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EUR 5030 e EURCYL - A COMPUTER PROGRAM TO G E N E R A T E F I N I T E ELEMENT MESHES FOR CYLINDER-CYLINDER INTERSECTIONS by P. DE W I N D T and J. R E Y N E N

Commission of the European Communities Joint Nuclear Research Centre - Ispra Establishment (Italy) Luxembourg, August 1973 - 22 Pages - 8 Figures - B.Fr. 40.—

EURCYL is a computer program dealing with the automatic mesh generation of cylinder-cylinder intersections, with special attention to the thick-walled vessel-nozzle junctions with curved transitions. Linear, parabolic and cubic isoparametric elements can be applied. The output consists of punched cards for topology and geometry.

EUR 5030 e EURCYL - A COMPUTER PROGRAM TO GENERATE F I N I T E ELEMENT MESHES FOR CYLINDER-CYLINDER INTERSECTIONS by P . DE WINDT and J. R E Y N E N



EUR 5030 e EURCYL - A COMPUTER PROGRAM TO GENERATE F I N I T E ELEMENT MESHES FOR CYLINDER-CYLINDER INTERSECTIONS by P . DE WINDT and J. R E Y N E N



E U R S 0 3 0 e

COMMISSION OF THE EUROPEAN COMMUNITIES

EURCYL A COMPUTER PROGRAM TO GENERATE FINITE

ELEMENT MESHES FOR CYLINDER-CYLINDER INTERSECTIONS

by

P. DE WINDT and J. REYNEN

1973

Joint Nuclear Research Centre Ispra Establishment - Italy

Technology Division

ABSTRACT


KEYWORDS

Ε-CODES PRESSURE VESSELS FINITE ELEMENT METHOD JOINTS NOZZLES GEOMETRY

- 3 -

C O N T E N T S

1. INTRODUCTION 5

2. TOPOLOGY 5

3. GEOMETRY 8

4. HOW TO USE 8

5. RESULTS 10

6. CONCLUSION 10

APPENDIX 1 12

APPENDIX 2 13

APPENDDC 3 14

APPENDIX 4 15

- 5

1. INTRODUCTION

The finite element method for structural and thermal analysis requires the subdivision of the structure into a large number of regions, called the mesh. This report deals with the automatic generation of three-dimensional meshes for general perpendicular cylinder-cylinder intersections. A computer program (EURCYL) has been written which, as output, produces punched cards for finite element programs. The program is particularly suited to generate a mesh for thick-walled vessel-nozzle junctions, including local reinforcement and transition radii at the intersection.

EURCYL is similar to the program described in 1 l , the difference lies in the more general geometry and the use of various types of isoparametric elements with a view to using the programs BERSAFE21 and FL.HE31.

2. TOPOLOQY

The general geometry of 1/4 of the cylinder-cylinder intersection as dealt with by EURCYL is represented in fig. 1 and 2, including the necessary dimensions, a cartesian (x,y,z) and a cylindrical (r, θ,ζ) coordinate system.

Three regions are recognized: A - D D - B - C - E

— nozzle zone — transition zone — vessel zone E - F

Fig. 2 : Two dimensional view of nozzle geometry

- 6 -

The topology of the elements corresponds to the topology of a wall (fig. 3) wi th the three directions and corresponding number of elements as indicated in Table 1 and fig. 4.

Table 1

Direction

Length Angular Thickness

Number of elements

NELL NELA NELTH

The number of elements in angular direction corresponds to 1/4 of the structure i.e.

0 < 0< 90° (first quadrant). The number of elements in length direction is subdivided into

the three zones mentioned before, as indicated in Table 2.

Table 2

Zone

Nozzle Transition Vessel

Total lenth

Number of elements

N E L N Ν ELT NELV

NELL = NELN + N E L T + N E L V

The numbering of elements is as indicated in fig. 3, in thickness, angular and length direction respectively. Since for most applications NELTH < NELA < NELL, this numbering gives the smallest bandwidth for a front solution

4 ).

The option NELEM is introduced in order to be able to continue a mesh wi th NELEM-1 elements already generated.

Three types of elements can be used corresponding to the isoparametric elements used in BERSAFE

2> and FLHE 3). They are given in Table 3 and f ig. 5.

