LIÊN NGÀNH CƠ KHÍ - ĐỘNG LỰC
63Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020
Strength analysis of oil tanker structure by nonlinear finite
element method
Phân tích sức bền giới hạn kết cấu tàu dầu bằng phương pháp
phần tử hữu hạn phi tuyến
Vu Van Tan
Email: vutannnn@gmail.com
Sao Do University
Date received: 09/7/2020
Date of review: 30/9/2020
Accepted date: 30/9/2020
Abstract
In the ultimate limit state design of ship hulls, the safety and e
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conomy have the most important position
in the whole design of ship structures. In this paper, ultimate strength of ship hull has been calculated by
using the finite-element software. The modeling method which is suitable for ultimate strength calculation
is gained. At the same time, ultimate loading capacity’s variation of series bulk carriers with length is
gained. Finally the effective way of increasing ultimate loading capacity of river-to-sea ships has been
obtained through changing thickness and material properties of key component of ship structure. It
provides references for the design of river-to-sea ships.
Keywords: Ultimate strength; analysis; hull oil tanker; bending mo - ment; ship structure.
Tóm tắt
Trong phân tích sức bền giới hạn kết cấu thân tàu, tính kinh tế và tính an toàn của kết cấu luôn có vai
trò quan trọng trong việc tính toán, thiết kế kết cấu. Trong bài báo này, phần mềm phân tích phần tử
hữu hạn ABAQUS được sử dụng để phân tích, tính toán sức bền giới hạn của kết cấu tàu. Mô hình hóa
kết cấu thân tàu để tính toán sức bền giới của tàu dầu đáy đơn, đồng thời xác định tải trọng giới hạn
của một số con tàu chở dầu với kích thước khác nhau. Kết quả phân tích, tính toán làm cơ sở để đưa
ra giải pháp nâng cao khả nĕng chịu tải của kết cấu thông qua việc thay đổi độ dày và đặc tính vật liệu
của thành phần kết cấu chính của tàu. Kết quả nghiên cứu là tài liệu tham khảo cho việc tính toán, thiết
kế tàu pha sông biển.
Từ khóa: Sức bền giới hạn; phân tích; tàu dầu; mô - men uốn; kết cấu tàu.
transverse ultimate strength and torsional ultimate
strength. The focus of the ultimate strength research
of different ship types is different, but the ultimate
strength of hull girder is usually the longitudinal
ultimate strength.
The ultimate longitudinal strength of a ship
have been traditionally designed to evaluated
by comparing the maximum stress of the cross
section of the hull under the action of the vertical
composite bending mo - ment with the allowable
stress value. Its essence is based on the linear
theory of elasticity.
Caculation and analysis of ultimate strength of ship
hull is an important part of ship structure design.
The ship hull is the typical thin-walled structure
which consists of stiffened plates, box girder and
1. INTRODUCTION
Ultimate strength analysis of ship structure is
based on is the classical theory of elasticity for a
long time. But with the analysis method improved,
people are beginning to realize that the influence
of buckling, yield and post-buckling of component
must be considered. There are four main methods:
nonlinear finite element method, direct calculation
method ideal, structure element method, gradually
failure analysis method.
The ultimate strength of ship hull can be broadly
divided into longitudinal ultimate strength,
Reviewers: 1. Assoc. Prof. Dr. Phan Anh Tuan
2. Dr. Ngo Huu Manh
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transvered stiffened web frames. The ultimate
strength of the ship hull depends on these structure
member. The ship hull structure is very complicated
three-dimensional thin-wallstructure. In analysis
and design of ship structure, the ultimate strength
analysis is an essential stage, which usually gives
an assessment result of the structural safety
condition [1].
Paik et al (2009 and 2010) [2, 3] used nonlinear
finite element to calculate ultimate strength of
plate structure and stiffened-plate under the effect
of vertical pressure. The research object is outer
bottom plate and stiffened-plate structures of
100,000 ton.
Paik [4] et al. Study characteristics of buckling
and ultimate strength of plate sttructure under
bending mo - ment and combined loads. Paik [5]
et al. also studied the elastic buckling of simply
supported plates, studied considered the influence
of residual stress on the elastic buckling of the
plate under the combined action of shear stress,
biaxial compressive stress and lateral compressive
stress. Come up with a formula for elastic buckling
equation of simply supported plate.
Yao [6] calculated the buckling and ultimate
strength of the plate under uniaxial compressive
stress, considered the influence of welding residual
stress and initial deformation.
Nishiliara [7], Shi GuiJie [8], Van Tan Vu [9] built up
four box girder model: single bottom tanker, double
bottom tanker, bulk carrier, container carrier.
