A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates
The second basic dynamic problem for thin elastic plates in Kirchhoff model is under consideration. The problem reduces to system of the nonstationary boundary equations by means of dynamic analogue of a single layer potential. The numerical solutions of these systems have been obtained. The investi...
Gespeichert in:
| Datum: | 2011 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України
2011
|
| Schriftenreihe: | Управляющие системы и машины |
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/82911 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates / Yu.S. Shuvalova, E.A. Strelnikova // Управляющие системы и машины. — 2011. — № 1. — С. 57-62. — Бібліогр.: 15 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-82911 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-829112025-02-23T20:18:26Z A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates Метод интегральных уравнений для структуры в форме тонких упругих пластин Метод інтегральних рівнянь для структури в формі тонких пружних пластин Shuvalova, Yu.S. Strelnikova, E.A. Технические средства информатики The second basic dynamic problem for thin elastic plates in Kirchhoff model is under consideration. The problem reduces to system of the nonstationary boundary equations by means of dynamic analogue of a single layer potential. The numerical solutions of these systems have been obtained. The investigation of convergence of method of discrete singularities for the plate of the rectangular form have been carried out. Рассмотрена вторая основная задача динамики тонких упругих пластин в рамках модели Кирхгофа. С помощью динамического аналога потенциала простого слоя задача сводится к системе нестационарных граничных уравнений. Получены численные решения этих систем. Исследованы сходимости метода дискретных особенностей для прямоугольной пластины. Розглянуто другу основну задачу динаміки тонких пружних пластин у рамках моделі Кірхгофа. За допомогою динамічного аналога потенціалу простого шару задача зводиться до системи нестаціонарних граничних рівнянь. Одержано чисельні розв’язки цих систем. Досліджено збіжності методу дискретних особливостей для прямокутної пластини. 2011 Article A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates / Yu.S. Shuvalova, E.A. Strelnikova // Управляющие системы и машины. — 2011. — № 1. — С. 57-62. — Бібліогр.: 15 назв. — англ. 0130-5395 https://nasplib.isofts.kiev.ua/handle/123456789/82911 539.3: 517.968+517.956 en Управляющие системы и машины application/pdf Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| topic |
Технические средства информатики Технические средства информатики |
| spellingShingle |
Технические средства информатики Технические средства информатики Shuvalova, Yu.S. Strelnikova, E.A. A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates Управляющие системы и машины |
| description |
The second basic dynamic problem for thin elastic plates in Kirchhoff model is under consideration. The problem reduces to system of the nonstationary boundary equations by means of dynamic analogue of a single layer potential. The numerical solutions of these systems have been obtained. The investigation of convergence of method of discrete singularities for the plate of the rectangular form have been carried out. |
| format |
Article |
| author |
Shuvalova, Yu.S. Strelnikova, E.A. |
| author_facet |
Shuvalova, Yu.S. Strelnikova, E.A. |
| author_sort |
Shuvalova, Yu.S. |
| title |
A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates |
| title_short |
A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates |
| title_full |
A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates |
| title_fullStr |
A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates |
| title_full_unstemmed |
A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates |
| title_sort |
method of integral equations for a structure in the form of thin elastic plates |
| publisher |
Міжнародний науково-навчальний центр інформаційних технологій і систем НАН та МОН України |
| publishDate |
2011 |
| topic_facet |
Технические средства информатики |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/82911 |
| citation_txt |
A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates / Yu.S. Shuvalova, E.A. Strelnikova // Управляющие системы и машины. — 2011. — № 1. — С. 57-62. — Бібліогр.: 15 назв. — англ. |
| series |
Управляющие системы и машины |
| work_keys_str_mv |
AT shuvalovayus amethodofintegralequationsforastructureintheformofthinelasticplates AT strelnikovaea amethodofintegralequationsforastructureintheformofthinelasticplates AT shuvalovayus metodintegralʹnyhuravnenijdlâstrukturyvformetonkihuprugihplastin AT strelnikovaea metodintegralʹnyhuravnenijdlâstrukturyvformetonkihuprugihplastin AT shuvalovayus metodíntegralʹnihrívnânʹdlâstrukturivformítonkihpružnihplastin AT strelnikovaea metodíntegralʹnihrívnânʹdlâstrukturivformítonkihpružnihplastin AT shuvalovayus methodofintegralequationsforastructureintheformofthinelasticplates AT strelnikovaea methodofintegralequationsforastructureintheformofthinelasticplates |
| first_indexed |
2025-11-25T03:57:25Z |
| last_indexed |
2025-11-25T03:57:25Z |
| _version_ |
1849733204008763392 |
| fulltext |
УСиМ, 2011, № 1 57
УДК 539.3: 517.968+517.956
Yu.S. Shuvalova, E.A. Strelnikova
A Method of Integral Equations for a Structure in the Form of Thin Elastic Plates
Рассмотрена вторая основная задача динамики тонких упругих пластин в рамках модели Кирхгофа. С помощью динамическо-
го аналога потенциала простого слоя задача сводится к системе нестационарных граничных уравнений. Получены численные
решения этих систем. Исследованы сходимости метода дискретных особенностей для прямоугольной пластины.