Table 3

EURCYL el. type

1 2 3

BERSAFE el.type

EZ24 EZ60 EZ96

Number of nodes

8 20 32

description

linear parabolic cubic

The node numbering is straightforward and proceeds in the angular, thickness and length direction respectively (fig. 6). The option NPOIN is introduced in order to be able to continue a mesh with NPOIN-1 nodes already generated.

EURCYL defines the bandwidth of the generated topology and the job is abandoned if the bandwidth exceeds a preset value defined by input (NBTOT).

EURCYL has options to generate 1/4, 1/2 or the complete intersection to be specified by input data NTHETA (Table 4). The node numbering starts at the angular plane ö-start. For option NTHETA = 4 the nodes of the first angular plane (ö-start) coincide with those of the last angular plane (ö-end). In the topology definition the former are retained. Asimilar situation occurs for NGAMMA = 180° (fig. 1) and NTHETA = 2 or 4, and also here the lower node numbers are retained.

Table 4

NTHETA

1 2 3 4

quadrants

1 1,4 1,2 1,2,3,4

ö-start

0° 90°

0° - 1 8 0 °

Ö-end

< 90

o 180 180

The output of the topology consists of the list of elements defined by nodes, in a right hand screw sequence (fig. 5).

Punched cards compatible with BERSAFE and FLHE are produced.

- 7 -

Thickness

Angular >

/

/ 2

2

6

10

14

18

/ U / / / '

1

S

9

13

17

/ .

' / /

5 y

9 y

13 , /

/ 17 /

3 /

/ 7 y

η y

« /

/ 19/

I Length

Fig. 3 : Element indexation

NELTH

NELN

NELT NELV

N2 N3

+ ' Fig. 4 : Element distribution

EZ 24, 8 nodes ( linear )

EZ 60, 20 nodes ( parabolic )

EZ 96, 32 nodes ( cubic ) i6

24

THicknes

22 2 ,

Length

Fig. 6 : Nodes indexation

Fig. S : Element types

3. GEOMETRY

The coordinates of the nodal points depend on the distribution and on the type of the elements. The distribution and the type of elements depend on their turn on the structure and the expected stress distribution. For the nozzle structure the type of element should preferably be the parabolic or cubic isoparametric ones, in order to represent accurately the geometry of the curved surfaces (the linear element EZ24 with straight edges has only been included for completeness). The distribution of elements should be fine in regions of steep stress gradients and can be coarser elsewhere.

In EURCYL the distribution of elements is controlled by input. As far as the angular direction is concerned, the distribution is homogeneous for the nozzle zone (A — D) and transition zone (D—B—C—E) and nearly homogeneous for the vessel zone (E — F), see fig. 4.

In the thickness direction the distribution is governed by a crowding factor CROWTH, according to a geometrical series with the smaller elements at the inside for CROWTH > 1 (see appendix 1).

In the length direction the distribution is defined by NELN, NELT, NELV (see chapter 1) with corresponding crowding factors CROWN, CROWTR, CROWV according to geometrical series with increasing elements in the direction away from the intersection.

For the determination of the coordinates of the nodal points, first the coordinates of the points A,D,B,C,E and F (fig. 2) for inside and outside surfaces and for the various angular planes have to be defined. For A and D the procedure is straight forward because they are on a cylindrical surface with axis z. The coordinates of Β and C follow from a transcendental equation, which is solved by iteration (appendix 3). Points C,E and F lie on a cylindrical surface with axis x. This surface is developped in a z-x plane in which the coordinates are defined. Once the points A,D,B,C,E and F are defined, the summit nodes are found by geometrical interpolation using the crowding factors. Next the midside nodes are defined.

For the structural options NTHETA Φ 1 the additional coordinates are found by symmetry.

The output of the geometry consists of a list of cartesian (x-y-z) or cylindrical (r,0,z) coordinates depending on the option NCOORD. Punched cards are produced to be used in subsequent runs with finite element programs.