Author conducted longitudinal bending tests
and calculations on a series of steel box girder,
and obtained the relationship of ultimate bearing
capacity under different scale ratios.
In this paper uses the universal finite element
software ABAQUS as the calculation tool to
calculate the ultimate strength of a single-hull oil
tanker, and compares it with the literature value
to verify the effectiveness of the software and the
parameter settings that should be paid attention
to when calculating. The bulk carrier performs
ultimate strength calculation to predict the ultimate
bearing capacity of the hull girder under two
dangerous conditions: sagging bending mo - ment
and hogging bending mo - ment.
2. CALCULATION OF ULTIMATE LONGITUDINAL
STRENGTH OF SHIP HULL GIRDER
2.1. Geometric and material properties
In this paper, a single hull oil tanker (Fig 1) will be
taken as the calculation object for research.
Fig 1. Mid-ship section of bulk carrier
The dimension and material properties of open box
girder model are shown in Table 1.
Table 1. Dimensions and material properties of
the model
No Dimension (mm) Type sy(MPa)
1 480×32 flat steel 313,6
2 797×15+200×33 T 313,6
3 447×11,5+125×22 T 313,6
4 549×11,5+125×22 angle bar 235,2
5 597×11,5+125×22 angle bar 235,2
6 597×11,5+125×22 angle bar 235,2
7 647×11,5+125×22 angle bar 235,2
8 350×25,4 angle bar 235,2
9 646×12,7+150×25 angle bar 235,2
10 697×12,7+150×25 angle bar 235,2
11 747×127+150×25 angle bar 313,6
12 747×12,7+180×25 angle bar 235,2
13 797×14+180×25 T 235,2
14 847×14+180×25 angle bar 313,6
15 847×14+180×32 T 235,2
16 847×15+180×25 angle bar 313,6
17 847×15+200×25 angle bar 313,6
18 897×15+200×25 angle bar 253,2
19 945×16+200×25 angle bar 235,2
20 897×15+200×25 angle bar 313,6
21 797×15+180×25 angle bar 313,6
22 347×11,5+125×22 angle bar 313,6
23 300×11,5+100×16 angle bar 313,6
24 397×25 angle bar 313,6
25 300×11,5+100×16 angle bar 313,6
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65Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020
No Dimension (mm) Type sy(MPa)
26 370×16 angle bar 313,6
27 230×12,7 angle bar 235,2
28 230×12,7 angle bar 235,2
29 300×25 angle bar 253,2
30 425×25 angle bar 313,6
31 370×16 angle bar 313,6
32 397×11,5+100×25 T 313,6
Yield stress of the material: s = 313,6 N/mm2.
Young’ smodulus: E = 2,1e5N/mm2.
Poisson’s ratio g = 0,3.
2.2. Selection of model
This paper calculate the ultimate strength bending
mo - ment of a series of ships hull structure. The
hull structure is extremely complicated. Therefore,
it is necessary to use a simplified and effective
model when performing ultimate strength analysis.
This studying assumes that the laterally strong
bones of the hull are strong enough so that the
overall damage of the plate frame will not occur.
Therefore, it is necessary to use a simplified and
effective model when performing ultimate strength
analysis. This studying assumes that the laterally
strong bones of the hull are strong enough so
that the overall damage of the plate frame will not
occur. The hull plates and longitudinal frames are
modeled by plate elements.
2.3. Nonlinear finite element mesh modeling
The quality of mesh size division is an important
step to ensure the ultimate strength calculation
results. The mesh size form is directly related to
the accuracy of the calculation and the calculation
time. The mesh density in a finite element model
is an important topic because of its relationship to
accuracy. Generally, the denser mesh size is, the
closer the calculation result is to the true value,
but the calculation time is also rapidly increasing.
Therefore, it is particularly important to adopt
reasonable element division when calculating the
ultimate strength of ship girder.
In order to investigate the influence of element grid
division on the ultimate strength of ship structure.
This paper divides the finite element model into
three models for different element densities (one
frame spacing, 1/2 frame spacing, 1/4 frame
spacing, each limited. The element model is shown
in Fig 2, Fig 3, Fig 4. The effect of mesh density on
the ultimate strength of the actual ship are 23.268
element, 22.074 element, and 22.068.