The second basic dynamic problem for thin elastic plates in Kirchhoff model is under consideration. The problem reduces to system of the non-
stationary boundary equations by means of dynamic analogue of a single layer potential. The numerical solutions of these systems have been
obtained. The investigation of convergence of method of discrete singularities for the plate of the rectangular form have been carried out.
Розглянуто другу основну задачу динаміки тонких пружних пластин у рамках моделі Кірхгофа. За допомогою динамічного
аналога потенціалу простого шару задача зводиться до системи нестаціонарних граничних рівнянь. Одержано чисельні
розв’язки цих систем. Досліджено збіжності методу дискретних особливостей для прямокутної пластини.
Introduction. Thin elastic plates are elements of
numerous structures being used in aerospace and
electronic engineering and many other industries.
That is why the development of the methods for a
calculation of strains arising in a plate is a very
important problem. The potential theory method is
suggested in the article to reduce the problems to
the systems of non-stationary boundary equations.
The plate of the rectangular form and the plate
with a square hole are considered for the further
numerical calculation. The method of the research
is based on the scheme developed in [1–4] for the
problems of elastodynamics and in [5–7] for the
transient diffraction problems for acoustic and
electromagnetic waves. The modern studied prob-
lems of mathematical modeling of thin elastic
plates also are directed to researches of floating
structures such as an ice cover of ocean, super-
tankers, floating platform (Megafloat), etc [8–13].
Notation and statement of the problem
A thin elastic plate of thickness consth oc-
cupying a domain ;
2 2
h h
, is considered,
where is bounded by a closed C2-curve .
From the standard Kirchhoff hypotheses it follows
that the displacement vector at 3( ; )x x , where
1 2( ; )x x x , has a form 3 1( ( , );x u x t 3 2 ( , );x u x t
, )u x t . ( , )u x t is the displacement of the middle
plane of the plate, , 1, 2i
i
i
x
. For the sake
of simplicity we consider only the homogeneous
case, i.e. the case of zero loading and zero initial
data. This does not lead to a loss of generality
since the existing of non-homogeneities can be
transferred to the boundary conditions. The func-
tion ( , )u x t satisfies the problem
2 2
1
2
ρ ( , ) ( , ) 0, ( , ) ;
( ,0) 0,
;
( ,0) 0,
( )( , ) ( , ),
( , ) ;
( )( , ) ( , ),
t
t
h u x t D u x t x t R
u x
x
u x
Qu x t g x t
x t R
Mu x t g x t
(1)
where
2 2
1 2 2 1
2 2
1 2 1 2
(1 ) [ ( )
( ) ] ,
nQu D u n n u u
n n u
2 2 2 2
1 2 1 2 2 1 1 2
(1 )
[2 ]
Mu D u
n n u n u n u
are the operations that correspond to the genera-
lized cutting force and the bending moment,
(0; )R ,
ρ
D
D
h
, t t
, n is the normal
derivative, 1 2( ) ( , )n x n n is a unit outward nor-
mal to , is the surface density of the plate, D
is its cylindrical stiffness, is the tangent deriva-
tive to and unit vector is obtained by turning
n on the angle
π
2
against the hour-hand.
Later on let us consider the interior II and ex-
terior II problems in interior domains
and 2 \R , respectively.