4. HOW TO USE

Card No. 1 : job title card

ces 1- 4 ces 5-80

AJOB TITLE

A4 job name for BERSAFE program 19A4 title of the job

Card No. 2: dimension card (see fig. 1 and 2)

ces 1- 6 ces 7-12 ces 13-18 ces 19-24 ces 25-30 ces 31-36 ces 37-42

ces 43-48

ces 49-54 ces 55-60 ces 61-66 ces 67-72 ces 73-78

RV(1) RV(2) FLV RN(1) RN(2) FLN RT(1)

RT(2)

FLVTO) FLVT(2) FLNT(1) FLNT(2) RP

F6.2 external vessel radius F6.2 internal vessel radius F6.2 vessel length F6.2 external nozzle radius F6.2 internal nozzle radius F6.2 nozzle length F6.2 outside transition radius

= 0 if transition not curved F6.2 inside transition radius

= if transition not curved F6.2 length of transition zone, outside vessel F6.2 length of transition zone, inside vessel F6.2 length of transition zone, outside nozzle F6.2 length of transition zone, inside nozzle F6.2 external radius of nozzle entry, in case of

conical form if = 0,RP=RN(1) (cylindrical form)

- 9

Card No. 3

ces 1- 6

ces 7-12

ALFAC1

ALFAC2

F6.2

F6.2

angle in degrees of transition nozzle part, if conical = 0 cylindrical angle in degrees of transition nozzle part, if conical = 0 if cylindrical

Card No. 4:

ces 1- 6 ces 7-12 ces 13-18 ces 19-24 ces 25-30 ces 31-36

ces 37-42

ces 43-48

ces 49-54

Card No. 5:

ces 1- 6

element and structure option card

NELN NELT NELV NELA NELTH NELTYP

NTHETA

NGAMMA

NCOORD

crowding factor card

CROWN

I6 I6 I6 I6 I6 I6

I6

I6

I6

number of elements in nozzle length number of elements in transition length number of elements in vessel length number of elements in angular direction number of elements in the thickness element option: = 1 type EZ24 = 2 type EZ60 = 3 type EZ96 structure option: = 1 quadrant 1 = 2 quadrant 1 + 4 = 3 quadrant 1 + 2 = 4 quadrant 1 + 2 + 3 + 4 angle in degrees of vessel sector (up to maximum 180°) coordinates option = 0 x-y-z = 1 r-ö-z

F6.2 crowding factor along the nozzle

ces 7-12

ces 13-18

ces 19-24

if > 1 elements increasing away from the transition

CROWV F6.2 crowding factor along the vessel if > 1 elements increasing away from the transition

CROWTH F6.2 crowding factor along the thickness if > 1 elements increasing away from the inside surface

CROWTR F6.2 crowding factor along the transition nozzle and vessel zones if > 1 elements increasing away from the junction

Card No. 6

ces 1-6 ces 7-12 ces 13-18

NPOIN NELEM NBTOT

I6 I6 I6

index of first nodal point index of first element maximum number of nodes allowed

in the bandwidth ¡f=0,NBTOT=99

- 10 -

5. RESULTS

The following results are printed:

— the input data — the total number of nodes ( 1 ) — the total number of elements ( 1 ) — the maximum bandwidth ( 1 ) — the topology — the geometry

(1) the job is immediately abandoned if these parameters do not agree with the BERSAFE and FLHE

limitations.

The topology and the geometry are punched on cards with the required formats for BERSAFE

2» or FLHE 3> use:

Topology cards

ces 1-4

ces 5- 6

ces 7-12

ces 13-16 ces 17-18

ces 19-22

ces 75-78

AJOB

11

NOEL

NNODES

NODES

A4

I2

I4

I2

1514

job name

card type number (BERSAFE)

blank

element number

number of nodes

nodes series

N.B. if NNODES > 15,a continuation card is used with I4 formats (ces 19-22, etc.) and NNODES

NNODES + 1

Geometry cards

ces 1- 4 ces 5- 6

ces 7-10

ces 11-18

ces 19-26

ces 27-34

AJOB

21

NODE

GNODE

GNODE

GNODE

A4

I2

I4

F8.3

F8.3

F8.3

job name

card type number (BERSAFE)

node number

X or R coordinate

Y or θ coordinate (0 in degrees)

Ζ coordinate

Appendix 4 gives an example of the printed results of a structure represented by the Calcomp plot of fig. 7. In fig. 8 another example of a Calcomp plot is given.

