An Investigation of Ultimate Strength for VLOC Stiffened Panel Structures

7/29/2019 An Investigation of Ultimate Strength for VLOC Stiffened Panel Structures

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Modern Transportation

June 2013, Volume 2, Issue 2, PP.23-38

An Investigation of Ultimate Strength for VLOC

Stiffened Panel StructuresHung Chien Do1, 2#, Wei Jiang1#, Jianxin Jin1, Xuedong Chen11. State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology,

Wuhan, 430074, China.

#Email: [email protected]

2. Faculty of Naval Architecture, Ho Chi Minh City University of Transport, Ho Chi Minh city, 70000, Vietnam.

#Email: [email protected]

Abstract

Ultimate strength of ship and offshore structures is a very important issue that has drawn considerable attention from researchers,

especially in the field of structural analysis applied to ship offshore, aircrafts, and base landings, etc. Finite Element Method

(FEM) has been applied and developed to solve the complicated problem accurately. Particularly, with the help of aid tool and

software, as well as Nonlinear Finite Element Method (NFEM), the ultimate strength of large model is improved significantly and

accurately. The aim of this paper is to investigate the ultimate stiffened panel strength in the cargo hold areas for a very larger ore

carrier built in China. The stiffened panel in the bottom, side and deck structures is a structural member which basically plays an

important role in construction of ship and offshore.

Keywords: Ultimate strength; Very Large Ore Carrier; compressive load; lateral pressure; stiffened panel.

1 INTRODUCTIONAs marine nowadays has been developed quickly and has become the key industry with many ships built year by

year in the world. Under the effect of global energy crisis, there have had many studies on the design of a new type

of vessel. The market of shipping is very large thanks to the lowest cost in terms of logistics. In China, with the rapid

development of economic, iron ore is necessary, and thus, carrier industry has been propelled to meet the huge

shipping. As a result, a very large number of ore carriers have been built to import ore from foreign countries.

However, the ships are designed by means of traditional method known as approaching margin working stress.

Recently, ship and offshore structures have been performed by nonlinear finite element analysis with a large number

of literatures concerning ultimate strength, ultimate limit state (ULS) aspects. These studies have been utilized in

plates, stiffened plates and three cargo holds in mid-ship areas(Amlashi and Moan 2009). Estimating the ultimate

strength of continuous plates are studied and developed by a simplified method which proposes formulae withaccurate predictions (Fujikubo, Yao, et al. 2005) on ultimate strength compared to NFEM results. Assessment on

ultimate strength for unstiffened plates surrounded by supporting members under combined uniaxial/biaxial

compressive loads and lateral pressures has been performed based on a series of benchmark studies on the

methods(Paik, Kim, and Seo 2008a). The rectangular plates under biaxial loadings also study the Elasto-plastic

buckling behavior (Wang et al. 2009). The one-bay plate models from the 1/2 + 1 + 1/2 bay continuous plate is

investigated by (Paik and Seo 2009a, b)to reveal the fact that the ultimate strength of unstiffened plate under biaxial

compressive loads is significantly influenced by rotational restrain under lateral pressure actions. A new method to

analyze the geometric nonlinear behavior of plates is developed by (Kee Paik et al. 2012), in which elastic large

deflection or post-buckling of plates with partially restraint rotation and the torsional rigidity condition are applied.

Regarding the stiffened panel assessment, the results are obtained in order to continuously develop improved

methods for prediction ultimate strength with accuracy and efficiency. To estimate the ultimate strength, there are


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some direct methods proposed by (Caldwell 1965, Mansour et al. 2008) and after simplified method (Smiths

method and the idealized structural unit method ISUM) is widely applied for analysis of hull girder under

longitudinal bending loads only. By applying the mentioned methods to analysis, the results are rapidly obtained, but

the accuracy depends on the average stress-strain relationship of individual structural members. The simplified

method is developed (Yao 2003)for evaluation of the collapse strength for hatch covers with a folding type and a

side sliding type of bulk carrier. (Paik, Kim, and Seo 2008b, c) performed ALPS/ULSAP method to determine the

ultimate limit state of stiffened panel under uniaxial or biaxial compression and lateral pressures, the results are

compared to ANSYS nonlinear finite element analysis(Inc. 2010).Related to the parameter effects on the collapse

behavior of stiffened panels, shaped model in study with two (1 + 1) full bays was studied by FEM. In addition to the

ultimate strength of plates, by means of nonlinear FE software to analyze two half bays plus one full bay (1/2 + 1 +

1/2 bay) model in the longitudinal direction by (Zhang and Khan 2009, Fujikubo, Harada, et al. 2005). A method for

ultimate assessment via nonlinear finite element analysis is developed by (Paik and Seo 2009a, b). The influence of

the stiffeners geometry and boundary conditions on the ultimate strength of stiffened panels under combined thrust

acting load including 3 bays, 1/2 + 1 + 1/2 bays, 1 + 1 bays and 1 bay, are analyzed by (Xu and Guedes Soares 2012).

