensions and the hh structure of each vessel.

Cost.m

9.7. Man Hours

This function will serve to calculate man hour of each ship according to its

dimensions, thickness of planchaje and curvature.

HHstructure

9.8. Structurecubierta

These functions will allow us to determine dimensions of stiffeners and plates, and

the weight of this, integrating the most restrictions as can it possible.

Pressures

Frequency

Sm (sectional Modules)

9.9. Structuredoublebottom

These functions will allow us to determine dimensions of stiffeners and plates, and

the weight of this, integrating the most restrictions as can it possible.

Pressures

Frequency

Sm (sectional Modules)




9.10. ANEX

RESULT OF STRUCTURECUBIERTA AND STRUCTUREDOUBLEBOTTOM

9.11. ANEX

PROGRAMMING CODE (DECK, BOTTOM, AND SIDE)

9.12. ANEX

Results from POSEIDON of the plate at frame Number 34, evaluating the results from

Matlab

9.13. ANEX

Results from POSEIDON of the longitudinal stiffeners at frame Number 34, evaluating

the results from Matlab

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