6. CONCLUSION

A computer program has been presented dealing with the automatic mesh generation for finite element analysis of cylinder-cylinder intersections. EURCYL is in particular suited for BWR pressure vessel nozzles.

REFERENCES

1) Krishnamurthy N. 'Three-dimensional finite element analysis of thick walled vessel-nozzle junctions with curved transitions" - 0RNL-TM-3315.

2) Hellen T.K. "BERSAFE (Phase 1) a computer system for stress analysis — Part 1: user's guide" — October 1970, CEGB Report RD/B/NI761.

3) Fullärd K. "FLHE, a finite element program for the calculation of temperatures in arbitrary structures. Part 1: user's guide" - CEGB Report RD/B/N1849.

4) Hellen T.K. "A front solution for finite element techniques" CEGB Report RD/B/N1459 - October 1969.

- 11 -

Figs. 7 and 8 : Calcomp example

- 12 -

APPENDIX 1

Crowding Factors

If N is the number of nodes to be generated on a straight or curved line defined by the parameters Χι and x^ with crowding factor R, the coordinates of the intermediate nodes are defined from:

Xj = Xi + (xN — xJ'CN CN=(Ri-i - 1 ) / ( R N " 1 - 1 ) C N = ( j - 1 ) / ( N - 1 ) f o r R = 1 .

These formulae are used to define the coordinates of the summit nodes in the thickness direction, and for the nozzle zone A — D and the vessel zone E — F in length direction (fig. 1).

- 13 -

APPENDIX 2

The distribution of the elements in the transition zone is defined by the number of elements N E LT and the crowding factor R.

The program has to define the number of elements to be attributed to the distances DB,BC and CE, respectively N1, N2 and N3 (fig. 4). An iterative procedure is applied.

As initial guess for the length of the elements in distance BC is taken.

A=(DB + BC+CE) /NELT (1)

The number of elements in DB, BC and CE become respectively

N1 = log(1 + (R-1) DB/A) / logR (2) N 2 = B C / A (3) N3=log(1 + (R-1)CE/A)/logR (4)

These equations express that for BC the distribution is homogeneous (3) and for DB and CE the distribution is according to a geometrical series with first term A and ratio R.

The sum of the calculated elements is compared to the prescribed number N ELT. N1 + N 2 + N 3 = SUM=NELT (5)

A correction is applied to A according to A=A(SUM/NELT)1 /2 (6)

and the iteration loop returns to eq. (1) until (5) is satisfied.

Equations (2) and (4) follow from the sum S of a geometrical series with N terms:

S= A (RN — 1) / (R - 1) (7)

Once N1, N2 and N3 are known, the summit nodes in BC are distributed homogeneously, and the summit nodes in DB and CE according to a geometrical series with ratio R (Appendix 1).

- 14 -

APPENDIX 3

The coordinates of points Β and C in an angular plane 0 are defined by transcendental equations which are solved by iteration.

The intersection of an angular plane 0 with the vessel (radius RV) is an ellipse with half axis.

RV/sin0 and RV (fig. 9)

The iteration starts with a first guess for the radius RC of point C in the plane of intersection. The vertical position of C is then defined by:

ZC=(RV2 - R C 2 sin20)1 '2

The angle j3 is defined by:

0=arctg(RC2 sin20/ZC)

The angle α and the coordinates of points Β become:

a = π/2 — αϊ — β

RB = RC + RT sinj3 - RT cosa,

ZB = ZC + RTcos|3 - RT sinaj

The radius of point D becomes:

RD=RB-(ZD-ZB)tga!

(1)

(2)

(3)

(4)

(5)

(6)

The value of RD is compared to the nozzle radius RN. The difference is subtracted from RC and the iteration continues with equation (1).

Equation (3) gives the value of a and the intermediate nodes between BC are defined by linear interpolation of the variable a.

