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Transcript of 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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 2
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 3
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 4
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.
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 5
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 6
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 7
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.
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 8
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 9
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 10
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 11
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.
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 12
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.
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FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 13
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 14
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.
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 15
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 16
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 17
= (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.
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 18
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]
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FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 19
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 20
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
Escuela Superior Politécnica del Litoral Ship Design II
FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 21
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
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FINAL DESIGN OPTIMIZATION OF 2,500 DWT BULK CARRIER
GROUP 2: STRUCTURAL OPTIMIZATION 22
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
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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
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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.
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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
the preliminary design.
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
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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
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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
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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.
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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
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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
the preliminary design.
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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
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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
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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
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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.
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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:
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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
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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
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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
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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:
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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
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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
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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.
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9. ANNEX
9.1. Distribution factors for sea loads on ship’s shell and weather decks
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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
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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)
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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