58 УСиМ, 2011, № 1
Function spaces
We introduce the function spaces by the sche-
me used in [15]. We choose and fix 0 . De-
note { : p> }C p C e . Let ; , , ( )L m kH and
; , , ( )L m kH be the spaces of functions ( )U p
( , ),u x p x , ( ) ( , ),F p f x p x , p C ,
respectively, are homeomorphisms from C to
standard Sobolev spaces ( )mH , ( )mH with
their finite norms
2 22
, , ; , ;σ
2 22
, , ; , ;σ
sup (1 ) τ,
σ τ.
sup (1 ) τ,
k
m k m p
k
m k m p
u p u d
p i
f p f d
Let ,G R R
and let L be the
Laplace transformation operator. The spaces
; , , ( )r m kH G
and ; , , ( )r m kH
consist of the in-
verse Laplace transformations 1( , ) ( , )u x t L u x p
and 1( , ) ( , )f x t L f x p of elements ( )u x, p
; , , ( )L m kH and ; , ,( ) ( )L m kf x, p H
respec-
tively. The norms of these spaces are defined by
, , ; , , ; , , ; , , ;
, .
m k G m k m k m k
u Lu f Lf
Let G R
. Denote by χ the trace op-
erators that are continuous from ; , , ( )r m kH G
to
1 3; , , ; , ,2 2
( ) ( )
r m k r m k
H H
for 3 , .2m k R
The element χ u
is the couple consisting of the
traces of ( , )u x t and nu on .
The solution of the problems is the element
;2,0,( , ) ( )ru x t H G
that satisfies
0 0
( , ) ,χ ,t t
G
a u v dt u vdxdt g v dt
(2)
for an arbitrary ( , ) ( )v x t C G with the com-
pact support. In (2) 1 2( , )g g g
and
0,
,χg v
is
the inner
22 ( )L -product.
Theorem 1. For any 1 2 3:- , ,2
, ( )
r k
g g g H
1:- , ,2
( ),
r k
H
, 0,k R the problems II ha-
ve the unique solutions ;2, 1( , ) ( )r k ,u x t H G
for
all 1, 0.k The estimates
3 11 22, 1, ; , , ; , , ;2 2k G k k
u c g g
hold, where c is some positive constant.
The dynamic single layer potentials
Let ( , )x t be the fundamental solution of the
equation of oscillations that satisfies
2 2( , ) ( , ) δ( , ),
( , ) 0, 0,
t x t D x t x t
x t t
where δ( , )x t is the Dirac function.
It is easy to verify that
2
θ( )
( , ) ,
4π 4
xt
x t si
D t D
where
sinμ
( ) μ
μz
si z d
and θ( )t is the charac-
teristic function of (0; ) . The dynamic single
layer potential with a defined on R two-
component density α( , )x t
is introduced by
1
R
, 2
( α)( , ) ( , τ)α ( , τ)
( , τ)α ( , τ) τ,n y y
V x t x y t y
x y t y ds d
where n,y is the normal derivative with respect to y.
Obviously at least for the smooth finite densi-
ties on R the potential satisfies in R the
homogeneous oscillation equation. If the densities
vanish as 0t then the potential satisfy the zero
initial data. The single layer potential and its first
derivatives are continuous when a point goes
across the boundary curve. The jump formulae for
the single layer potentials has the form
1
0
2
0
( α) ( , ) α ( , )
( α) ( , ),
( , ) ,
( α) ( , ) α ( , )
( α) ( , ),
QV x t x t
QV x t
x t R
MV x t x t
MV x t
(3)
where the superscripts «» denote the limiting value
of the corresponding functions when ( , )x t tends to
R from R
and the superscript «0» deno-
tes the direct value of the corresponding integral.
УСиМ, 2011, № 1 59
The representation of the solutions of the prob-
lem (1) by the single layer potential yields the sys-
tems
1
2
( ) ( , ) ( , ),
( , )
( ) ( , ) ( , ),
QV x t g x t
x t R
MV x t g x t
. (4)
The solvability of the system (4) is proved in a
one-parameter scale of Sobolev-type function in
[14].
Theorem 2. For all 3; , ,2
H
r k
g
1; , ,2r k
H
, 1, 0k the potentials ( α)( , )V x t
,
with densities α( , )x t
that are the solutions of (4),
are the solutions ;2, 1, ( )r ku H G
of the prob-
lems II .