Fig. 9 : Transition profile in a angular plane θ

15 -

APPENDIX 4

PROGRAM EURCYL THREE DIMENSIONAL MESH GENERATION

TEST STRUCTURE

GENERAL 2-DIMENSIONAL VUE WITH DIMENSIONS

40.J10 ANGLE ( V l t D l t B l ) > 30."O ANGLE (V2,D2,B2»= r>.0

* * * * * * * * * * * * * * A l

30. σο * I I _ I I _ *

* . *

10.03

2P.DC

• en

- * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * F 1 CI E l *

21?. OP *

8P .0"

— — __ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * C2 E2 F2

20 .00

IPO.90

OS

I

120.OP

100.PO

GENERAL 3-DIMENSIONAL VIEW WITH ELEMENT INFORMATION

2 EL.

2 EL.

3 EL. 2 EL.

* * * * * * * £ * * * * * * * *D * * * * * *B

* - — - — * C Ê F * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* ZZZZZZZZZZZZZZZZZZZZZZZZ ZZZZZZZZZZZZZZZZZ*'

* * * / * * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * * / / / * / / / / *

* / / / / / / * * / / / / / / / / *

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uitiin* *ii imit uutti*

*Ullllll mut t*

l l l l l l l l Y lllllfll *ltllll

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*/¿</¿//<///¿{í**************************************************************

* / / / / -~-™----~—----ΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖΙΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖΖ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

1 E L .

1 EL.

STRUCTURE TAKEN INTO CONSIDERATION

* * *

* * * / * * *

*///* * „, * * / / / * * Xy/ft . * * * * * * * GAMMA = 90 DEGREES

* / / / * * * * * / / / * . * * * / / / * * * * / / / * . * * * / / / * * *

*///f% · ¿ZZZZZZI * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * j j ; * * * * * * / / / * · *zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz ZZZZZZZZZZ z*

* / / / / / / * * * * * * * * * * * * * * * * * * * * * * * * * * « ^ * / / / / / / / / *

ituuni * minuti* . · A * / / / / / / / * A * M .

* / / / / * » · M ^ » ♦ ♦ ♦ ♦ A * * * * * * . * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * mG

A

. G . .

co

ι

THE STRUCTURE I S DEFINED AROUND THE X - A X I S BY A SECTOR OF 90 DEGREES

QUARTER A STRUCTURE IS CONSIDERED AROUND THE Z - A X I S WITH POSIT IVE X - AND Y-COORDINATES

EZ60 IS THE ELEMENT TYPE ************************ THERE THERE THERE THERE THERE

ARE ARE ARE ARE ARE

2 3 2 2 1

ELEMENTS ALONG THE NOZZLE (FROM A TO D) ELEMENTS ALONG THE TRANSITION (FROM D TO E) ELEMENTS IN THE 90 DEGREES NOZZLE SECTOR (BEWARE THE STRUCTURE CHOICE) ELEMENTS ALONG THE VESSEL(FROM E TO F) ELEMENTS ALONG THE THICKNESS

THE OUTER PART OF THE NOZZLE IS CONICAL OR CYLINDRICAL,ANGLE = 30.000 DEGREES

THE INNER PART OF THE NOZZLE IS CONICAL OR CYLINDRICAL,ANGLE 0.0 DEGREES

THERE ARE POINTS AND ELEMENTS BEFORE THIS MESH

FOR THIS PROBLEM 14 ELEMENTS AND 146 NODES ARE EXPECTED NUMBER OF ELEMENTS ALONG THE TRANSITION FROM NOZZLE TO VESSEL

EXTERNAL PART

INTERNAL PART

1 FROM D TO Β 1 FROM Β TO C 1 FROM C TO E 1 FROM D TO Β 1 FROM Β TO C 1 FROM C TO E

CO

I

CROWDING FACTOR ALONG THE NOZZLE(CROWN) 1.00 THE VESSEL(CROWV) l . J P THE SECTOR(CROWTH) 1.00 THE TRANSITION(CROWTR) 1.10

LIST OF EL. WITH THEIR N.P.(CARDS PUNCHED ALSO FOR BERSAFE»

