A Study on the Optimum Structural Design of Surface Effect Ships

ELSEVIER

Marine Structures 9 (1996) 519-544 © 1996 Elsevier Science Limited

Printed in Great Britain. All rights reserved 0951-8339/96/$15.00

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A Study on the Optimum Structural Design of Surface Effect Ships

Chang Doo Jang, Seung I1 Seo

Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, Korea

& Sang Keun Kim

Rese~rch Institute of Shipbuilding, Hanjin Heavy Industries Co. Ltd, Busan, Korea

(Received 6 January 1994)

ABSTRACT

In t.~is study, a method to design hull structures of surface effect ships with minimum weight is proposed, and computer programs following the method are also developed. The proposed method considers structural characteristics inherent to surface effect ships by rational structural analyses, but adopts a simplified analysis model to enhance computing efficiency during optimization process. The proposed method uses design loads and strength criteria suggested by the class rules of DnV, but the interaction effect of longitudinal girders and transverse web frames are considered by the simple and accurate grillage analysis method. As design of the midship section is accomplished through optimum design of partial structures such as stiffened plates and complex girders and frame structures, global optimization of all design variables is avoided and computing efficiency is raised. And also, the proposed method contains the simple torsional strength and analysis routine and optimization process of transverse bulkheads against pitch connection moment. Applying the proposed method to ship design, 20% reduction of hull weight was confirmed, and it can be shown that hull weight varies with the change of frame space and there exists optimum frame space.

Key words: minimum weight design, optimization procedure, stiffened plate, simplified grillage analysis, torsional strength, rationality.

519

520 Chang Doo Jang, Seung I1 Seo, Sang Keun Kim

1 INTRODUCTION

Surface effect ships are constructed throughout the world for military and commercial purposes due to merits such as reduction of resistance, increase of lifting efficiency and wide deck area. However, surface effect ships have different structural characteristics to other displacement type vessels which result from twin hull, small length-to-breadth ratio and dynamic effects due to high speed. In addition, much design and construction experience is not accumulated. In these circumstances, more rational structural design methods based on analysis are needed.

As high speed is the most important merit of surface effect ships, every endeavor to maximize speed should be made. Among the endeavors, reduction of hull weight to increase propulsion and lifting efficiency at the same engine power is included. In this study, considering current needs concerning structural design of surface effect ships, an optimal structural design method satisfying the needs is proposed and applied to actual design works. The method pursues rationality and simplicity. In other words, the proposed method considers structural characteristics inherent to surface effect ships by rational structural analyses, but adopts a simplified analysis model to enhance computing efficiency during optimization process.

Most naval vessels are constructed following the design procedure suggested by the U.S. Navy. 1 In this procedure, structural design is accomplished by synthesis of individual members satisfying the suggested strength criteria, and longitudinal strength is the primary design consid- eration. During synthesis, the procedure uses only simple formulas origi- nated from structural mechanics, and does not include the concept of design by analysis. As the result, the procedure can not consider the correct effect of interaction between longitudinal girders and transverse web frames in initial design stage. Hughes e t al. 2 developed an optimal structural design method which included an efficient finite element method for design purposes. Although the method adopted efficient elements and algorithms, solution of simultaneous equations with large degrees-of-freedom is inevi- table. When the solution process is combined with the optimization procedure, computing time increases rapidly and computing efficiency decreases.

A generalized slope deflection method 3 was proposed for efficient and rational structural design of tankers. The method used the beam theory and executed matrix operations resembling the finite element method, but took account of the effect of variable cross section in one beam element and enabled reduction of degrees-of-freedom. The method has appropriate rationality and simplicity. However, in the application of the method, the authors separated the optimization process into optimization for longitudinal members and that for transverse members because 3-

Optimum structural design of surface effect ships 521

dimensional analysis of the whole structure by the generalized slope deflect:ion method was very time consuming. So, the allowable bending stress requirement in longitudinal girders could not be constraint. In addition, variation of the primary stress level during design cycle was not considered.

In this study, rational structural analysis methods are proposed, which are siraple enough to be applied to the time consuming optimization process, but can take account of the effect of interaction between longitudinal members and transverse ones and structural characteristics inherent to surface effect ships. Also, a design principle appropriate to surface effect ships is proposed, in which global optimization of the midship section is attained by integration of optimized substructures for the increase of computing efficiency.