Systems of the boundary equations
The plate of the rectangular form and the plate
with a square hole are considered (fig. 1, 2).
Fig. 1
Fig. 2
The obvious kind of the boundary equations
system (4) is received, taking into account the
jump formulae (3). For example, the equations on
1 : 1( ;0)x x , 10 x a , look like
1
1 1
2 12 12
1
1
α ( ,0, )
2
θ( )(1 )
α ( ,0, ) ( , )
4 π( )
x t
t
s t Q x s t ds
D x s
4
1 1 1 2 2 1
2
α ( , ) ( , , ) α ( , ) ( , , )
i
i i
i
s t Q s x t s t Q s x t ds
1
2 2
142 2
10
α ( ,0, ) α ( ,0, τ)
( ) ( τ)
s t s
Q ds
x s t
4
1 1
32
2
2 2
4 1 12
α ( , ) α ( , τ)
( τ)
α ( , ) α ( , τ)
τ ( , ).
( τ)
i
i
i
i
s t s
Q
t
s t s
Q ds d g x t
t
1
2 1 1 11 1
1
α ( ,0, ) α ( ,0, ) ( , , )
2
x t s t M s x t ds
4
1 1 1 2 2 1
2
α ( , ) ( , , ) α ( , ) ( , , )
i
i i
i
s t M s x t s t M s x t ds
1
1 1
13
0
α ( ,0, ) α ( ,0, τ)
( τ)
s t s
M ds
t
4
1 1
3
2
2 2
4 2 12
α ( , ) α ( , τ)
( τ)
α ( , ) α ( , τ)
τ ( , ).
( τ)
i
i
i
i
s t s
M
t
s t s
M ds d g x t
t
ijM , ijQ , 1, 4, 1, 2i j are integrated on t, and
have no features on a spatial variable. The func-
tions
1 1
1 1 1
1 1
1
0
( , )
θ( ) ( , ) sin
( , )
θ( τ)sin τ,
( τ)
i
i i
i
i
w x s
M t m x s t
t
w x s
p t d
t
2 1
2 2 1
2 1
2 1
( , )
θ( ) ( , ) cos
( , )
θ( ) ( , ) sin ,
i
i i
i
i
w x s
M t m x s
t
w x s
t p x s t
t
1 1
1 1 1
1 1
1 1
( , )
θ( ) ( , ) cos
( , )
θ( ) ( , ) sin ,
i
i i
i
i
v x s
Q t q x s
t
v x s
t h x s t
t
60 УСиМ, 2011, № 1
2 1
22 2 1
2 1 2 1
2 2 1
( , )1
θ( ) ( , ) sin
( , ) ( , )
θ( ) cos θ( ) ( , ) sin .
i
i
i i
i i
v x s
Q t q x s
t t
v x s v x s
t h t z x s t
t t
ijM , ijQ , 1, 4, 3, 4i j have no singularities.
The results turn out similar on other sides of the
border.
Calculation results
Let us consider the interior problem. The plate
has the sizes 1 1 0,1 (m), the Poison coeffi-
cient 0,3 , the density 3ρ 7800 /kg m , Yuong
module 2,1 10E MPa . The boundaries of a pla-
te are free. Thus the problem
2 2ρ ( , ) ( , ) ( , ),
( , ) (0;1) (0;1)
( ,0) 0,
(0;1) (0;1)
( ,0) 0,
( )( , ) 0,
( , )
( )( , ) 0,
t
t
h u x t D u x t q x t
x t R
u x
x
u x
Qu x t
x t R
Mu x t
(5)
is solved. Let’s consider various kinds of loads.
The point displacements of medial plane of a plate
under loads 0 sinq q t and 2 2
0 ( 2) ( 9)q q t t
are represented in fig. 3 and fig. 4, respectively
( 1 2 0,5x x ).
Fig. 3
Also let us solve an exterior problem. The plate
with the square hole of the sizes 1 1 0,1 (m) is
under consideration for Poison coefficient 0,3 ,
plate density 3ρ 7800 /kg m , Yuong module E =
= 2,1 10Mpa. The boundaries of a plate are free.