1 2 3 4 5 6 7 8 9

IP 11 12 13 14

1 3

2D 22 39 41 58 60 77 79 96 98

115 117

BANDWIDTH * * * * * * * * * * * ^ 4

6 7

25 26 44 45 63 64 82 83

101 102 120 121 25

9 11 28 3^ 47 49 66 68 85 87

104 106 123 125

NODES

IP 12 29 31 48 5* 67 69 86 88

ir>5 107 124 126

11 ]3 30 32 49 51 68 70 87 89

106 108 125 127

7 8

26 27 45 46 64 65 83 84

102 103 121 122

3 5

22 24 41 43 60 62 79 81 98

1PP 117 119

2 4

21 23 40 42 59 61 78 8? 97 99

116 118

14 15 33 34 52 53 71 72 9Π 91 109 11? 128 129

17 18 36 37 55 56 74 75 93 94

112 113 131 132

18 19 37 38 56 57 75 76 94 95 113 114 132 133

15 16 34 35 53 54 72 73 91 92

110 111 129 130

2Γ> 22 39 41 58 6P 77 79 96 98

115 117 134 136

25 26 44 45 63 64 82 83

1*1 102 12P 121 139 14P

28 3« 47 49 66 68 85 87

104 !«6 123 125 1*2 144

29 31 48 50 67 69 86 88

ir»5 107 124 126 143 145

30 32 49 51 68 70 87 89 106 108 125 127 144 146

26 27 45 46 64 65 83 84

102 1*3 121 122 140 141

22 24 41 43 60 62 79 81 98 ino 117 119 136 138

21 23 40 42 59 61 78 80 97 99 116 118 135 137 1

to o

COORD. SYSTEM X - Y - Ζ * * * * * * * * * * * * * * * * * * * * * * *

LIST OF N.P. WITH COORD. (PUNCH ON CARDS WITH BERSAFE FORMAT)

1 2 3 4 5 5 7 ? Q

ir> 11 12 13 1 4 Î 5 16 17 18 I

e»

2 ? 21 22 2 3 2 4 2 5 2 6 27 2 6 2 9 31 31 32 33 3 4 3 5 3 6 3 7 3 8 3 9 4 ^ 4 1 4 2 43 4 4 4 5 4 6 4 7 4 8 4 9 5 0 51 52 53

3 5 . 0 0 0 3 2 . 3 3 6 2 4 . 7 4 9 1 3 . 3 9 4

C P o n 3 2 . 5 0 0 2 2 . 9 8 1

P . O P P 3 0 . Π 0 Ρ 2 7 . 7 1 6 2 1 . 2 1 3 1 1 . 4 8 1

0 . 0 0 0 3 6 . 2 5 0 2 5 . 6 3 3

O.OOO 3 0 . 0 0 0 2 1 . 2 1 3

PoCVC 3 7 . 5 0 O 3 4 . 6 4 5 2 6 . 5 1 6 1 4 . 3 5 1

OoOPP 3 3 . 7 5 0 2 3 . 8 6 5

O.OOO 3 C 0 * 0 2 7 . 7 1 6 2 1 . 2 1 3 1 1 . 4 8 1

r.o^v 3 8 . 7 5 0 2 7 . 4 0 0

0 . 0 ^ 0 3 0 . 0 P P 2 1 . 2 1 3

O.OOO 4 0 . 0 0 0 3 6 . 9 5 5 2 8 . 2 8 4 1 5 . 3 0 7

C . o o n 3 5 . COn 2 4 . 7 4 9

0 . 0 0 0 3 C O 0 O 2 7 . 7 1 6 2 1 . 2 1 3 1 1 . 4 8 1

p.con 4 3 . 6 1 8 3 2 . 0 8 8

0.0 13.394 24.749 32.336 35.000

C O 2 2 . 9 8 1 3 2 . 5 0 0

O.o 1 1 . 4 8 0 2 1 . 2 1 3 2 7 . 7 1 6 3 0 . 0 0 0

O.o 25.633 36.2 50

0 . 0 2 1 . 2 1 3 3 0 . 0 0 ^

C π 1 4 . 3 5 1 2 6 . 5 1 6 3 4 . 6 4 5 3 7 . 5 0 3

0.0 23.865 33.750 O.P 11.480 21.213 27.716 30.000 CO

27.400 38.75"