2 STRUCTURAL DESIGN PROCEDURE OF SURFACE EFFECT SHIPS

Recently, structural design by direct calculation has been applied to real ship design, but complex hydrodynamic and structural theories and a lengthy computing time prevent its common utilization. As a more practical design approach, a lengthy semi-direct design approach which neglects direct calculation of hydrodynamic loads is preferred because of its simplicity and reliability. Therefore, the design procedure proposed in this study is based on the semi-direct design method. The detail procedure is shown in Fig. 1.

2.1 Basic assumption and simplification

(1) Global behaviors of the surface effect ship subjected to hull girder loads follow the simple beam theory.

To confirm the beam behavior of the twin hull structure, we carried out detailed finite element analysis for the simple twin hull as shown in Fig. 2. Dimensions of the structure are 35m x 10m x 5m and geometric arrangements are similar to the surface effect ship. The twin hull structure is assumed to be made of plates of the same thickness. To realize the simple bending state at midship, concentrated loads of the same magni- tude are applied at different positions. To calculate stresses due to the hull girder bending moment at the midship section, the structure is divided into membrane elements as shown in Fig. 3 and finite element analysis is carried out using the commercial package program ANSYS. Considering

522 Chang Doo .lang, Seung 11 Seo, Sang Keun Kim

Initial Structural Arrangement J

Data Input I

Calculation of Design Loads I

Assumption of Primary Stress Distribution

Design of Stiffened Plate Element

Calculation of Hull Girder Section Modulus

I Calculation of New Primary Stress [

[ Design of Transverse Bulkhead against Torsion J

] Analysis of Cross Structure subjected to

Transverse Bending Moment

J

Fig. 1. Procedure of structural design of high speed surface effect ships.


C . L 5OOO

12501 I UPPER DK 1250 5~Y DK 2500~/

(a) Midship Section ( plate thickness : 6 rnin )

<- ~ ->1

B-ID ~'ID

t II~ON

(b) Side Profile Fig. 2. Box-shaped twin hull structure.

/ / / / / q / / / / / / 1 1

,//// ."I L-d ..-'/'.I

Pig. 3. Finite element model of the twin hull structure.


symmetric conditions, only one quarter is modeled. The results are shown in Figs 4 and 5. Bending stresses of the midship section are also calculated using the simple beam theory. According to Fig. 4, bending stress distribution is linear at the side shell and the maximum difference between the two methods is only 5%. According to Fig. 5, bending stresses at the center of the decks show some differences because of shear lag effect. However, the bending stress of the side is larger than that of the center of the deck. As design of the deck is carried out based on the maximum primary stress of the deck, variation of the primary stress along the deck does not influence determination of the thickness of the deck. From the calculated results, we can conclude that the global behavior of the normal twin hull structures obeys the beam theory.

(2) Primary structural members such as longitudinal girders and transverse web frames have negligible torsional rigidity, compared with bending rigidity, as they make thin walled open sections.

(3) Effective resisting members against hull girder torsional moment are transverse bulkheads; and side hulls of the surface effect ship are rigid compared with the cross structure.

(4) Global optimization of the midship section is attained by assem- bling optimized results of the substructures.

Simple beam theory ..... Finite element analysis

5000

~4000

aooo

o

2000

! N 10o0

0 -80

i i i i i i i i i i ! 1111 , l l l l l r t l l l r l l l l l l l ; l l l l ~i,1,11 -60 - 4 0 - 2 0 0 20 40 60 80

Normal stress (*e-3, N/ram**2)

Fig. 4. Bending stress distribution along the side shell at midship section.


.~ 6o-

z c4

"~-" 40

O

20 @

O

Simple beam theory . . . . . Pini te e l e m e n t analys is

0 1 , 1 1 1 1 1 ~ l , t , , , , , l l l l l l l l r , ~ , l 1 1 1 1 , f i , l l , , l ~ , , 1 , , I 0 1000 2000 3000 4000 5000

Distance f r o m the c e n t e r l ine ( m m )

Fig. 5. Bending stress d i s t nbu t i on a long the upper deck at midship section.