Fig. 4
The problem
2 2
( ;0) (1; ) ( ;0) (1; )
( , )
ρ ( , ) ( , ) ( , ), ( , )
( ;0) (1; ) ( ;0) (1; )
( ,0) 0,
( ,0) 0,
( )( , ) 0,
( )( , ) 0,
t
t
x
x t R
h u x t D u x t q x t x t
R
u x
u x
Qu x t
Mu x t
is solved. Let us consider various kinds of loads.
The point displacements of a medial plane of plate
under loads 0 sinq q t and 2 2
0 ( 6) ( 9)q q t t
are represented in fig. 5 and fig. 6, respectively
( 2 0,5x ).
Fig. 5
Later on we consider the plate point dis-
placements in various time moments under load
0 sinq q t for the interior (fig. 7) and the exterior
(fig. 8) problems.
УСиМ, 2011, № 1 61
Fig. 6
Fig. 7
Fig. 8
Investigation of the convergence of the me-
thod of discrete singularities
The grid on space and time variable is changed
to research the method convergence. The problem
(5) is considered. The displacement in a plate cen-
ter is considered for the grid with a time step
π π π
, ,
6 10 15
t t t (fig. 9) and for the grid
with a space step
1 1 1
, ,
8 12 15i i ix x x . The
close results are received. So, it allows to make a
conclusion about the method convergence.
Fig. 9
Fig. 10
Conclusion
The second basic initial–boundary– value prob-
lems for thin elastic plate are under considera-
tions. Its purpose is to prove the results about
unique solvability of boundary equations systems
that appear as a result one solves the correspond-
ing mixed initial–boundary–value problems by the
potential theory methods. The potential theory al-
lowed finding the unknown quantities on domain
boundary without any calculations in the whole
domain and also makes it possible to study the
uniformity internal and external problems.
62 УСиМ, 2011, № 1
In the work the solutions of dynamic problems
are represented by the surface potentials of a sin-
gle layer. These surface potentials are constructed
on the basis of a fundamental solution of a thin
elastic plate oscillations equation. The representa-
tion by surface potentials leads to a boundary sys-
tem with respect to the unknown densities of a
potential. To prove the unique solvability of these
boundary systems, the Laplase transformation for
a time variable is used in the boundary systems
and also in the corresponding initial problems.
The results about solvability of elliptic problems
with parameters are used and the boundary opera-
tors properties which arise in stationary systems
with a parameter following that transformation are
investigated. The study of the dependence of the
boundary operators on the Laplace transformation
parameter, their bijectivity and holomorphic ones
in a right-hand half-plane of the complex plane,
after returning to the original space makes it pos-
sible to prove a theorem about the solvability of
the initial boundary equation systems in one-para-
meter scale of functional spaces of a Sobolev type.
The obtained results create the sound base for
constructing the corresponding convergent nume-
rical methods.
1. Chudinovich I.Yu. The boundary equation method in
the third initial boundary value problem of the theory
of elasticity. Part 1. Existence theorems // Mathemati-
cal Methods in the Applied Sciences. 1993. 16, Is-
sue 3. P. 203215.
2. Chudinovich I.Yu. The boundary equation method in
the third initial boundary value problem of the theory
of elasticity. Part 2. Methods for approximate solutions
// Ibid. P. 217227.
3. Chudinovich I.Yu. Boundary equations in dynamic
problems of the theory of elasticity // Acta Applican-
dae Mathematicae. 2001. 65. P. 169–183.
4. Чудинович И.Ю. К решению граничных уравнений
в задачах дифракции упругих волн на простран-
ственных трещинах // Дифференциальные уравне-
ния. 1993. № 29. C. 1648–1651.
5. Chudinovich I.Yu., Dieng S. Potential theory methods in
diffraction problems for acoustic waves // C.R. Acad.
Sci. Paris. 1995. 320. P. 885889.
6. Chudinovich I.Yu., Dieng S. The solvability of the boun-
dary equations of the transient diffraction of acoustic
waves on manifolds having a boundary. // C.R. Acad.
Sci. Paris. 1995. 320. P. 10191023.
7. Chudinovich I.Yu. The solvability of boundary equa-
tions in mixed problems for nonstationary Maxwell`s
system // Mathematical Methods in the Applied Sci-
ences 1997. 20, Issue 5. P. 425448.