In scope of this paper, we consider the difference of ultimate strength results between two half bays plus one full bay

(1/2 + 1 + 1/2 bays) models under various parameters. In actual structures, a stiffened panel often includes plates,

stiffeners, longitudinal girders and transverse floors. The model including 27 longitudinal stiffeners can be translated

into 2 bays + 1 span (2B1S), 2 bays + 2 spans (2B2S), 2 bay + 3 spans (2B3S), 3 bays + 1 span (3B1S), 3 bays + 2

spans (3B2S) and 3 bays + 3 spans (3B3S) models. They are under uniaxial and biaxial compressive acting load with

or without lateral pressure, satisfying simple supported boundary condition.

The aim of this study is to improve the economic efficiency in ship design and construction technology, the reducing

ship hull structural weight is taken into account. The plates and stiffened panel are basic assembly structures in a

ship. They are found in the deck, side and bottom structures, and even appear in the superstructures. In order to solve

this problem, a hypothetical ship is studied and focused on the plates and stiffened panels in the cargo hold area (Do,

Jiang, and Jin 2012). In this paper, the ultimate strength of the very large ore carrier is investigated with rectangular

plates and stiffened panel object ship. By applying International Associate Classification Societies Common

Structural Rules (IACS CSR) to bulk carrier class type and NFEM, the stiffened panel and plate models are designedand analyzed, in order to choose models complying with actual requirements (IACS 2006a, b).

2 ULTIMATE STRENGTH OF HYPOTHETICAL MODELShip bottom stiffened panel is subjected to combined biaxial compressive load and lateral pressure. Generally, the

thickness of plate, the properties of stiffeners as well as longitudinal girder and transverse floor are determined by

designer throughout Common Structure Rules. In this study, these particulars are applied in a hypothetical of very

Large Ore Carrier (VLOC) built in China with deadweight of about 380,000 DWT, and known as the largest Bulk

Carrier class; amid ship section and a cross sectional stiffener are shown in Fig. 1. The material, high tensile AH 36,

is used for ship both of plating and component of structures, whose properties: Yield stress with 355Y

MPa;

Youngs modulus with E = 205.8 GPa and Poissons ratio 0.3

, are taken into account in ANSYS NFEM.Choosing plating and stiffened panel structures in the bottom of cargo hold is conveniently ultimate strength analysis

because the structural shaped is hardly to be changed in three dimensions. This candidate method complies with

requirement and guider of IACS CSR system.

TABLE 1 GEOMETRIC PROPERTY OF THE STIFFENED PANELS

Model a mm b mm ns tpmm hwmm twmm bfmm tfmm

2B1S / 3B1S 3660 915 4 21.80 470 10 162 16

2B2S / 3B2S 3660 915 8 21.80 470 10 162 16

2B3S / 3B3S 3660 915 12 21.80 470 10 162 16

Note: B = bay and S = span, i.e. 2B1S = 2-bay 1-span model


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2.1 Numerical model f or analysis

In the cargo hold of object ship of our study, the structures can be summarized as follows:

The bottom with double hull structures including outer bottom and inner bottom, stiffeners along longitudinaledges, the distance of two stiffeners close to each other is b, similarly, the distance of two transverse floors is a .

The length of 2-bay and 3-bay panels is 2a and 3a, respectively (a and b are shown in Table 1).

In the port and starboard side, structural system is single hull with the adoption of transverse frame system. On the deck, the longitudinal structural system and single deck are used with longitudinal stiffeners, girders and

transverse frames.

Inner bottom stiffened panels

Deck stiffened panels

Side plating

Outer bottom stiffened panels

FIG. 1STIFFENED PANELS IN THE MIDSHIP FIG. 2PLATESTIFFENER AND STIFFENED PANEL

The procedure to determine the properties of plating and stiffened panel plate thickness can be specified into two

steps. Firstly, by using the formula of CSR, the thickness of plates and the particular of stiffeners in case of mild

steel are calculated. Secondly, the correction formulae are used to accurately determine the principal dimension for

high tensile steel. In ship structural design, plate and stiffeners frequently welded to each other are seen as

combination structures which are called continuous stiffened plate structure in Fig. 2(a) and plate-stiffener

combination model in Fig. 2(b). The particulars of stiffened panel cross section are described in Table 1/Fig. 1, these

models have the same dimensions of cross sectional stiffener (hw and twis the height and thickness of web plates, bf

and tf is the breadth and thickness of flange plates, respectively) and tp is thickness of plate, and the differences

between six models are the number of stiffeners ns (ns = 4, 8, 12 stiffeners), longitudinal girders and transverse floors.

The principal parameters affect ultimate strength of plate and stiffened panels under compressive load are the plating

and beam-column slenderness, defined as follows(Hughes, Paik, and Bghin 2010): the slenderness of plating,

Yp

p

b

t E

(1)

Where, tp is the thickness of bottom plate and Yp is the yielding stress of plates; and there is a difference between

Yp and Y when the plate and the stiffeners are not made of unique type of material. In this study, the plating and

the stiffeners are assumed to be made of same material type that means 355Yp Y MPa. The column

slenderness:

Ya

r E

(2)

Where, ris the radius of inertia defined as follows,

s

I

r A (3)


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I andAsare the inertial moment and area, respectively, of cross-section including effective width p.