In general, summation of the optimized results of substructures does not give the global optimized results. However, when the objective function of the global structure is the linear sum of the objective functions of the substructures and the constraint equations of one substructure are also linearly independent of those of the other substructures, summation of the optimized results gives the global optimized results. In the case of optimization of the midship section, these conditions are generally satisfied, because the sectional area of the midship section is the linear sum of the stiffened plates and the strength criteria of each stiffened plate are effective by themselves, according to our design optimization strategy. However, constraint for the hull girder bending stress yields the equation which iincludes all design variables, but this constraint is not active. That is to say, actual hull girder bending stresses of the surface effect ships are small and, in general, they do not cause any significant design modifica- tion.

2.2 Initial data input

Initial structural arrangement is carried out, referring to General Arrangements, and data such as geometric configuration and material properties are prepared.

526 Chang Doo Jang, Seung II Seo, Sang Keun Kim

2.3 Calculation of design loads

Design loads are calculated by the class of DnV. 4 Local loads such as hydrostatic pressure, stowage weight and slamming pressure are calculated. Among local loads, slamming pressure is the most severe, which results from dynamic effects accompanied by high speed. Primary hull girder loads are hogging and sagging bending moments due to the difference of weight and buoyancy at off-cushion state and crest landing and hollow landing at on-cushion state as shown in Fig. 6. Hull girder loads inherent to surface effect ships with twin hulls are pitch connection moment and transverse bending moment as shown in Fig. 6.

2.4 Assumption of primary stress distribution

Longitudinal hull girder bending moment causes compressive or tensile stress in individual members. The compressive or tensile stress can be calculated, on the condition that the hull girder behaves like a beam subjected to bending moment. Therefore, primary stresses, i.e., compressive or tensile stress, in individual members vary linearly across the midship section. As the distribution of primary stresses is the function of the sectional property of the midship section, it changes during the design cycle.

2.5 Minimum weight design of stiffened plates

Hull structure of the surface effect ship consists of primary structural members like longitudinal girders and transverse web frames, and stiffened plates with plating and stiffeners. In this study, a stiffened plate is defined as the combined structure of plate and stiffeners bounded by primary structural members as shown in Fig. 7. The objective function for optimal design of the stiffened plate can be expressed as eqn (1), which represents relative weight of the stiffened plate.

where b t

n

hw tw bf 9

F = bt + n (hw tw + bftf)

= breadth of the stiffened plate -- thickness of plating = number of stiffeners = web height of stiffener = web thickness of stiffener = flange breadth of stiffener = flange thickness of stiffener.

(1)

Optimum structural design of surface effect ships

Bending Moment at Crest Landing

527

Bending Moment at Hollow Landing

o m ' cnt

Pitch Connection Moment

Fig. 6. Hull girder loads.

Design constraints are imposed using the rules of DnV. Major constraints are as follows.

(1) Thickness requirement of plating based on allowable bending stress

t >>. c~bl~"bSv~ (2)

528 Chang Doo Jang, Seung 11 Seo, Sang Keun Kim

I b i L L. / I_ L.

(a) Sectional view of the stiffened plate

_ _ ~ t

h w I ~ l ~ tf

(b) Details of a stiffener

Fig. 7. Model for optimization of stiffened plate.

where s = p =

a p b = cpb =

k p b =

stiffener spacing design pressure allowable bending stress of plating factor depending on boundary conditions of plate field correction factor for aspect ratio of plate field.

(2) Buckling stress requirement of plating

ap~ >~ aa (3 )

(J ael p = kpcE (4)

av ( a y ) % ( 5 ) %c = aelp when aetp < ~- = cry 1 4"-~tp' when aelp > -~-

where apt = buckling stress of plating aetp = , elastic buckling stress of plating kpc = buckling stress factor depending on aspect ratio and

boundary conditions E = modulus of elasticity aa = calculated actual compressive stress

O p t i m u m s truc tural design o f sur face e f f ec t ships 529

77 = stability factor ay = yield stress of material.

(3) Section modulus requirement of stiffeners

ml 2 sp Z > ~ - -

¢T sb

where Z = section modulus of the stiffener m = bending moment factor l = stiffener span ash = allowable bending stress of the stiffener

(6)

(4) Buckling strength requirement of stiffeners

~sc >I aa rl

G aet~ = k~E A l 2

where asc =

Uel s = IA =

A =

buckling stress of the stiffener following shown in eqn (5) elastic buckling stress of the stiffener

the

k$c

(7)

(8)

rule

moment of inertia of the stiffener with effective flange cross sectional area of the stiffener with effective flange bending stress factor depending on boundary conditions.

