• Nie Znaleziono Wyników

On the optimization of hull forms with respect to seakeeping

N/A
N/A
Protected

Academic year: 2021

Share "On the optimization of hull forms with respect to seakeeping"

Copied!
22
0
0

Pełen tekst

(1)

TECHNI$CE UP1VEtZITELT Labortoum vcor

Scheepshydromecha

J M kE k

1it.

,y ço

Archief

Mekeiweg 2 2628 CD

,t4)4

1fC

0

teLg786B73.FaxO16781833

/

C

ON THE OPTIMIZATION OF HULL FORMS WiTH

RESPECT TO SEAKEEPING

GJ.Grigoropoulos T.A.Loukakls

Naval Atchitect, PhD Prof. N.T.U.A.

ABSTRACT

A method for

analytical seakeeping optimization is described. The method Is based on a computer code with predicts seakeeping

performance when the ship profile, the design waterline,, the sectional area curve and the distribution along the ship of the centroid, KB(x),

of the

cross sections are prescribed.

The code can

automatically generate variant hull forms differing from a parent In.

the main

dimensions and in one or more parameters such as Cp, LCF, LCB,

KB distribution, Cp etc.

When appropriate ranges for the principal characteristics and

parameters of the hull form under Investigation are prescribed, a

formal optimization procedure is used to obtain the variant with the

best seakeeping behaviour. The optimization procedure uses as

objective function the weighted average of a number of peak ship

responses In regular waves for a number of ship speeds and headings

and determines the optimum hull form using the HoOke and Jeeves

Algorithm.

The applicabfflty of the method is demonstrated using as examples a

reefer ship, a containership, a destroyer-type ship and a fishing vessel.

(2)

1. INTRODUCI'ION

Seakeeping Is the branch o Naval Architecture, which deals with the prediction of the dynamic behaviour of the ship in waves. Indeed, this

has been the main goal of Seakeeping from the development of the

first practical strip theory In 1955 by Korvin-Kroukovsky1 until 1980,

when Bales2 published a paper formally treating the optimization of

seakeeping performance of Destroyer-type hull forms. By that time

the analytical tools available to the profession have been shown to be

reliable enough to be used for optimization purposes, whereas

seakeeping experiments cannot be used for the same purpose due to

the excessive time and cost involved.

The description of the efforts of several researchers

In the area of

Seakeeping optimization during the last decade can be found In Ref. 3

by Grigoropoulos and Loukakis and a similar description of earlier

efforts can be found in Ref. 4.

In the aforementioned Ref. 3

a new method for

developing hull

forms with superior seakeeping qualities was presented. The new

method was used for the analytical development of an optimized hull

form for a reefer ship. Models of both the parent and the

optiinimum hull forms were tested at the Towing Tank of N.T.U.A. and the analytical predictions have been experimentally vetlfled.

The purpose of the present paper is to present additional results for

the reefer ship and to

further demonstrate the applicability of the new optimization procedure using three other hull forms:

a containership, a destroyer-type hull form and a fishing vessel.

2. SEAKEEPING CONSIDERATIONS IN SHIP DESIGN

AND THE NEW METHOD

The Incorporation of superior seakeeping qualities In

a new ship

design is obviously desirable, although seakeeping is not usually a

dominant parameter In the design process, especially for merchant ships.

(3)

However, recent studies have shown that seakeeping considerations

can and should be incorporated from the beginning in the design

procedure but that there is also room for considerable seakeeping

Improvements even when the displacement and the principal

characteristics

of a new design have been determined without any

seakeeping considerations.

The new method has been developed with the above two application areas In mind, that is It can either be incorporated directly in the

preliminary design spiral or It can be used to modify a parent hull

form.