The effective width of plating element is defined:

2

2 1p

(4)

2.2In iti al imperf ection

The initial imperfection of plate in the form of initial deflections and residual stress is caused by welding during a

complex fabrication process and they are subjected to significant uncertainty related to the magnitude and spatial

variation. These initial imperfections are the important parts of the ultimate strength assessment accurately because

they reduce the strength performance and in calculating, they should be a significantly influential parameter. Many

literatures throughout theories as conducted Fourier analysis and measurements were performed at several point of

plate, and provided a total description analysis of the deformed surface of plate. The initial distortions of the

stiffeners are specified into two types depending on the direction of deflection such as y direction orzdirection.

Concerning a column type, the former of initial distortion follows the high direction of stiffeners and then other type

corresponding to a torsional initial distortion along sideways. In this paper, an equivalent initial imperfection is

applied as initial distortion of the stiffened panels, as follows(Hughes, Paik, and Bghin 2010):

The local panel with initial deflection:

0sin sinpl pl

m y yw w

a b

(5)

Where, 20 0.05pl pw t and m , the number of half buckling waves, dependent on ratio of a/b, generally, is equal to

a/b, but ifm is not an integer, it should be determined as a minimum integer which satisfies a condition as follows,

1a

m mb

(6)

The initial deflection of stiffeners as column type is:

0sin

c c

xw w

a

(7)

The initial deflection of stiffeners depends on angular rotation about panel-stiffener in the side-ways:

0sin

s s

xw w

a

(8)

Where, w0c = w0s = a/1000 in (7)and(8).

Lateral pressure pLongitudinalstiffeners

Transv

ersefloo

rs

x

y

z

a/2

a/2

a

B

A

C

A

C

b bBottom plate

T type Longitudinal stiffeners

x

y

y

x

FIG.3NUMERICAL OF STIFFENED PANEL FIG.4 STIFFENED PANEL UNDER COMBINED LOADS

In finite element analysis (FEA), the initial imperfections are firstly calculated by formulae (5), (7) and (8), and after

that the shapes of initial imperfections for each model are applied by ANSYS program design language (APDL).

Actually, the evaluation of the ultimate strength is usually calculated in two steps:


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Step 1: Determining the first eigenvalue mode of buckling cause axial compressive load with linear analysis. When

this step is completed, the initial imperfection is applied to the plate, column-type and side-way of stiffeners. In this

step, the parameter of initial deflection formula in ANSYS depends on the result of first buckling linear analysis.

Step 2: After applying the initial imperfection completely to models (in this step, UPGEOM function is applied), the

ultimate strength of numerical model is nonlinearly analyzed.

Hence, for convenient investigation, the effects of the boundary on the ultimate strength, the equivalent initial

imperfections of the numerical model in the present paper are assumed as follows:

Plate initial deflection wopl= b/200, the initial imperfection magnitude of local shaped plate. Column-type initial deflection woc = a/1000, the initial imperfection magnitude of the stiffeners. Side-ways initial deflection wos = a/1000, the initial imperfection magnitude of the stiffeners.The numerical models built including the geometric and material nonlinearities, elasticplastic large deflection are

taken into account. During the linear as well as nonlinear analysis, the SHELL 181 element of ANSYS is used in the

numerical model in Fig. 3, which is a four nodes element with six degrees of freedom at each node and can account

for linear, large rotation and large strain nonlinear.

2.3 Boundary condition

Generally, the stiffened panels are supported on the stronger member, and two types of boundary condition are

frequently applied, namely simple supported and clamped. In the longitudinal structure system under combined axial

compressive loads, when the acting load in the longitudinal edges is predominant, the effect of these two conditions

is negligible as results of ultimate strength. When transvers axial compressive loads are predominant, the effect of

boundary condition in the direction of longitudinal edges is significant. In scope of this study, for convenient

calculation, the simply supported is adopted, with the 1/2 + 1 + 1/2 model of stiffened panels, including the numbers

of 27 stiffeners and 2 bays as transverse floors in Fig.4. The parameters of this simple supported boundary condition

are described as follows(Paik, Kim, and Seo 2008b),

Along AA and CC edges, the symmetric condition is applied withROTY=ROTZ= 0, all nodes and stiffenersnodes having an equal displacement in thex direction;

Along AC and AC, the simply supported boundary condition is applied with UZ= 0 andROTY=ROTZ= 0,including an equal displacement in they direction for each edge;

Along the transverse floors (T1T1, T2T2 in Fig. 5 and T1T1, T2T2, T3T3 in Fig. 6), the boundarycondition is applied such that UZ= 0 for plate nodes, and UY= 0 for nodes of stiffener webs;

Along the longitudinal girder (L1L1, L2L2, L3L3 in Fig. 5 and Fig. 6) with UZ = 0 for plate nodes.