(5) Torsional buckling stress requirement of stiffeners

Uel t - - _ _

where k Cl 4

u4EIw

¢7tc ~ U'--~a (9) r/

7r2EIw( k ) 11. (10) if12 m 2 + - ~ +G-~e

~ t c :

¢7el t ~-

m = I t = I e =

torsional buckling stress of the stiffener following the rule shown in eqn (5) elastic torsional buckling stress of the stiffener number of half waves St Venant's moment of inertia polar moment of inertia of profile about connection of stiffener to plate


t >>- tmi,

where lmin = minimum thickness by the class rules.

Detailed optimization schemes are as follows.

(1)

(2) (3)

I w = warping constant of profile about connection of stiffener to plate

c = spring stiffness exerted by supporting plate panel.

(6) Minimum thickness requirement of plating, web plate and flange plate

(11)

Assumption of stiffener spacing and minimum cross sectional area of the stiffened plate element. Selection of the plate and the stiffener among the material list. Examination of the selected plate and stiffener satisfying the constraint equations. If the selected plate and stiffener do not satisfy the constraint equation, a new plate and a new stiffener are selected.

(4) Calculation of sectional area of the stiffened plate element and comparison with the assumed minimum sectional area. If the newly calculated sectional area is less than the minimum sectional area, the minimum sectional area are modified.

Within the given space range and material list, the above procedure is repeated and final minimum results are obtained.

2.6 Design of primary structural members

Longitudinal girders and transverse web frames bounded by bulkheads and shell structures are considered as primary structural members which support stiffened plates. As longitudinal girders and transverse web frames subjected to lateral loads make a complex structure, the behavior of each member can be described only by numerical methods such as the finite element method. The complex structure which makes a grillage can be modeled as an assemblage of beam elements in the plane which has 3 degrees-of-freedom at each node, i.e. vertical translation and two rota- tional components. As mentioned before, for structural analysis routines to be used in the optimization process, they must be rational enough to secure reasonable accuracy and simple enough to enhance computing efficiency. In accordance with these needs, in this study, a simplified analysis method to analyze grillages is proposed. In this method, torsional rigidity of the beam is assumed to be zero, because most primary structural members have shapes of T or L type and torsional rigidity of these open sections is negligible, compared with bending rigidity of the section. Using this assumption, the effect of interaction between girders and web


,(

/ zz

B

~ 6 ~ h tf t

** br 3

Fl F2 F3

Fig. 8. Structural model for analysis of the grillage structure.

frames can be included in reaction forces as shown in Fig. 8. Deflections in the web frames can be calculated by the following equation.

6 i --- - d i k F k + v i (12)

where 6; = deflection of the web at intersection i dig = influence coefficient of the web frame


Fk = reaction force at intersection i v; = deflection of the web frame at intersection i when only

uniform load is applied.

In eqn (12), influence coefficients by concentrated force and deflection by uniform load for a simply supported beam can be calculated by Timoshenko beam theory. 5

Influence coefficients of the beam by a unit concentrated force can be calculated by the following equations.

In the case where 0 <~ x <~ ap

6 ( x ) = 6 ~ ( - b x 12 x2 x ( ~ ) + + b2) + ~ 1 - (13)

In the case where ap <~ x <~ l

[ ] x l a P ( 1 7) 6(x ) - bp __~p (X _ ap)3 _ (fl _ b2p)X + X3 + - ~ . ~ 6-f f l l . -

(14)

,(w4w, 3w, ) ,(w, w) v(x )=~ - ~ +i5 - 2--? -x +~-Z -Tx+-2 x2

where w = uniform load.

(15)

Deflections in the girders can be expressed by the following equation.

3~ = eikFk (16)

where 5; = deflection of the girder at intersection i eik -- influence coefficient of the girder.

From the compatibility condition at each intersection,

3i = 6 i (17)

simultaneous equations can be obtained as follows

(elk + d ik)Fk = Vi. (18)

By solving eqn (18), reaction forces and deflections can be calculated, and internal bending moments and shear forces can also be calculated

where l = length of the beam I = moment of inertia of the beam section ap = distance of loading point from the origin A,. = effective shear area of the beam b, = t - a t .

Deflection of the beam by uniform load can be calculated by the following equation


using the equilibrium condition. Calculated results shown in Table 1 support the validity of the proposed simplified analysis method.