In both cases the objective of the new procedure is not to ensure,

for example, that a hull. form will have less than a predetermined

amount of deck wetness in a specified sea state. Nobody designs

ships In this manner. The objective Is to ascertain that a ship designed with a very complex objective function and many practical

constraints In mind, will have as good seakeeping qualities as possible. The last reservation is In order because there are Indications

that Increased seaworthiness is usually accompanied by somewhat

increased resistance. However, as it will be discussed in the sequel, the interplay Is not really between seakeeping qualities and ship

resistance. Rather, the real problem Is how to ensure good

propulsion characteristics both In calm water and in waves, coupled

with good seakeeping performance. That Is the propulsion system of the ship should be Included in the optimization scheme.

3.. A BRIEF DESCRIPTION OF THE NEW METHOD

The new method for optimizing hull forms for seakeeping has been

described In detail In Refs. 3 and 5. However,

for the sake

of

completeness, the main tools and assumptions of the method and a

brief description of the formal optimization scheme will be presented

(4)

3.1 Hull Form Desrlption

The hull form is described lfl adequate detail for seakeeping

calculations, but In a simple form to allow for the generation of the

man variants required by the op;Irrj12tiOn scheme. Thus, the

hull form Is considered to be known If the following characteristics

are specified: the main dimensions LBP, B, T the sectional area curve S(x), the waterline curve B(x), the longftudinai profile curve Z(x) and

the curve of the loflgitudinal distribution of the centroids of the ship

sections KB(X).

From these curVes all traditional ship design variables can be derived

I.e. A, CB, Cp, CM, Cvp, Cp, LCB, LCF, KB e.t.c.

3.2 Hull Form Variants.

To obtain variant hull

forms from a parent,

described as above,

Lackenby' S6 method was extended so that waterlines and sectional

area curves of any shape can be accomodated and, more Important,

that any of the

six form parameters {Crp, LCF, CB, LCB CM,

KB(x)) can be. independently varied. Thus, vaiiant hull forms differing In one parameter otily can be generated and by successive

applications of the method, hull forms with prescribed values of these parameters are obtained.

3.3 AnalytIcal Tools for Seakeeping Calculation

As is common practice in all seakeeping optimization work a strip theory7 Is used for the calculations, coupled in the ptesent method

with a threepararneter LewLs-forrn representation of the ship

sections. In the Usual two-parameter Lewis-form representatiOn of

ship sections, the beam, the draft and the ectiona1 area. describe the

section. The aforementioned description of the hull form provides the

required third parameter KB(x), the centroid of the section. In this

manner, a more detailed description

of the hull

forth Is available,

which has been shown8 that it can have an important effect on the

(5)

calculations.

3.4 The figure Of metit

To obtain an optimum solution a figure of merit should be specified.

lii contrast to other methods, which In general use the seakeeping

performance at sea to define a flgure of merit, the present method

postulates that

"ship responses at sea are rninirrium when the corresponding

peak value of their Response Amplitude Operator (R.A.0) is minimum" and that, therefore. seakeeping optimization

can be athleed on the basis of regular wave results only.

Numerical compUtations have shown that this assertion is true for ships with displacement and dimensions close to those of the parent hull form.

However, the magnitude of the peak value Of the relatIve vertical

motion R.A.O. is not adequate to describe seakeeping events related

to the underwater part of the hull, as bottom slarnrriing and propeller ernergenée. Thus, these events can not be expUcitly lnàluded In the

optimization process and the correspondUg peforrnance of the

optimum hull form can be established only a posteriorl. This is a

slight shortcoming when, draft Is kept constant or Is changed only a

little

ftom the

parent, because the mjnimlzatlon of the relative

motion provides a strong indication that the corresponding seakeeping

events wifi also be reduced. 3.5 The optimization problem

With the previous discussion in mind, the opthnivtion problem. can

be stated as follows:

Find the variant with the optimum seakeeping performance of a parent hull form, described by the set of four curves S(x), B(x),

(6)

6

Z(x) and KB(x) and Identified by the set of design variables (LBP,

B, T, CB, C, LCB, LCF, KB) under given constraints.

Seakeeping performance Is expressed as

the wlghted sum of the

peak values of a prescribed set of ship responses In regular waves, for various ship speeds and headings. Optimum performance

corresponds to the minimum value of this sum, which Is the object

function of the problem.