A

A

C

C

T1'

T2'

T1

T2

L1

L2

L3

L1'

L2'

L3'

A

A

C

C

T1'

T2'

T1

T2

T3

T3

L1

L2

L3

L1'

L2'

L3'

FIG.52 BAYS + 3 SPANS PANEL MODEL FIG.63 BAYS + 3 SPANS PANEL MODEL

Where UX, UY, and UZ are translation constraints in the x coordinate, y coordinate and z coordinate,respectively; similarly, ROTX, ROTY and ROTZ indicate rotational constraint around the x coordinate, y


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coordinate andzcoordinate, respectively.

It is noticed that the boundary condition for 2 bays + 1 span and 2 bays + 2 spans is similarly applied to the case of 2

bays + 3 spans when 2 spans (L2L2 and L3L3) or 1 span (L3L3) is excluded. In addition, the boundary condition

for 3 bays + 1 span and 3bays + 2 spans is applied to similar boundary condition of 3 bays + 3 spans in Fig. 6.

The definition and application of boundary condition are the important parts in computation as well as assessment of

collapse state behavior.

2.4 Load conditi on

In this paper, numerical models are applied to compressive load as following procedure,

Case 1: Acting the uniaxial compressive along edges in the x coordinate (i.e. model under uniaxial x without

lateral pressurep).

Case 2: Acting lateral pressure included compressive load in Case 1 (i.e. model under uniaxial x with lateral

pressurep).

Case 3: Acting the biaxial compressive along edges in the xcoordinate andy coordinate (i.e. model under biaxial

with ratio of : 0.8: 0.2x y , without lateral pressurep).

Case 4: Acting lateral pressure included compressive load in Case 3 (i.e. model under biaxial with ratio of

: 0.8: 0.2x y , without lateral pressurep).

The ratios of :x y (including 1.0:0.0, 0.9:0.1, 0.8:0.2, 0.7:0.3, 0.6:0.4, 0.5:0.5, 0.4:0.6, 0.3:0.7, 0.2:0.8, 0.1:0.9,

and 0.0:1.0) are used in the design hull girder loading condition of the object ship. The lateral pressure p is

determined by loading condition in operational assumption. In the full load condition, the hydro static pressure

presses on outer bottom with the extreme magnitude, p = 0.23 MPa. Combined load conditions in this study are

shown in Fig. 4.

2.5 Mesh model

In evaluation of ultimate strength, the number of finite elements for rapidly and accurately obtained results can be

determined especially using FEM and mesh is the computation strategy. Concerning mesh and elements are divided

in the models(ISSC 2009, 2012), for the bottom plates in Fig. 4, the number of rectangular plateshell elements

along the breadth direction b and the length direction a are 6 and 20, respectively. In Fig. 5 and Fig. 6, for the

stiffener web in the height direction and the flange in the breadth direction, the number of plate-shell elements is 4

and 2, respectively.

3 RESULT AND DISCUSSIONS3.1 Ul timate strength of 2 bay sti f fened panel model

In this section, there are three considered model such as 2 bays + 1 span (1/2+1/2 span) 2B1S, 2 bays + 2 spans(1/2 + 1 +1/2 span) 2B2S and 2 bays + 3 spans (1/2 +1+1+1/2span)2B3S. The results obtain from ANSYS are

shown in Fig. 25, Fig. 27 and Fig. 29. They are under longitudinal and transverse compressive load with effect of

lateral pressures defined by full load condition of VLOC.

1) Ultimate strength of 2-bay stiffened panel without lateral pressureThese collections of ultimate strength results are described in the Table2, in order to evaluate the difference of the

results obtained from models, and a coefficient of variation (COV %) also known as relative variability, is equal to

the standard deviation of a distribution divided by its mean which is included. When longitudinal compressive load

is predominant : 1.0 :0.0, : 0.9 : 0.1x y x y and : 0.8: 0.2x y ), the ratio of longitudinal ultimate

strength (LUS) and yielding stress /xu Y (in the x direction) with the acquired appropriate COV is very small

(0.01%, 0.02% and 1.43%). While the difference of transverse ultimate strength (TUS) from these cases issignificant (i.e. COV = 27.73%, 21.16% and 7.90%). In case of predominant transverse compressive load


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( : 0.0 :1.0, : 0.1: 0.9x y x y and : 0.2 : 0.8x y ), the values of COV are insignificant, and the

maximum of COV is 6.42%. It is clear that the applied method complies with the case of the predominant

longitudinal and transverse compressive load.

TABLE 2 ULTIMATE STRENGTH OF 2-BAY PANELS

Case of calculation

Without lateral pressure (p = 0) With lateral pressure (p = 0.23 MPa)