C O 2 1 . 2 1 3 30.OOP

1 5 . 3 0 7 2 8 . 2 8 4 3 6 . 9 55 40." OOP

O.o 24.749 35.000

o.o 1 1 . 4 8 " 2 1 . 2 1 3 2 7 . 7 1 6 3 0 . p n o

0 . 0 3 2 . 0 8 8

2 0 P . 0 0 n 2 η η . ο ρ ό 2 0 C noo 20Ο.ΟΓ0 2 0 O . 0 0 0 2 0 o . n r o 2 0 ο . ο ρ ο 2 0 0 . p o o 2 ñ r . n r o 2 0 0 . n ^ r 20cnro goo.pr»^

2 O C 0 ñ ñ 18 5 . n n o 1 8 5 . 0 0 0 18 5 . 0 0 0 1 8 5 . 0 0 « 185.000

Ιδδ.Ο^Ο 170.noo 170.noo

170.000 170.oor« 170.OCO 17θ.000 170.000 17Π.00Ο 1 7 0 . 0 0 0 1 7 0 . n o o 1 7 C . n o o 1 7 A . o n o 1 7 0 . 0 0 0 1 5 5 . 0 0 0 1 5 5 . 0 0 0 1 5 5 . 0 Γ " 1 5 5 . 0 0 0 15 5.0OO 15 5 . 0 0 0 1 4 0 . 0 0 0 140.OOo 1 4 0 . 0 0 0 1 4 0 . 0 0 0 1 4 C OO « 1 4 η . 0 0 0 1 4 0 . o n n l ^ o . n o o l ^ ò . o n n I 4 0 . n o o 1 4 0 . η η ό 1 4 C 0 0 O 140.ΓΟ0 13 2 . 5 0 0 1 2 8 . 8 6 6

54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 ?o 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

10? 101 102 103 1 0 4 105 1 0 6

O.OOO 3 0 . 0 0 0 2 1 . 2 0 5

O.OOO 4 7 . 2 3 5 4 4 . 5 1 6 3 5 . 8 9 1 2 0 . 619

0 . 0 0 0 3 8 . 6 1 8 2 8 . 5 4 4

O.OOO 3 0 . 0 0 0 2 7 . 7 1 5 2 1 . 1 9 7 1 1 . 4 8 2

O.OOO 5 0 . 8 9 5 3 7 . 7 5 2

O.OPO 3 1 . 4 6 4 2 2 . 0 2 5

0 . 0 0 0 5 5 . 8 9 5 5 1 . 8 7 5 4 0 . 2 8 7 2 2 . 3 2 2

0 . 0 0 0 4 5 . 4 4 8 3 2 . 2 0 4

0 . 0 ^ 0 3 5 . 0 0 0 3 2 . 0 9 7 2 4 . 1 2 0 1 2 . 8 4 3

0 . 0 0 0 6 5 . 8 9 5 4 7 . 3 5 8

0 . 0 0 0 5 5 . 4 4 8 3 9 . 2 7 5

O.OPO 7 5 . 8 9 5 7 0 . 3 5 3 5 4 . 4 2 9 2 9 . 9 7 5

0 . 0 0 0 7 5 . 8 9 5 5 4 . 4 2 9

O.oon 75 .895 70 .353 54 .429

47 .698 C O

21.205 30 .002 0 . 0 18.439 3 5 . 8 9 1 49 .779 55.395

0 . 0 28 .544 42 .703

0.^ 11.480 21 .197 27 .719 30 .004

O.P 37 .752 57 .014

0 . 0 22.025 30 .9 22

0 . 0 21 .487 40 .287 53 .889 59 .128

Oo<> 32 .204 46 .233

O.P 13.295 24 .120 31 .006 33 .337

0 . 0 4 6 . 8 7 4 67 .615

0 . 0 38.752 54.725

0 . 0 28.969 53 .298 69 .696 75 .632

0 . 0 52.880 74 .314

O.P 28.842 52.462

1 2 4 . 0 6 2 1 2 2 . 5 0 0 1 2 0 . 9 8 6 1 1 9 . 4 9 7 12 5 . 0 0 0 1 2 3 . ^ 3 6 1 1 7 . 7 3 2 1 1 1 . 2 8 9 1 0 8 . 1 2 3 1 1 5 . 0 0 0 1 0 9 . 8 5 2 1 0 3 . 5 5 8 1 0 5 . OOn 1 0 4 . 1 * 6 1 0 1 . 9 7 2