The constraints to be Included In the optIrnI2atIon problem are

classified In the following two categories:

Equality conditions established by hydrostatic and stability considerations or economical reasoning.

Inequality constraints imposed by common design practice

limitations.

- In the first class of constraints the following relations are included:

The relation between the displacement, the main dimensions

and the block coefficient:

S = CB * LBP

* B * T

= constant

Geometrical relations that hold between the various form

parameters, Le.

I

CB=CV,rp*C\rp

I

CB= CM *CHP

In the second class of constraints the following Inequalities should be taken into account for reasons shown In parentheses:

I

LCB1<LCB<LCB2 ()

(7)

GM>GMM (transverse stability)

CWp1<CW<Crp2 (deck space, calm Water resistance)

CM1<CM<C,1j (calm water resistance)

The following characteristics of the opt ion problem can help In selecting the appropriate optimization method:

the non-linearity of the constraints

the existence of both equality and inequality constraints the unlmodality of the object function, experimentally

verified by setting up the optimization procedure from different starting points and arriving at the same result

O the continuous character of all decision variables.

On the basis of the above the direct optimization method proposed

by Hooke and

Jeeves9 In conjuction with the External Penalty

Function Method1° has been selected. The External Penalty Function Method is used to convert the constrained optimization problem to

an unconstrained one and Is more efficient than the Internal Penalty

Function Method. The method of Hooke and Jeeves is simple to

program and has found to be very effective for the particular

optimization problem in comparison to other direct search methods.

4. APPLICATIONS OF THE NEW METHOD

The optimization procedure has been applied In four cases, which will

be presented In this section. But before proceeding with the

presentation, it should be clarified here that the hull forms, which are

developed by the computer code, do not possess fair ship lines. The representation of their cross sections is

the one provided by the

three- parameter Lewis-form, see for example fig. 4. Thus, when the

optimization procedure has yielded an "optimum hull form", a set of ship lines which

incorporate as many of the

characteristics

of the

analytical calculations as possible, should be developed manually. Obviously, the seakeeping characteristics of this final hull form will be

(8)

8

corresponding to the afOre mentioned procedure will be 1abeled "parent", "optimum" and "faked opthnum".

For all cases treated, the object function necessary fOr the

optimization procedure was chosen as

the sum of the peak R.A.O.

values for vertical acceleration and relative motion ax

a point

0.1

LBp behind the forward perpendlicular. 4.1 The reefer ship case

For an Initial experimental verification of the optlinitatlOn procedut

the hull

form of

a

93.4 m long

reefer ship was selected and

optimized with respect only to secondary hull form parameter, i.e.

LCB, LCF and KB(x). In this way the contention, that even

with cOnstant principal characteristics the seakeeping performance of a

ship can be significantly improved, could be Validated..

The principal and secondary hull fotm characteristics of the "parent", "optimum" and 'Taired. optimum" for the reefer Vessel are shown in

Table 1. In the same Table the r.m.s. values for the vertical

acce1eraton and vertici telative motion ax a point 0.1 *LBp behind

the Forward Perpendicular are shown. The seakeeping resUlts pertain to a sea State With a significant wave height H'/3=4 m and a modal

period Tp=10 sec The ship speed for the calculations was 14 knots.

The constrained secondary hull form parameters were allowed to

change during the optimization as follows:

8(LCB, LCF)=±0.O4LBp, 8Cp=±0.04Cjp, 6KB=±O02T

From the contens of Table 1

it can be seen that In order to obtain

an optimum hull form

the procedure Increased C, shifted LCF

forward and shifted the VCB downwards, all as much as allowed. It

(9)

The optimized hull form had a considerable reduction In both

acceleration and relative motion in comparison to the. parent by 19%

and 21% respectIvely. However, when a set of ship lines had to be

produced, not all characteristics of the "optimum" hull form could be retained and the "faired optimum" hull form was developed for which

the reduction of the aforementioned responses was 13% and 16%

respectively. The body plan of the parent and the falred optimum hill forms are shown In Fig. 1.