2B1S 2B2S 2B3S COV 2B1S 2B2S 2B3S COV

: 1.0 :0.0x y

/xu Y

0.7474 0.7475 0.7475 0.01% 0.6528 0.6530 0.6530 0.01%

/yu Y

0.0429 0.0747 0.0715 27.73% 0.4560 0.4612 0.5095 6.21%

: 0.9 : 0.1x y

/xu Y

0.7498 0.7500 0.7502 0.02% 0.6160 0.6076 0.6076 0.80%

/yu Y

0.1539 0.1064 0.1110 21.16% 0.5512 0.6469 0.6434 8.84%

: 0.8:0.2x y

/xu Y

0.7246 0.7446 0.7403 1.43% 0.4453 0.4913 0.4907 5.55%

/yu Y

0.1332 0.1485 0.1557 7.90% 0.7041 0.6493 0.6514 4.65%

: 0.7 : 0.3x y

/xu Y

0.6804 0.5049 0.6727 16.01% 0.4706 0.4131 0.4157 7.49%

/yu Y

0.6680 0.3444 0.5353 31.53% 0.3827 0.4362 0.4393 7.59%

: 0.6 :0.4x y

/xu Y

0.5755 0.2675 0.5500 36.81% 0.2065 0.2695 0.2105 15.42%

/yu Y

0.7011 0.3337 0.6043 34.85% 0.4479 0.3645 0.4430 11.19%

: 0.5:0.5x y

/xu Y

0.4594 0.1332 0.4334 53.02% 0.1306 0.1565 0.1147 15.74%

/yu Y

0.7042 0.3917 0.6503 28.71% 0.3811 0.3198 0.4346 15.18%

: 0.4 :0.6x y

/xu Y

0.3570 0.0545 0.3365 67.81% 0.0608 0.0890 0.0654 21.10%

/yu Y

0.6887 0.4845 0.6546 17.95% 0.3375 0.2031 0.3281 25.90%

: 0.3:0.7x y

/xu Y

0.3007 0.1329 0.3090 40.14% 0.0198 0.0147 0.0398 53.61%

/yu Y

0.6954 0.5879 0.7020 9.68% 0.4004 0.3883 0.4886 12.86%

: 0.2 :0.8x y

/xu Y

0.1705 0.1720 0.1910 6.42% 0.0781 0.0679 0.0254 48.92%

/yu Y

0.5494 0.5637 0.6150 5.98% 0.4565 0.4215 0.2431 30.62%

: 0.1: 0.9x y

/xu Y

0.1574 0.1659 0.1661 3.04% 0.0993 0.1070 0.1075 4.43%

/yu Y

0.3592 0.3926 0.3937 5.13% 0.3997 0.4417 0.4432 5.77%

: 0.0 :1.0x y

/xu Y

0.1692 0.1765 0.1793 2.99% 0.1449 0.1411 0.1149 12.21%

/yu Y

0.2895 0.3180 0.3275 6.35% 0.4785 0.4699 0.3556 15.78%

In the contrast to compare these cases (in case of : 0.7 :0.3, : 0.6 :0.4, : 0.5: 0.5,x y x y x y

: 0.4 :0.6 and : 0.3:0.7x y x y ), the difference of ultimate strength in both of xdirection and ydirection

is significant. However, the distinction between results of 2B1S and 2B3S is very small, while the results derived

from 2B2S are smaller than that from other two models (2B1S and 2B3S). According to the analysis of these modelsand application cases, when computing the ultimate strength of stiffened panel without lateral pressure, the reliable

of result from 3 models can be obtained as the longitudinal or transverse compression is predominant, in other cases

of load acting, the 2B1S and 2B3S models derived result with insignificant difference. Meanwhile, if the 2B2S

model is used, it must be carefully considered.

The series of results obtain from 3 models 2B1S in case of under compressive load without lateral such as 2 bay + 1

span (1/2 +1/2 span)2B1S, 2 bay + 2 span (1/2 + 1 +1/2 span)2B2S and 2 bay + 3 span (1/2 +1+1+1/2 span)

2B3S are shown in Fig. 7, Fig. 9, and Fig. 11(describing the relation of STRAIN and /xu Y Ultimate strength

alongxdirection), in Fig. 8, Fig. 10 and Fig. 12 in which STRAIN and /yu Y are explained.

2) Ultimate strength of 2-bay stiffened panel with lateral pressureIn case of 2 bays stiffened panel without lateral pressure, the ultimate strength is obtained from three model methods,


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and the variability of these results can be accepted when the predominant of longitudinal or transverse thrust loading

are applied along the edges of stiffened panels. In this subsection, three of these models can be also considered when

lateral pressure is in application, which is calculated from extreme full load condition with pressurep = 0.23 MPa.

The summary of the results is described in Table 2, and the difference of three model methods is negligible when the

longitudinal compressive is predominant (i.e. : 1.0 : 0.0, : 0.9 :0.1, : 0.8: 0.2 andx y x y x y

: 0.7 : 0.3x y ), the two models of cases, 2B2S and 2B3S obtain results with a very small deviation. Withuniaxial longitudinal compressive load, the COV value of three models is 0.01%, and under biaxial compressive load,

the maximum value of COV is 8.84% less than 10%.