From this mesh density, it can be seen that the
refinement from one one frame spacing to 1/2
frame spacing reduce significantly the calculation
value of the limit bending mo - ment. When refined
to 1/4 frame spacing, the calculated value of the
ultimate bending mo - ment changes very little,
but the time consumed in the calculation is greatly
increased. Therefore, when the mesh density
of the calculation model is relatively loose, the
dense mesh can indeed be effective improve the
calculation accuracy. But when the mesh is dense
enough, continuing to refine the model mesh has
little effect on the calculation results, and will cause
unnecessary increase in computer time.
Fig 2. Finite element model for one frame spacing model
Fig 3. Finite element model for 1/2 frame spacing model
Fig 4. Finite element model for 1/4 frame spacing model
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2.4. Boundary conditions
Boundary conditions also have an impact on the
calculation results of ultimate strength. In this
section use the multi-point constraint (MPC)
function provided in of the finite element model for
boundary conditions [8, 9]. Assume that the rigid end
face rotates around the neutral axis, and gradually
increase the bending mo - ment value; apply a rigid
fixed .There are two different boundary conditions
for simply supported: (1) Simply supported, all
nodes on the end face restrain the displacement
of the ship in the length direction Uz= 0, the depth displacement Uy = 0 of the node restraint on the upper and lower slabs, and the node restrains the
ship on the side slab Displacement in the width
direction Ux = 0; (2) Rigidly fixed, constraining 6 degrees of freedom of all nodes on the end face.
3. CALCULATION RESULT OF A SERIES OF
REAL SHIP MODELS
This paper, ABAQUS software was usedfor ultimate
strength alanysis of bulk carrier structure.
3.1. Analysis of a 80 m bulk carrier
The mid-ship section structure are shown in Fig
5. The frame spacing is 2.800 mm, the Young’s
modulus is E = 2,1×105N/mm2, and the Poisson’s
ratio: g = 0,3.
Fig.5. Mid – ship section of 80 m bulk carrier
Table 2. Dimensions and material characteristics of
80 m bulk carrier structure
No Dimension
(mm) Type
s
(MPa)
1 140×90×12 angle bar 235,2
2 125×80×12 angle bar 235,2
3 160×100×12 angle bar 235,2
4 100×63×7 angle bar 235,2
5 125×80×10 angle bar 235,2
6 180×10 angle bar 235,2
The finite element model of an 80 m bulk carrier is
shown in Fig 6. The calculation results of the ultimate
bending mo - ment are as follows: Fig 7 shows the
sagging bending mo - ment - deformation (rotation
angle) curve in the model. The calculated ultimate
bending mo - ment value of the middle arch is 2,8
× 1011N.mm; Fig 8 shows the hogging bending mo
- ment - deformation (rotation angle) curve of the
model. The calculated of ultimate bending mo -
ment value is 2,44 × 1011N.mm.
Fig 6. Finite element model of 80 m bulk carrier
Fig.7. Sagging bending mo - ment-deformation curve
Fig 8. Hogging bending mo - ment - deformation curve
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67Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020
3.2. Analysis of 110m bulk carrier
Fig 9. Mid – ship section of 110 m bulk carrier
Table 3. Dimensions and material characteristics of
110 m bulk carrier structure
No Dimension (mm) Type s(MPa)
1 160×100×12 angle bar 235,2
2 140×90×14 angle bar 235,2
3 180×110×14 angle bar 235,2
4 110×70×7 angle bar 235,2
5 140×90×12 angle bar 235,2
6 180×10 angle bar 235,2
The finite element model of an 80 m bulk carrier
is shown in Fig 10. The calculation results of the
ultimate bending mo-ment are as follows: Fig 11
shows the sagging bending mo - ment-deformation
(rotation angle) curve in the model. The calculated
ultimate bending mo-ment value of the middle arch
is 5,32 × 1011N.mm; Fig 12 shows the hogging
bending mo-ment-deformation (rotation angle)
curve of the model. The calculated of ultimate
bending mo-ment value is 5,03 × 1011N.mm.
Fig.10. Finite element model of 110 m bulk carrier
Fig 11. Sagging bending mo-ment-deformation curve
Fig 12. Hogging bending mo-ment-deformation curve
3.3. Analysis of 140 m bulk carrier
Fig 13. Mid – ship section of 140 m bulk carrier
Table 4. Dimensions and material characteristics of
140 m bulk carrier structure
No Dimension (mm) Type s(MPa)
1 160×100×16 angle bar 235,2
2 160×100×14 angle bar 235,2
3 200×125×14 angle bar 235,2
4 110×70×10 angle bar 235,2
5 160×100×12 angle bar 235,2
6 180×10 angle bar 235,2
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The finite element model of an 140 m bulk carrier
is shown in Fig 14. The calculation results of the
ultimate bending mo-ment are as follows: Fig 15
shows the sagging bending mo-ment-deformation
(rotation angle) curve in the model. The calculated
ultimate bending mo-ment value of the middle
arch is 1,06×1012N.mm; Fig 16 shows the hogging
bending mo-ment-deformation (rotation angle)
curve of the model. The calculated of ultimate
bending mo-ment value is 9,55×1011N.mm.