PARENT HULL

- OPTIMUM HULL

'C

Fig. 1:. Body Plan of Parent and Faired Optimum Reefer Ship

- - - - I.

--

-WauJFihj

-

/ I...

/ 4111ArF &UF'.

-

I I / I,,! \\ - I /

A.

ii -

r ' /

- - ----

----

p. 2 2 I

(10)

Tahkl: Gcomctrfcil CharacterIstfc. and Seakeeping Responses of Optimization Examples

CASE L8p B' T Ap C8 Cp CM Cp LCB LCF KB V.ACC.. R.MOT.

[mj, [rn] [rn] [t] [m2] [%L.BP] [%LBp:J [rn] [m/s2] Em] REEFER PARENT 93.4 17.0 6.5 6108 1222 0.577 0.749 0.974 0.770 -3.23 -5.04 3.62 2.056 2.116 REEFER OPTIMUM CONSTANT LBPB,T 93.4 11.0 6.5 6108 1284 0.577 0.713 0:.1985' 0.809 -2.33 -0.98 3.49, 1:666 _19% 1.722 -21%

REEFER FAIRED OPT

CONSTANT L8.8.T 93.4 17.0 6:5 6108 1256 O577 0.730 0.979 0.790 -1.67 -1.24 3.64 1.793 -13% 1.821 -16% REEFER OPTIMUM 1 'VARIABLE L8.8 89.9 16.2 6.5 6108 1306 0.634 0.705 0.985 0.899 -2.21 -1.23 3.49 1.493 -27% 1.619 -26% REEFER OPTIMuM 2 VAP.IIABLE 98.1 16.2 6.5 .6108 1220 0.577 0.149 0.97.4 0.770 -3.23 -1.46 3.62 1.719 1.784 LBP,B -14% -18%

DESTROYER PARENT 128.0 15.1 4.2 3135 1359 0.450 0:639 O.759 0.704 -3.11 -6.41 2.58 2.112 2.016 DESTROYER. OPTIM. CONSTANT 128.0 15.1 4.2 3735 1438 0.450 0.604 0.747 '0.745 -2.98 2.60 2.49 1.721 1.689 LBP.BT -21% -16% CONTAINER' PARENT 11,75.0 25.4 9.5 244.94 3153 '0.566 '0.1,98 01.957 0.709 -2.01 -3.91 5.20 1.115 '2.036 CONTAFNER OPT'I'M. '175.0 CONSTANT L8B.T 25:4 9..,5 24494 3293 0:566 0.764 ogs8 0.741 -1.00 0.32 . 5.01 0.1910 -18% 1.722 -15% IRLIIANTIIU I'Ak[NI 12 96 3 826 1 0 20 2 30 60 0 396 0 641 0 720 0 618 -3 31 -0 05 0 60 3 010 0 432 TREHANTI'RII OPTIM, CONSTANT L8,B..T. 12.96 3.826 1.0 20.2 31.65 '0.396 0.62.1 0.71.9 0.638 0.46 3.52 0.58 2.680 -'11% 0.367 -15% iR[IIA.FAIQID OPT. CONSTAW[ 12.96 3.626 1.0 20.4 31.20 O.'iO4 0..63 0.113 0.634 -1.91 0.98 0.61 2.802 0.402 L8pB..T -7% -1%

(11)

N S N T0 0 A.V.A. = Absolute Vertical Acceleration R.V.M. = Relative Vertical Motion

Fig. 2: Analytical and Experimental Responses. Reefer Ship.

V5=14 knots. ANALYTICAL RESULTS PARENT HULL

- OPTiMUM HULL

EXPERIMENTAL. RESULTS * PARENT HULL S QPTIMTJM HULL

(12)

-N N N C' C 12 ANALYTICAL RESULTS PARENT HULL

- OPTIMUM HULL

EXPERiMENTAL RESULTS * PARENT HULL o OPTIMUM HULL

Fig. 3 : Analytical and Experimental Responses. Reefer Ship.