The objective function of the grillage for optimization can be expressed by the following equation.

F - - (belt + lwl hwl + bjl tyl)nla + (be2t + tw2hw2 + bf2tf2)n2b (19)

where r/1

~/2 -~

hw]

twl =

,t, fl A~w2 ---- it, w2

b f2 =

i X =

bel, be2 =

number of girders number of web frames length of girders length of frames web height of girders web thickness of girders flange breadth of girders flange thickness of girders web height of frames web thickness of frames flange breadth of frames flange thickness of frames effective breadth of plating.

Major constraints which must be imposed in scantling are as follows.

(1) Allowable bending and shear stress criteria I:a all members, bending and shear stresses which can be calculated

T A B L E 1 Calculated Results by Simplified Grillage Analysis and Finite Element Analysis Code ANSYS 6 for the Grillage Shown in Fig. 8 (Length = 4 m, Breadth = 4 m, Thickness of Plating = 10 mm, Effective Flange = 650ram, Size of Girder and Frame

= 150 × 8 + 80 × 10, Uniform Load = 10N/mm)

Intersection number

Deflection by simp. Deflection by analysis (mm) ANSYS

(turn)

Error

6.247 6.026 3.5% 8.665 8.384 3.2% 6.247 6.026 3.5% 8.709 8.430 3.2%

12.11 11.76 2.9% 8-709 8.430 3.2% 6.709 6.026 3.5% 8.665 8.384 3.2% 6.247 6.026 3.5%


from the above mentioned method should not exceed allowable limit by the class rules.

(2) Torsional buckling stress requirement Primary stresses of the girders should not exceed torsional buckling stress given as eqn (10).

(3) Minimum thickness requirement

Detailed optimization procedures using Hooke & Jeeves' direct search method 7 are as follows.

(1) Initial assumption of design variables shown in eqn (19) and their increments for direct search.

(2) Local search for finding decreasing direction of the objective function which includes the penalty functions to represent the constraint equations.

(3) Pattern move of the design variables for global move. (4) Examination of convergence of the design variables. If convergence

is not attained, local search and pattern move is repeated.

2.7 Calculation of hull girder section modulus and new distribution of primary stresses

After determining all structural members of the midship section, primary stresses and section modulus for the new midship section are calculated.

2.8 Test for convergence of primary stresses

Newly calculated primary stresses are compared with the assumed primary stresses, and the differences are also calculated. If the differences are within the allowable limit, following design step is carried out. Otherwise, new primary stresses are assumed to be initial values and the design process is repeated.

2.9 Design of transverse bulkheads against torsional moment

Pitch connection moment causes torsion in the cross structures. As effective resisting structures against torsional moment are transverse bulkheads, the transverse bulkheads are designed to withstand the torsional moment. Shear stresses in the transverse bulkheads resulting from the torsional moment are calculated by the rationally simplified model.

Based on the assumption that side hulls are rigid compared with the cross structures, the cross structures can be modeled as Fig. 9. Vertical deformations of the transverse bulkheads are assumed to be varied line-


. . . . . \ \

Fig. 9. Model for torsional strength analysis.

arly along the ship length. Shear forces at the end of the cross transverse bulkheads can be expressed as follows.

Vi : - k i ui

ui : - k i [Tn (Un -- Ul) + Ul ]

where Vi =

ll i = 1i =

ki =

(20)

(21)

shear force at the end of the cross transverse bulkhead i relative end deformation at the transverse bulkhead i distance of the transverse bulkhead i from the origin spring constant of the transverse bulkhead i.

The rules of BV 8 recommend the expression of spring constants of cross structures by the beam theory, but the expression by BV does not include the effect of shear deformation. As in short beams with large depth, shear deformation can not be neglected, spring constants of the cross transverse bulkheads are modified as in the following equation including the effect of shear deformation.

1 k i = LS i Li (22)

- - q . 12 El i GAsi

where Li = L = msi ~-

length of the cross transverse bulkhead i sectional moment of inertia of the cross transverse bulkhead i effective shear area of the cross transverse bulkhead i.

From the force and moment equilibrium conditions, the following simultaneous equations can be derived.