8. Hazard Ch. Spectral Theory For an Elastic Thin Plate
Floating on Water of Finite Depth // SIAM J. Appl.
Math. 2007. 68, Issue 3. P. 629–647.
9. Linton СМ., Chung H. Reflection and transmission at
the ocean/sea-ice boundary // Wave Motion. 2003.
38, N 1. P. 43–52
10. Кулешов А.А., Мымрин В.В., Разгулин А.В. О сильной
сходимости разностных аппроксимаций задачи по-
перечных колебаний тонких упругих пластин // Ж.
Вычисл. матем. и матем. физ. 2009. 49, № 1.
С. 152–177.
11. Кулешов А.А. О численном методе решения задачи
поперечных колебаний тонких упругих пластин
// Матем. моделирование. 2005. 17, № 4. С. 10–26.
12. Одиноков В.И., Сергеева A.M., Захарова Е.А. Постро-
ение математической модели для численного ана-
лиза процесса разрушения ледяного покрова // Там
же. 2008. 20, № 12. C. 15–26.
13. Ткачева Л.А. Гидроупругое поведение плавающей
пластины на волнах // ПМиТФ. 2001. 42, № 6.
C. 79–85.
14. Gassan Yu.S., Chudinovich I.Yu. Boundary Equations
in basic Dynanic Problems for Thin Elastic Plates //
Вiсн. Харк. нац. ун-ту, Серiя «Математика, при-
кладна математика i механіка». 2000. № 475.
С. 250258.
15. Агранович М.С., Вишик М.И. Эллиптические задачи с
параметром и параболические задачи общего вида
// Успехи матем. наук. 1964. 19, 3. С. 53161.
Поступила 11.11.2010
Тел. для справок: (0572) 742-3568 (Харьков)
E-mail: Yul0k@mail.ru, estrel@ipmach.kharkov.ua
© Yu.S. Shuvalova, E.A. Strelnikova, 2011
<<
/ASCII85EncodePages false
/AllowTransparency false
/AutoPositionEPSFiles true
/AutoRotatePages /None
/Binding /Left
/CalGrayProfile (Dot Gain 20%)
/CalRGBProfile (sRGB IEC61966-2.1)
/CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2)
/sRGBProfile (sRGB IEC61966-2.1)
/CannotEmbedFontPolicy /Error
/CompatibilityLevel 1.4
/CompressObjects /Tags
/CompressPages true
/ConvertImagesToIndexed true
/PassThroughJPEGImages true
/CreateJobTicket false
/DefaultRenderingIntent /Default
/DetectBlends true
/DetectCurves 0.0000
/ColorConversionStrategy /CMYK
/DoThumbnails false
/EmbedAllFonts true
/EmbedOpenType false
/ParseICCProfilesInComments true
/EmbedJobOptions true
/DSCReportingLevel 0
/EmitDSCWarnings false
/EndPage -1
/ImageMemory 1048576
/LockDistillerParams false
/MaxSubsetPct 100
/Optimize true
/OPM 1
/ParseDSCComments true
/ParseDSCCommentsForDocInfo true
/PreserveCopyPage true
/PreserveDICMYKValues true
/PreserveEPSInfo true
/PreserveFlatness true
/PreserveHalftoneInfo false
/PreserveOPIComments true
/PreserveOverprintSettings true
/StartPage 1
/SubsetFonts true
/TransferFunctionInfo /Apply
/UCRandBGInfo /Preserve
/UsePrologue false
/ColorSettingsFile ()
/AlwaysEmbed [ true
]
/NeverEmbed [ true
]
/AntiAliasColorImages false
/CropColorImages true
/ColorImageMinResolution 300
/ColorImageMinResolutionPolicy /OK
/DownsampleColorImages true
/ColorImageDownsampleType /Bicubic
/ColorImageResolution 300
/ColorImageDepth -1
/ColorImageMinDownsampleDepth 1
/ColorImageDownsampleThreshold 1.50000
/EncodeColorImages true
/ColorImageFilter /DCTEncode
/AutoFilterColorImages true
/ColorImageAutoFilterStrategy /JPEG
/ColorACSImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/ColorImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/JPEG2000ColorACSImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/JPEG2000ColorImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/AntiAliasGrayImages false
/CropGrayImages true
/GrayImageMinResolution 300
/GrayImageMinResolutionPolicy /OK
/DownsampleGrayImages true
/GrayImageDownsampleType /Bicubic
/GrayImageResolution 300
/GrayImageDepth -1
/GrayImageMinDownsampleDepth 2
/GrayImageDownsampleThreshold 1.50000
/EncodeGrayImages true
/GrayImageFilter /DCTEncode
/AutoFilterGrayImages true
/GrayImageAutoFilterStrategy /JPEG
/GrayACSImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/GrayImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/JPEG2000GrayACSImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/JPEG2000GrayImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/AntiAliasMonoImages false
/CropMonoImages true
/MonoImageMinResolution 1200
/MonoImageMinResolutionPolicy /OK
/DownsampleMonoImages true
/MonoImageDownsampleType /Bicubic
/MonoImageResolution 1200
/MonoImageDepth -1
/MonoImageDownsampleThreshold 1.50000
/EncodeMonoImages true