(13)

Two meter models with these lines have been bull and tested In the Towing Tank of NTUA for both resistance and seakeepitig. As it has

been reported in Ref. 3, the resistance Characteristics

of the two

models were quite sitnilar with the parent being somewhat better at the higher speeds, whereas the optimized hull fOrm was superior to

the parent In waves, as predicted. The analytically determined r.m.s.

vertical acceleration and vertical

relative motion for the two hull

forms Is shown In FIgs. 2 and 3 for ship speeds V5=l4 knotS and 17

knots. As it can be seen frrr these figures the superior seakeeping

performance of the optimized hull form Is preserved for all sea

states and headings and for the higher speed, whereas the

optimization was done for head seas and V5=l4 knots only. On the

same figures the experimental results are plotted

and one

can

observe that the predicted differences in seakeeping performance are

to a large extent verified experimentally, even though the absolute values of the responses might not be predicted accurately by strip theory calculations, as Is hi particular true for the relative motion

response.

To further demonstrate the Use of the method, the optimization was

performed on the reefer hull form under the following constraints:

z,T=constant, 8LBp=±O.O5LBp, 8B=±O.05B

ÔCB=±O.1CB, ÔKB±O.02T, 6(LCB,LCF)=±O.O4Ls

In this case no restriction was imposed on Cp but the waterplane

area was allowed to increase by up to 7%.

The results of this optimization are aLso shown In Table 1, where the case is denoted as "Reefer Optimum 1". In this case the optimization

has yielded a shorter, less bearny and fatter ship, with a very large

waterplane coefficient. The vertical acceleration and relative motion in

this case are further reduced by 27% and 26% respectively, but the resulting hull form Is not practical from the resistance point of view due to the excessive waterplane coefficient.

(14)

14

The final optimization example for the reefer ship Is also shown in

Table I and Is denoted as "Reefer OptImum 2". The constraints

imposed In this case are the same as for the previous except for the

value of Cp, which is kept constant. As It can be seen from the

Table, the optimum hull form Is longer, narrower and with LCF

shifted considerably fOrwards. The rrns values for vertical acceleration and relative motion are reduced by 14% and 18% respectively. If this

hull form has also reduced resistance characteristics, It might

represent a better alternative for the final product than the parent.

An indication of the relative resistance characteristics between the two hull forms can be obtained using the FORMDATA method which

gives a 10% advantage in resistance to the optimized hull form for a ship speed of 17 knots.

4.2 The contalflership case

As a second example, the hull form of a successful large containership was selected for optimization. This hull form, denoted as S-175, Is being used by the International Towing Tank Conference as a vehicle for comparative seakeeping studies and in this case the

accuracy !

analytical results has been verified experimentally. The

optimization was performed on the secondary hull form parameters only and the results are shown also in Table 1. The body plans of

the two hull: forms, In three -parameter Lewis-form representation are

shown in FIg. 4. The ship speed of the optimization corresponds to

Fr.No.=0.2 and the sea state is

the same as

for the reefer ship.

From the contents of the Table It can be concluded that by increasing Crp, moving LCB and LCF forwards and lowering VCB, the vertical

acceleration and relative motion are reduced by 18% and 15%

respectively. The analytically determined, i-ms vertical acceleration for

(15)

Fig. 4 Body Plan of Parent and Optimum Containership. Lewis-form

representation

4.3 The Destroyer-type case

The characteristics

of the parent and the optimum hull

form are

shown in Table 1. On the basis of the optimization results, which was performed on the secondary hull form parameters only, at Fr.No=O.3

and for the same as previously sea state,. it can again be concluded that by increasing C, moving LCB and LCF forwards and lowering

VCB, the vertical acceleration and relative motion can be reduced by 21% and 16% respectively. The anaiytically predicted ship responses for the two hull forms are shown in Fig. 6.

\\\i\

\ \

\\

\

\ ,' \ \

\,

\\\

'.

\

\\\\\

\\

\

'\:

\

\

\

\

v,

/1.../I/1i//

/

Ii ,./

/

/ / /

/

/1 1 1

f

I,

/

/ /

/1 ,/

,/

/

#/.