FIG.7LUS OF 2B1S WITHp = 0 FIG.8TUS OF 2B1S WITHp = 0

FIG.9LUS OF 2B2SWITHp = 0 FIG.10TUS OF 2B2S WITHp = 0

FIG.11LUS OF 2B3S WITHp = 0 FIG.12TUS OF 2B3S WITHp = 0(LUS = LONGITUDINAL ULTIMATE STRENGTH, TUS = TRANSVERSE ULTIMATE STRENGTH)

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

ULTIMATE STRENGTH OF 2 BAY - 1 SPAN PANEL, WITHOUT LATERAL PRESSURE

xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x:

y= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y = 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


yu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x:

y= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y = 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x

:y

= 0.7:0.3

x:

y= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y= 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7


yu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x:

y= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y= 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x:

y= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y= 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


yu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x:

y= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y= 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0


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In other cases, the variations in ultimate strength are significant, however, the deviation of results derived from 2B1S

and 2B3S are hardly negligible. It is clear that the lateral pressure and the number of transverse floor as well as

longitudinal girders affecting the ultimate strength with full structural model that the result obtained will be more

accurate than the other model.

FIG.13LUSOF 2B1S,p = 0.23 FIG.14TUSOF2B1S,p = 0.23 MPa

FIG.15LUSOF 2B2S,p = 0.23 FIG.16TUSOF 2B2S,p = 0.23 MPa

FIG.17LUS OF 2B3S,p = 0.23 FIG.18TUS OF 2B3S,p = 0.23 MPa

The comparisons between the results obtained without lateral pressure (in Fig. 7, Fig.9 and Fig.11) and with lateral

pressure (in Fig. 13, Fig. 15 and Fig. 17) the ultimate strength (in Table 2) along the longitudinal edge (xdirection)

decreases about 15% when acting of later pressure. However, the ultimate strength along the transverse edge (y

direction) is significantly increased; which is described in Fig. 14, Fig. 16 and Fig. 18. It is certain that the

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

ULTIMATE STRENGTH OF 2 BAY - 1 SPAN PANEL, WITH P = 0.23 MPa

xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x:

y= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y= 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


yu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x:

y= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y= 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7


xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x:

y= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y= 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7


yu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x:

y= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y= 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7


x

u/

Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x

:y

= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y= 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7


y

u/

Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.9:0.1

x:

y= 0.8:0.2

x:

y= 0.7:0.3

x

:y

= 0.6:0.4

x:

y= 0.5:0.5

x:

y= 0.4:0.6

x:

y= 0.3:0.7

x:

y= 0.2:0.8

x:

y= 0.1:0.9

x:

y= 0.0:1.0


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translations of combined load direction take an important role in the capacity of ultimate strength, particularly from

xdirection toydirection.

In addition, the strain values different when models reach ultimate limit state are also discussed. With the appearance

of hydrostatic pressure, the model is quicker to reach buckling state. In comparison with longitudinal ultimate

strength in case of without lateral pressure (in Fig. 7, Fig. 9 and Fig. 11), the maximum value of strain is 0.0018 and

with lateral pressure (in Fig. 13, Fig. 15 and Fig. 17), the maximum value strain is about 0.0017. It is clear that theeffect of lateral not only decreases the longitudinal ultimate strength, but also increases the possibility to reach

ultimate limit state faster. However, in some cases, the later pressure can increase the capacity of transverse ultimate

strength.

3.2 Ul timate strength of 3-bay sti f fened panel model

In section 3.1, the series of results are obtained from computation of 2-bay models, the structural form in calculating

as well as the appearance of lateral pressure affect ultimate strength capacity. In this section, this problem should be

illustrated more clearly especially with longitudinal ultimate strength, and the collection of 3-bay stiffened panels

include 3 bays + 1span (3B1S), 3 bays +2 spans (3B2S) and 3 bays+ 3 spans (3B3S). The summaries of results

obtained from these models are shown in Fig. 26, Fig. 28 and Fig. 30.

TABLE 3 ULTIMATE STRENGTH OF 3-BAY PANELS

Case of calculationWithout lateral pressure (p = 0) With lateral pressure (p = 0.23 MPa)

3B1S 3B2S 3B3S COV 3B1S 3B2S 3B3S COV

: 1.0 :0.0x y /xu Y 0.7432 0.7437 0.7436 0.03% 0.6315 0.6263 0.6357 0.75%

/yu Y 0.0448 0.0456 0.0456 1.08% 0.5377 0.4620 0.5519 9.34%

: 0.8 :0.2x y /xu Y 0.7068 0.7288 0.7121 1.61% 0.4139 0.4233 0.4108 1.56%

/yu Y 0.1059 0.2304 0.1557 38.21% 0.6785 0.6619 0.6671 1.27%

: 0.6 :0.4x y /xu Y 0.5546 0.3154 0.5536 28.90% 0.1856 0.1038 0.2105 33.49%

/yu Y 0.6911 0.1877 0.5758 54.43% 0.2536 0.6873 0.4430 47.13%

: 0.4 :0.6x y /xu Y 0.3545 0.0752 0.3217 60.95% 0.0219 0.1088 0.0566 70.10%

/yu Y

0.6956 0.3857 0.6331 28.67% 0.3205 0.6827 0.5749 35.36%

: 0.2 :0.8x y /xu Y 0.2413 0.2432 0.2262 3.93% 0.0581 0.0543 0.0637 8.07%

/yu Y 0.6853 0.6864 0.6645 1.81% 0.3200 0.3135 0.3506 6.05%

: 0.0 :1.0x y /xu Y 0.1152 0.1196 0.1139 0.03% 0.0958 0.0845 0.0817 8.58%

/yu Y 0.5844 0.5914 0.5780 1.08% 0.2752 0.2293 0.2253 11.39%

1) Ultimate strength of 3-bay stiffened panel without lateral pressureTable 3 details the longitudinal ultimate strength obtained from three models in each appropriate case under