~-'~ ( li ) ~-~ li Ul ki 1 - ~n + Un ki ~ = 0

i = 1 i = 1

(23)

Ul kili 1 - ~ + un ki ~ = Alp (24) i = 1 i = 1

where Mp = pitch connection moment Ul,Un = relative end deformation of the first and the last

transverse bulkhead, respectively l, = distance of the last transverse bulkhead from the origin.

By solving the above equations and substituting the results into eqns (20) and (21), shear forces at the end of the transverse bulkheads can be calculated and shear stresses can also be calculated by the following equation.

Vi "C i = - - (25)

Asi

where T i ~--- shear stress at the transverse bulkhead i.

The objective function for optimization of the transverse bulkheads is the same as that of stiffened plates, but design variables are plate thickness and size of stiffeners, assuming that spacing of stiffeners are determined by that of deck longitudinal stiffeners. Constraints are as follows.

(1) Thickness requirement of plating based on allowable bending stress. (2) Section modulus requirement of stiffeners. (3) Shear buckling stress requirement of plating.

~c 1> ~ (26) r/

(t)2 "Eel p : ktc E s (27)

"gy "~c = Zelp w h e n "~elp < ~

where Zc = Tel p :

kt¢ =

"/Ty =

( = Zy 1 - zy when Zelp > ~ (28)

shear buckling stress of plating elastic shear buckling stress of plating shear buckling stress factor depending on aspect ratio and boundary conditions calculated actual shear stress by eqn (11) shear yield stress of material.


SI~'ll

Sead

( I

8mlam~

Fig. 10. Longitudinal section of surface effect ship.

(4) Allowable shear stress requirement for preventing yielding. (5) Minimum thickness requirements for all members.

Optimum combination of plate and stiffeners is found among the material list by repeated comparison.

2.10 Analysis of cross structures subjected to transverse bending moment

Cross structures between side hulls shown in Fig. 10 undergo transverse compressive or tensile stresses by transverse bending moment. The cross structures under a global bending moment will behave as one structure. So, global behavior of the cross structures can be described approximately by the beam theory - - like longitudinal strength analysis. Section modulus for main cross structures across the longitudinal section of the ship is calculal:ed and compressive or tensile stresses by the transverse bending moment are calculated using the following equation.

Mt o',,t = - - (29)

Zt

where 17at = transverse compressive or tensile stress of cross structure Mt = transverse bending moment ~ t = section modulus of main cross structures about longitudinal

neutral axis.

3 RESULTS OF O P T I M U M DESIGN

3.1 Results of optimum design of stiffened plates

When the loading condition and dimensions of the stiffened plate are given, variation of opt imum plate thickness, sectional area of a stiffener and the stiffened plate is shown in Fig. 11, according to the number of stiffeners. Discrete variation in Fig. 11 is due to selection of plates and


_ C C C C C C C ~ o Q

25

-~ z0

15

5.

o . ~ c c c P l a t e T h i c k n e s s or.v== S e c t i o n a l Area of S t i f f e n e r ~ Total Sectional Area(*lO)

Fig.

0 i i 1 ~ 1 1 1 1 1 1 1 1 ~ i i i i l l l ~ l l l l l l F i i

0 5 10 15 N u m b e r of S t i f f e n e r

11. Results of optimum design of stiffened plate (length = 2m, breadth = lm , compressive stress = 40 N/mm 2, allowable bending stress = 90 N/mm2).

stiffeners among the material list. Results shown in Fig. 11 can be explained as follows.

Increase in the number of stiffeners accompanies the decrease of breadth of each panel and stiffener spacing, and causes reduction of plate thickness and size of stiffener. However, further increase of stiffeners makes the sectional area of the stiffened plate increase, because plate thickness and size of stiffener can not decrease below a certain limit, by minimum requirement, and an increase in the number of stiffeners causes an increase in the sectional area of the stiffened plate. As a result, an opt imum number of stiffeners exists. As normal pressure increases, the sectional area of the stiffened plate tends to decrease monotonously with the increase of stiffeners, as shown in Fig. 12. In this case, plate thickness and size of stiffener is not governed by minimum requirements, and the effect of an increase of sectional area due to an increase of the number of stiffeners is overcome by the effect of a decrease of sectional area due to a decrease of stiffener spacing.