/

/ (;I

i';'

/

,/.f/

PARENT HULL OPTIMUM HULL

(16)

-16

ANALYTICAL RESULTS PARENT HULL

- OPTIMUM HULL

(17)

ANALYTICAL RESULTS PARENT HULL

- OPTIMUM HULL

Fig. 6 Analytical Responses of Destroyer-type Hull Form.

(18)

4.4 The fishing vessel case

The final example of seakeeping optimization pertains to a hull form

particular to fishing vessels of the Trehantiri type, which abound In

Greek waters. By performing the optimization for the secondary hull form parameters only, at a ship speed corresponding to Fr.No.=O.3 and for a sea state with a significant wave height H1/3=1.2 m and a

modal period Tp=5.48 sec, the results of Table 1 were obtained. The

optimum result was again achieved by increasing Cp, moving LCF

and LCF forwards considerably and somewhat lowering VCB. After these modifications the values of the vertical acceleration and relative motion were reduced by 11% and 15% respectively. Nevertheless, no

hull form reminiscent of a trehantiri could be designed on the basis

of these characteristics. When, finally,

a set of ilnes was produced,

the computed seakeeping performance did not show considerable

Improvement. The characteristics of the parent, optimum and faired

optimum trehantiri hull forms are shown In Table 1. The body plans

of the parent and the faired optimum are shown In

Fig. 7 and the

analytically computed seakeeping performance of these two hull forms Is shown In Fig. 8.

18

PARENT :HULL - OFTIMUM: HULL

Fig. 7 : Body Plan of Parent and Faired Optimum Fishing Vessel.

--

-:

2 ( -I

,J

4/

\.

...

II

S

/

L

:

N

(19)

ANALYTICAL RESULTS PARENT HULL

- OPTIMUM HULL

(20)

20

5. DISCUSSION AND CONCLUSIONS

The main advantages of the present seakeeping optimization method

can. be summarized as follows:

The use of the three-parameter Lewis-form representation of

the ship sections allows the desirabifity of U forms or V form to be Investigated.

The method Is suitable for immediate incorporation in the

preliminary design spiral and It can readily accommodate all necessary design constraints.

The method Is very efficient so that It can nm on a personal computer as It circumvents the need of computing both the full

R.A..O. and the performance at sea for all hull form variants. The method does not. depend on empirically imposed seakeeping

criteria.

The method Is complemented by the suggestion that the final

assessment of seakeeping performance should include propul-sive performance In waves.

To ifiustrate the last of the above points, the powering diagrams of

both the parent and the optimum hull form of the reefer ship are

shown in Fig. 9. The iflvoluntary speed reduction curves are computed by taking, Into account the added resLstance in waves and computing

the maximum attainable ship speed on the basis of the engine and propellet characteristics (assumed to be the same for both ships in this case). From these curves It can be concluded that the reduced

added resistance of the optimum ship compensates in the higher sea

states for her slightly higher calm water resistance. The voluntary

speed reduction curves, which complement the powering diagram,

indicate that the vertical acceleration has reached a predetermined

limit. The combined Involuntary-voluntary speed reduction curve

determines the region of operation of the vessel at sea arid therefore it describes the capability of the Vessel to fulfill Its transport mission

economically. The expanded region of operation

of the

optimized

vessel Is a very strong indication of the effect of good seakeeping

characteristics on overall ship performance.

(21)

most obvious changes ifl hull fOrm geometry, which are beneficial to

seakeeping, are the Increase of the waterplane area and the shifting

of Its center of area forwards. As these changes are usually accompanied by an Increase in ship resistance, one has to be careful In specifying the amount of permissible changes In the values of these parameters. More generally, all constraints should be specified by an

experienced Naval Architect., since creative ship design cannot be done

by the computer alone.

All optimization examples were performed with respect. to vertical

motions only. This is adequate because lateral motions, especially roll, can be treated by blldge keel design, rudder and skeg design,

anti-rolling devices, changes in GM etc.

Finally, it seems that the optifliization procedure Is insensitive to ship speed and/or heading, which greatly reduces the computation effort.