/MonoImageFilter /CCITTFaxEncode
/MonoImageDict <<
/K -1
>>
/AllowPSXObjects false
/CheckCompliance [
/None
]
/PDFX1aCheck false
/PDFX3Check false
/PDFXCompliantPDFOnly false
/PDFXNoTrimBoxError true
/PDFXTrimBoxToMediaBoxOffset [
0.00000
0.00000
0.00000
0.00000
]
/PDFXSetBleedBoxToMediaBox true
/PDFXBleedBoxToTrimBoxOffset [
0.00000
0.00000
0.00000
0.00000
]
/PDFXOutputIntentProfile ()
/PDFXOutputConditionIdentifier ()
/PDFXOutputCondition ()
/PDFXRegistryName ()
/PDFXTrapped /False
/CreateJDFFile false
/Description <<
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
/BGR <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>
/CHS <FEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000410064006f006200650020005000440046002065876863900275284e8e9ad88d2891cf76845370524d53705237300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002>
/CHT <FEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc9ad854c18cea76845370524d5370523786557406300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002>
/CZE <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>
/DAN <FEFF004200720075006700200069006e0064007300740069006c006c0069006e006700650072006e0065002000740069006c0020006100740020006f007000720065007400740065002000410064006f006200650020005000440046002d0064006f006b0075006d0065006e007400650072002c0020006400650072002000620065006400730074002000650067006e006500720020007300690067002000740069006c002000700072006500700072006500730073002d007500640073006b007200690076006e0069006e00670020006100660020006800f8006a0020006b00760061006c0069007400650074002e0020004400650020006f007000720065007400740065006400650020005000440046002d0064006f006b0075006d0065006e0074006500720020006b0061006e002000e50062006e00650073002000690020004100630072006f00620061007400200065006c006c006500720020004100630072006f006200610074002000520065006100640065007200200035002e00300020006f00670020006e0079006500720065002e>
/DEU <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>
/ESP <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>
/ETI <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>
/FRA <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>
/GRE <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>
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
/HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 5.0 i kasnijim verzijama.)
/HUN <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>
/ITA <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>
/JPN <FEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002>
/KOR <FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e>
/LTH <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>
/LVI <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>
/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
/NOR <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>
/POL <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>
/PTB <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>
/RUM <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>
/RUS <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>
/SKY <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>
/SLV <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>
/SUO <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>
/SVE <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>
/TUR <FEFF005900fc006b00730065006b0020006b0061006c006900740065006c0069002000f6006e002000790061007a006401310072006d00610020006200610073006b013100730131006e006100200065006e0020006900790069002000750079006100620069006c006500630065006b002000410064006f006200650020005000440046002000620065006c00670065006c0065007200690020006f006c0075015f007400750072006d0061006b0020006900e70069006e00200062007500200061007900610072006c0061007201310020006b0075006c006c0061006e0131006e002e00200020004f006c0075015f0074007500720075006c0061006e0020005000440046002000620065006c00670065006c0065007200690020004100630072006f006200610074002000760065002000410064006f00620065002000520065006100640065007200200035002e003000200076006500200073006f006e0072006100730131006e00640061006b00690020007300fc007200fc006d006c00650072006c00650020006100e70131006c006100620069006c00690072002e>
/UKR <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>
/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|