3.2 Minimum weight design of grillages

When loading conditions, dimensions of the grillage and the number of longitudinal girders are given, the variation of volume of the grillage with


400

350"

~300-

~ 250

~ 200

~ 1 5 0

50~

c e c c e N o r m a l P r e s s u r e = I 0 k N / m ~ ~ N o r m a l P r e s s u r e = 5 0 k N / . m ~ ~ - 6 - A N o r m a l Pressure = 1 0 0 k n / m a

0 7" 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

0 5 10 15 Number of Stiffener

Fig. 12. Variation of sectional area of stiffened plate with the change of number of stiffeners and normal pressure.

increase of the number of transverse web frames is shown in Fig. 13. As the number of web frames increases, loads supported by each girder and web frame are reduced and the size of each member decreases. However, the decrease of size of web frames becomes less due to minimum requirements. So, the total volume of the grillage increase with increase of the number of web frames is as shown in Fig. 14.

3.3 Modeling of midship section and results of optimum design

Length of the design ship is 38 m and design speed is 45 knots. The ship is constructed out of aluminum. As the positions of bulkheads and decks were determined by general arrangements, the positions of longitudinal girders are determined accordingly. Nodes are taken at the intersection points of longitudinal bulkheads, shell plates, decks and longitudinal girders Plates and stiffeners surrounded by primary structural members, bulkheads or side shells are modeled as stiffened plates, and primary structural members such as longitudinal girders and transverse web frames between transverse bulkheads and side shells or longitudinal bulkheads are modeled as grillages. Curved web frames are modeled as 2-dimensional frame structures. In grillage or frame analysis, the stiffened plates

540 Chang Doo Jang, Seung 1l Seo, Sang Keun Kim

18

16

m 14

¢d

i0 = = = = -- Girder ~ c c c c Trans. Web

i l r l + r l l t 1 1 1 1 1 1 1 1 1 r l l ~ l l l l I I I I I I I l ~ l l l l l l l l l r l l l l l l I I 1 ~ 1 1 1 1 I

2 3 4 5 6 7 Number of Trans. Web Frame

Fig. 13. Variation of area of longitudinal girder and transverse web frame (length = 3 m, breadth = 5m, pressure = 10kN/m 2, compressive stress = 3 0 N / m m 2, allowable bending

stress = 90 N/mm2).

are included as effective flanges of the primary members. The stiffened plates and longitudinal girders which contribute longitudinal strength are included in the calculation of hull girder section modulus and primary stress distribution. Modeling results are shown in Fig. 15.

3.4 Optimized results and discussion

Optimized results for the design ship are summarized in Table 2. Compared results were determined at the initial design stage by the usual manual calculation. According to Table 2, most optimized results show tendencies that plate thickness and stiffener spacing become less, compared with the results of initial design. These tendencies are similar to those of Fig. 11. On the other hand, sizes of transverse web frames are different, according to the length of span and design loads. These results are mainly due to variation of bending moment and stresses.

When the transverse web frame space is varied, the change of volume per unit length amidships is shown in Fig. 16. Sizes of longitudinal stiffeners and transverse web frames become smaller with the decrease of frame space, because spans of stiffeners become shorter and loads


4 0 0 -

A

v

,~ 3 0 0 -

200

1 0 0 - 0

N o r m a l P r e s s u r e = 10 k N / m ~ N o r m a l P r e s s u r e 50 k N ~ m ~

-'~-'-'-" N o r m a l P r e s s u r e =100 k N / m B

/ J

z f

I I I I l l l l l l l l ~ l l l l l l l I t I I I I I I I I 1 11111 I I I l l l l I I I I I I I I I I I I I I I I I

2 3 4 5 6 7 N u m b e r o f T r a n s . W e b F r a m e

Fig. 14. Variation of minimum volume of grillage with the change of number of frame and normal pressure.

sustained by each web frame become smaller. However, decrease of sizes of web frames has a certain limit due to minimum design requirements and the effect of increase of volume due to increase of the number of web frames overcomes the effect of decrease of volume of stiffeners due to decrea,;e of span. As a result, below a certain frame space, the total volume starts to increase. This explanation can be verified by Fig. 12, which shows the decrease of sectional area with decrease of frame space. Opt imum transverse frame space can be determined by compromising conflicting factors, i.e., smaller sizes of longitudinal members and larger volume of transverse web frames with decrease of web frame space.

Final results show a 20% reduction of volume per unit length and 19% of sectional area of the midship section, compared with the initial design results.