Fig 14. Finite element model of 140 m bulk carrier
Fig 15. Sagging bending mo-ment-deformation curve
Fig 16. Hogging bending mo-ment-deformation curve
Table 5. Relation between the ultimate strength and
ship length (×1011N.mm)
Ultimate strength status 80 m 110 m 140 m
Sagging bending
mo-ment 2,44 5,03 9,55
Hogging bending
mo-ment 2,8 5,32 10,6
4. CONCLUSION
This paper used the finite element software
ABAQUS as the calculation tool to calculate the
ultimate strength of a single-hull oil tanker, and
compares it with the literature values. The effect
of meshing density, boundary conditions, and
initial loading ratio coefficients on the hull girder
were analysed. In addition, the ultimate strength
calculation of a series of bulk carriers is carried,
and the ultimate load-bearing capacity of the hull
girder under two dangerous conditions of sagging
and hogging bending mo-ment.
The ultimate strength calculation of a series
of hull oil tanker structure were analysed, The
ultimate strength of the hull girder under two
dangerous conditions of sagging bending mo-
men-deformation, and hogging bending mo-men-
deformation were analysed. The ultimate strength
calculation show that, the ultimate bending mo-
men increases with the increase of the ship length,
and the ultimate bending mo-ment of the middle
arch is always greater than the ultimate sagging
mo-ment. When the length of the ship is less than
110 m, the ultimate bending mo-ment increases
with the length of the ship. The relationship is linear.
When the length of the ship is greater than 110 m,
the growth rate of the limit bending mo-ment was
obviously accelerated.
REFERENCES
[1] IACS (2012), Common Structure Rules for Bulk
Carriers [S].
[2] Paik J K, Seo J K (2009), Nonlinear finite
element method models for ultimate strength
analysis of steel stiffened-plate structures
under combined biaxial compression and lateral
pressure actions - Part I: Plate elements[J], thin-
Walled Structures, 47: 1008-1017.
[3] JeomKee Paik (2010), Large deflection behavior
and ultimate strength of stiffened panels [C],
The Society of Naval Architects and Marine
Engineers.
LIÊN NGÀNH CƠ KHÍ - ĐỘNG LỰC
69Tạp chí Nghiên cứu khoa học, Trường Đại học Sao Đỏ, ISSN 1859-4190, Số 3 (70) 2020
[4] JeomKee Paik, Bong Ju Kim, Jung Kwan
Seo (2008), Methods for ultimate limit state
assessment of ships and ship-shaped offshore
structures: Part I—Unstiffened plates [J], Ocean
Engineering, 35: 261–270.
[5] JeomKee Paik, Bong Ju Kim, Jung Kwan
Seo (2008), Methods for ultimate limit state
assessment of ships and ship-shaped offshore
structures: Part II stiffened panels [J], Ocean
Engineering, 35: 271–280.
[6] Yao T, Fujikubo M, Yanagihara D, et al (1998),
Influence of welding imperfections on buckling/
ultimate strength of ship bottom plate subjected
to combined biaxial thrust and lateral pressure
[A], Thin-Walled Structures, Research and
Development, 2nd International Conference
on Thin-walled Structures, 425- 432.
[7] Nishihara S (1984), Ultimate Longitudinal
Strength of Midship Cross Section. Naval Arvh.
And Ocean Engine, (22), 200-214.
[8] Shi Gui-jie, Wang De-yu (2012), Residual
ultimate strength of open box girders with
cracked damage [J], Ocean Engineering, 43:
90–101.
[9] Van Tan Vu, Wei Guo Wu (2014), Nonlinear
Finite Element Method Ultimate Strength
Analysis of Open Box Girders, International
journal of advanced materials research, Vol
919, PP:177-182.
Vu Van Tan
- Training and research process:
Dr Vu Van Tan is a Dean of Mechanical Engineering Department, Sao Do University,
Hai Duong, Vietnam. He studied doctoral courses at School of Transportation,
Wuhan University of Technology, Wuhan, Hubei, China. He is doing research in
Ship structural analysis and design.
- Mobile phone: 0911.422.658
- Email: vutannnn@gmail.com
AUTHORS BIOGRAPHY
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