On the basis of the above it can be concluded that the inclusion of

the seakeeping performance In ship design Is both desirable and possible by the use of the method presented herein.

18

is

14 12 1 C' I. nvolutitary SDeec : 11.85 kn OPTIMUM _ 0RM PARENT 0RM

- .-.

_kj2

! eCk Wetness ano S1ar;

\

I=4.L1m

Absolute Vertical Acceleration at 10% of LBP aft of F.P.

(0.2 g rins)

Criteria are not eceeCe

Vo i untary

Soeeø Reudt ion

4

_6

Hi/a rrj

Fig. 9: Powering Diagram in Waves. Reefer Ship in Fully

Developed Head Seas.

(22)

6. LIST OF REFERENCES

Korvin-Kroukovsky, B.V.(1955). IEivestlgatlon of Ship Motions In

Regular Waves. Trans. SNAME, VoL 63

Bales NK. (1980). OptimIzing the Seakeeping Performance of

Destroyer-Type Hulls, 13th ONR Symp on Naval Hydrodynamics Tokyo, Japan.

Grigoropoulas G.J. and Loukakls TA. (1988). A New Method for Developing Hull Forms with Superior Seakeeping Qualltles. CADMO 88. Southampton. Great Britain.

Report of the Seakceping Committee. 17th I.T.T.C. (1984)

Gdteborg, Sweden.

Grigoropoulos GJ. (1988). Hull Form Optimization with Respect to Seakeeping, Ph.D. Thesis,, N.TIJ.A., Athens, Greece

Lackenby H. (1950). On the Systematic Geometrical Variation of Ship Forms, Trans. INA, Vol. 92, p. 289.

Salvesen N., Tuck E.O. and Faltlnsen 0. (1970). Ship Motions and Sea Loads, Trans. SNAME, Vol. 78, pp. 250-287.

Athanassoulls GA. & Loukakis TA. (1985). An Extended-Lewis

Form Family of Ship Sections and Its. Applications to Seakeeping

Calculations, LS.P., Vol. 32, No.366, pp.33-43.

Hooke

R. & Jeeves TA.

(1961). DIrect Search Solution of

Numerical and Statistical Problems, Journal of Assoc. for Computing Machinery, VoL8, No.4, p. 212.

Wangdahl G.E. (1972). The External Penalty Function

Optimization Technique and Its Application to Ship Design, The Uzth. of Michigan, Ann Arbor, Rep. No.129.

Cytaty

Powiązane dokumenty

The method gives a good approximation of nor- mal hull forms; this is illustrated in Figure 1 which shows the body plan of a standard frigate hull form and the form described by

Od ukazania się drugiej publikacji, o której chciałbym wspomnieć, upłynęło już trochę wody (nie tylko w Zawichoście). Pewnym frag- mentem owej publikacji nikt się chyba dotąd

Jako dyscyplina akademicka AI pojawiła się na przełomie XX/XXI wieku, zajmuje się problematyką projektowania i organizacji informacji w różnych postaciach z uwzględnieniem

13 Tak pisał o tym Rimantas Miknys w nekrologu Rimantasa Vebry: „Jako pierwszy rozpoczął analizę teoretycznych aspektów historii odrodzenia: kwestii periodyzacji,

Tajemnica Trójcy Przenajświętszej ukazuje się stopniowo przez adora- cję 104. Wiara nie jest więc wyłącznie doktryną do przyjęcia, lecz zakorzenia się w

W całej dziedzinie poezji rom antycznej, nie tylko na obszarze liryki, dostrzega się owe w spółdziałanie czynników em ocjonalnych i wyobrażeniow ych; z w zajem

Drogiemu Księdzu, jako Redaktorowi Naczelnemu pisma „ S a h a ­ toris Mater” oraz wszystkim Współpracownikom na dalszą owocną działalność Ojciec Święty z serca

Artykuł umieszczony jest w kolekcji cyfrowej bazhum.muzhp.pl, gromadzącej zawartość polskich czasopism humanistycznych i społecznych, tworzonej przez Muzeum Historii Polski