compressive load along the longitudinal and transverse edges. The difference of these values is small as the

longitudinal thrust load is predominant ( : 1.0 : 0.0 and : 0.8: 0.2x y x y ), and the maximum value of COV

is 1.61%, particularly in the uniaxial compressive load, the COV is 0.03%. According to the analyses of results and

the accuracy of ultimate strength derived from the 3 bay panel models are higher than 2 bay panel models. In

uniaxial compressive load, 2-bay models give the average value ratio of ultimate strength and yields stress

/ 0.7475xu Y and this value is obtained from 3 bay model of / 0.7435xu Y .

In case of the transverse thrust load is predominant (i.e. : 0.0 :1.0 and : 0.2 : 0.8x y x y ), the COV of

longitudinal is also good agreement, and the maximum value of COV is 3.93%, meanwhile, this value of COV in 2

bay panels model is 48.92%. Obviously, the 3 bay models give much more accurate results than 2 bay models in the

appropriate case behavior. Actually, in the assessment of ultimate strength, a suitable choice of calculation definesthe accurate results. Concerning the transverse ultimate strength in Table 3, these models give also better results than


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2 bay panel models, the value of COV derive is small in the case of the longitudinal and transverse compressive load

are predominant, in : 0.0 :1.0 and : 0.2 : 0.8x y x y , the maximum of COV is 1.81%.

FIG.19 LUS OF3B1S,p = 0 FIG.20TUS OF3B1S,p = 0.23 MPa

FIG.21LUS OF3B2S,p = 0 FIG.22LUSOF 3B2S,p = 0.23 MPa

FIG.23LUS OF 3B3S,p = 0 FIG.24LUS OF 3B3S,p = 0.23 MPa

In the other case, when the difference of longitudinal and transverse compressive load is insignificant (i.e.

: 0.6 :0.4 and : 0.4 : 0.6x y x y ), similar to 2 bay panel model, the value of COV is very big especially

3B2S gives the long ultimate strength much lower than 3B1S and 3B3S. The difference of 2B1S and 3B1S are about

3.6% and 0.7% of the longitudinal ultimate strength as the : 0.6 : 0.4 and : 0.4 :0.6x y x y , respectively,

and in consideration of transverse ultimate strength, these differences are 1.4 % and 1.0 %. In regard to 2B3S and

3B3S, the error results of : 0.6 : 0.4x y are 0.7% and 4.7% for longitudinal and transverse ultimate strength,

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.8:0.2

x:

y= 0.6:0.4

x:

y= 0.4:0.6

x:

y= 0.2:0.8

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7


xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.8:0.2

x:

y= 0.6:0.4

x:

y= 0.4:0.6

x:

y= 0.2:0.8

x:

y= 0.0:1.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8ULTIMATE STRENGTH OF 3 BAY - 2 SPAN PANEL, WITHOUT LATERAL PRESSURE

xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.8:0.2

x:

y= 0.6:0.4

x:

y= 0.4:0.6

x:

y= 0.2:0.8

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7ULTIMATE STRENGTH OF 3 BAY - 2 SPAN PANEL, WITH P = 0.23 MPa

xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.8:0.2

x:

y= 0.6:0.4

x:

y= 0.4:0.6

x:

y= 0.2:0.8

x:

y= 0.0:1.0

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8


xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.8:0.2

x:y = 0.6:0.4

x:

y= 0.4:0.6

x:

y= 0.2:0.8

x:

y= 0.0:1.0

0 0.5 1 1.5 2 2.5 30

0.1

0.2

0.3

0.4

0.5

0.6

0.7


xu

/Y

Strain (x10-3)

x:

y= 1.0:0.0

x:

y= 0.8:0.2

x:y = 0.6:0.4

x:

y= 0.4:0.6

x:

y= 0.2:0.8

x:

y= 0.0:1.0


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respectively. Concerning the error results of : 0.4 : 0.6x y , these values are 4.4 % and 3.3 %.