4 CONCLUSIONS

In this study, a method to design hull structures of surface effect ships with minimum weight was proposed, and computer programs following the method were also developed. Applying the proposed method to ship

542 Chang Doo Jang, Seung 1l Seo, Sang Keun Kim

10'

17 18 19 20 23 24 25 26

11 12 DrYl3Deck 14 15

3 7

,16

N I []

o i °

[] Stiffened Plates []

@

@ @ @ @ @

3 4 5 6

Girder and Transverse Web Frame

Fig. 15. Modeling of midship section for optimization.

0

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Optimum structural design of surface effect ships

TABLE 2 Compar i son of Opt imized Results with Initial Design (Uni t mm)

543

Location Design Plate Size of Space of Size of tran. Size of girder stage thick, longi, longi, web frame

Side Initial 8 65 x 65 x 6 285 210 x 6 + 100 x 8 Shell O p t i m u m 5 40 x 40 x 4 235 4 3 9 x 4 + 181 x 7 Wet Initial 6 65 x 65 x 6 300 210 x 6 + 100 x 8 Deck O p t i m u m 6 40 x 40 x 4 235 233 x 4 + 58 x 5 Dry Initial 4 50 x 50 x 6 300 210 x 6 + 100 x 8 210 x 6 + 100 x 8 Deck O p t i m u m 4 4 0 x 4 0 x 4 300 1 2 0 x 4 + 3 4 x 5 1 6 5 x 4 + 3 4 x 4 U p p e r Initial 6 50 x 50 x 6 300 210 x 6 + 100 x 8 210 x 6 + 100 x 8 Deck Op t imum 5 4 0 x 4 0 x 6 240 1 2 0 x 4 + 3 4 x 5 1 2 0 x 4 + 3 4 x 5 Trans Initial 6 50 x 50 x 6 300 Bhd O p t i m u m 4 40 x 40 x 6 235

T A B L E 3 Summarized Results

Initial Optimum Reduction

Section area, cm 2 3510 2860 19% Volume/un i t length, cm 2 4360 3480 20% Web frame space, m m 900 1000

design, a 20% reduction of hull weight was confirmed. The proposed method uses design loads and strength criteria suggested by the class rules of DnV, but interaction effects of longitudinal girders and transverse web frames are considered by the simple and accurate-grillage analysis method developed in this study. As design of the midship section is accomplished through optimum design of partial structures such as stiffened plates and complex girder and frame structures, global optimization of all design variables is avoided and computing efficiency is raised. Also, the proposed method contains the simple torsional strength analysis routine and optimization process of transverse bulkheads against pitch connection m o m e n t .

The optimization method proposed in this study is said to have rationality which can describe structural behavior inherent to surface effect ships with twin hulls, and efficiency which is necessary in repeated calculation proces,;es. Also, the proposed method can be used in other ships similar to surface effect ships such as catamarans. From the optimized results, it can be shown that hull weight varies with the change of frame space and there exists optimum frame space.


"~3600 1

34oo

A ~3200-

3000

J

z z c c c V o l u m e p e r L e n g t h = = = = = S e c t i o n a l A r e a

~ 2 8 0 0

o

2 6 0 0 . . . . . . . . . , . . . . . . . . . ~ . . . . .

600 1000 1400 Frame Space (ram)

Fig. 16. Variation ofvolume withthechangeof~amespace.

Y

REFERENCES

1. Naval Sea Systems Command, Structural design manual for naval surface ships, NAVSEA 0900-LP-097-4010, 1976.

2. Hughes, O. F., Mistree, F. & Zanic, V., A practical method for the rational design of ship structures. J. Ship Research, 24 (1980) 101-113.

3. Jang, C. D. & Na, S. S., On the minimum structural weight design of oil tankers by generalized slope deflection method. PRADS '87, 1987.

4. Det Norske Veritas, Tentative rules for classification of high speed and light craft, 1991.

5. Dym, C. L. & Shames, I. H., Solid mechanics - - A variational approach, McGraw-Hill, NY, 1973.

6. Swanson Analysis System, ANSYS engineering analysis system user's manual, 1989.

7. Hooke, R. & Jeeves, T. A., Direct search solution of numerical and statistical problems. J. Association for Computing Machinery, 8 (1961).

8. Bureau Veritas, Rules and regulations for the classification of ships of less than 65 m in length, 1990.

Documents

A Study on the Optimum Structural Design of Surface Effect Ships