FIG.25VON-MISES STRESSES OF 2BAY FIG.26VON-MISES STRESSES OF 3-BAY MODELS

(WHEN LONGITUDINAL COMPRESSIVE LOAD IS PREDOMINANT - AMPLIFICATION FACTOR OF 25)


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FIG.27 VON-MISES STRESSES OF 2-BAY FIG.28 VON-MISES STRESSES OF 3-BAY MODELS

(MODELS ARE UNDER BIAXIAL COMPRESSIVE LOAD - AMPLIFICATION FACTOROF 25)


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FIG.29 VON-MISES STRESSES OF 2-BAY FIG.30 VON-MISES STRESSES OF 3-BAY MODELS

(WHEN TRANSVERSE COMPRESSIVE LOAD IS PREDOMINANTAMPLIFICATIONFACTOR OF 25)

Otherwise, these error results of 2B2S and 2B3S are 17.9% and 43.8% for : 0.6 : 0.4x y appropriate ratio of

/xu Y

and /yu Y ; for : 0.4 : 0.6x y , these errors are 38.1% and 20.4% of /xu Y and /yu Y ,

respectively. Following this analysis, when an assessment on the ultimate strength of stiffened panel is made, these

models 3B1S and 3B3S give good agreement results, and in actual calculation, they are also applied to a structuralstiffened panel of the deck and bottom. If the 3B2S model is used for calculation in the case that the longitudinal or


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transverse compressive load is predominant, while in another case, the results are obtained with large error and it

should be contrasted to carry out the experience. The longitudinal ultimate strengths in this case are shown in Fig. 19,

Fig. 21 and Fig. 23. Dealing with the effect of lateral pressure, these models will be considered in the following

subsection.

2) Ultimate strength of 3-bay stiffened panel with lateral pressure p = 0.23 MPaIn the present study, three models 3B1S, 3B2S, and 3B3S under combined biaxial compressive load and lateral

pressure p = 0.23 MPa are considered. The ultimate strengths of these three stiffened panels are shown in Table 3

and Fig. 20, Fig. 22 and Fig. 24. The error of longitudinal ultimate strength is insignificant when the compressive

along longitudinal edges or transverse edges of these panels appropriate : 1.0 :0.0, : 0.8:0.2x y x y ,

: 0.2 : 0.8 and : 0.0 :1.0x y x y . This maximum value of COV is 8.58%, especially when structural is

under only compressive load in the x-direction, often called uniaxial compressive, COV = 0.75%, i.e. a very small

value. In these cases, the difference of transverse ultimate strength values is also negligible, when the panel is under

combined biaxial compressive load with lateral pressure p = 0.23 MPa, the maximum value of COV is 6.05 % less

than 10 %, and this error is adopted.

Following these results, the capacity of ultimate strength when lateral pressures take part in the combination of load

acting is reduced about 15.1% - 24.9% in the case of uniaxial compressive, and in case of structures under biaxial

compressive, this reduction is 41.9% - 75.2%, which is referred to Table 3. In the transverse ultimate strength aspect,

when the lateral pressure is applied to structures, the ratio of /yu Y increases significantly when the longitudinal

compressive load is predominant. In case of : 0.4 : 0.6 and : 0.6 :0.4x y x y , the error of ultimate strength

obtained from these three models is very large. However, the average difference of value between with and without

lateral pressure for transverse ultimate strength is negligible. In the general calculation of ultimate strength in ship

structural longitudinal system, the longitudinal compressive load is always predominant, and the ratio of :x y

frequently is 1.0:0.0 to 0.7:0.3. Because with the ship having length above over 90 meters the system of structures in

the main hull is frequently longitudinal. The predictable results of ultimate strength applied to longitudinal structural

system can be obtained with small error values.

4 CONCLUSIONIn the investigation of ultimate strength for VLOC as well as the large bulk carrier, the necessity to carry out

experiments of stiffened panel is not neglected. However, with the larger model in the actual process of predicting,

the ultimate limit state is very complicated, because it requires the giant size of equipment that is not real. To solve

this problem, the performances of finite element method in nonlinear analysis are applied and operated. Designers

can build a large model, division a lot of elements, with the power and resources of the computer unit processor

(CPU), which needs complicated requirements. In the course of calculation, the designers know how to build a

suitable for models as well as strategy simulation and it plays an important role in accurate results. In this paper, the

problem is solved, the conclusions are as follows:

1)

Concerning the uniaxial compressive load, the ultimate strength is obtained from the stiffened panel withinsignificant error.

2) During the investigation on biaxial combined load with or without lateral pressure, the accuracy has beenobtained from the case of the predominant longitudinal or transverse compressive load.

3) The lateral pressure applied to the stiffened panel should reduce about 15% capacity of longitudinal ultimatestrength; meanwhile, the transverse ultimate strength is significantly increased. This conclusion shows that the

lateral pressure takes an important part in capacity of ultimate strength of ship structures.

4) In comparison between 2 and 3 bays stiffened panels, the 3 bay models give more accuracy than 2 bay modelswith the same condition of boundary and acting load.

5) By applying NFEM to this study, the results of ultimate strength allow predicting ultimate limit state withoutexperiments when condition of equipment is not demanded for actual requirements.

Although the NFEM is coded by ANSYS, the results are obtained from a series of models in outer bottom with

high reliability; and these models in the other area of ship structures (i.e. on the deck structures, in the inner bottomstructures, inside as well as in bulkhead structures) should be analyzed by other FEM software in the future.


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[2] Caldwell, J. B. 1965. "Ultimate Longitudinal Strength." Trans. Royal Inst. Nav. Arch no. 107:411-430.[3] Do, Hung Chien, Wei Jiang, and Jian Xin Jin. 2012. "Estimation of Ultimate Limit Statefor Stiffened-Plates Structures: Applying

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