9 9 . 8 5 9 9 8 . 9 9 3

1 2 1 . 3 4 0 1 1 4 . 7 5 3 1 0 6 . 0 2 3 1 0 1 . 4 6 4

9 8 . 7 5 7 9 6 . 1 0 7

1 2 0 . 0 0 0 1 1 8 . 0 6 1 1 1 3 . 0 3 5 1 0 7 . 2 1 9 1 0 4 . 4 2 2 1 1 0 . 0 0 0 1 0 5 . O 4 1

9 9 . 3 5 1 100.OOn

9 9 . 1 1 2 97.047 95.072 9 4 . 2 7 9

120.COO 1 1 0 . 4 6 6

9 9 . 1 3 8 1 0 0 . 0 0 0

9 2 . 1 8 6 8 3 . 6 9 7

1 2 0 . 0 0 0 1 1 6 . 4 5 1 1 0 7 . 5 1 4

97.686 93.166

1 1 0 . 0 0 0 96.324 8O.757

1 0 0 . 0 0 0 95.750 8 5 . 1 3 3

1 0 7 1 0 8 1 0 9 1 1 0 1 1 1 1 1 2 1 1 3 1 1 4 1 1 5 1 1 6 1 1 7 1 1 8 1 1 9 1 2 P 1 2 1 1 2 2 1 2 3 1 2 4 1 2 5 1 2 6 1 2 7 1 2 8 1 2 9 1 3 0 1 3 1 1 3 2 1 3 3 1 3 4 1 3 5 1 3 6 1 3 7 1 3 8 1 3 9 1 4 P 1 4 1 1 4 2 1 4 3 1 4 4 1 4 5 1 4 6

2 9 . 9 7 5 0 . 0 0 0

8 1 . 9 2 2 6 5 . 8 2 2

O.nr io 8 Ì . 9 2 2 6 5 . 8 2 2

0 . 0 0 0 8 7 . 9 4 8 8 5 . 1 7 6 7 7 . 2 1 5 3 9 . 9 8 8

0 . 0 0 0 8 7 . 9 4 8 7 7 . 2 1 5

0 . 0 0 0 8 7 . 9 4 8 8 5 . 1 7 6 7 7 . 2 1 5 3 9 . 9 8 8

0 . 0 0 0 9 3 . 9 7 4 8 8 . 6 0 7

O.OPO 9 3 . 9 7 4 8 8 . 6 0 7

0 . 0 0 0 1 0 0 . 0 0 0 1 0 0 . O P P 1 0 0 . 0 0 0

5 0 . 0 0 0 0 . 0

1 0 0 . 0 0 0 1 0 0 . 0 0 0

0 . 0 1 0 0 . 0 0 0 1 0 0 . 0 0 0 1 0 0 . 0 0 0

5 0 . 0 0 0 0 . 0

6 7 . 6 9 8 7 2 . 9 9 7

0 . 0 8 0 . 7 2 5 9 4 . 3 0 6

0 . 0 7 2 . 2 1 5 8 4 . 4 9 1

0 . 0 5 9 . 0 6 3

1 0 1 . 9 7 0 1 0 6 . 6 8 5 1 0 8 . 3 4 2

O . P 9 4 . 6 4 ?

1 0 0 . 6 7 3 0 . 0

5 1 . 3 2 7 8 7 . 3 1 0 9 1 . 5 6 9 9 3 . 0 0 4

0 . 0 1 1 5 . 4 0 4 1 1 7 . 0 4 9

0 . 0 9 6 . 7 7 6 9 8 . 2 3 6

0 . 0 8 4 . 8 5 3

1 2 0 . 0 0 0 1 2 0 . 3 0 0 1 2 0 . 0 0 0

0 . 0 1 1 0 . P 0 0 1 1 0 . 0 0 P

0 . 0 7 0 . 7 1 1

1 0 0 . 0 0 0 1 0 0 . 0 0 3 1 0 0 . O O P

7 3 . 6 0 0 6 8 . 3 4 8

1 2 0 . 0 0 0 8 8 . 7 8 8 7 4 . 2 A 5

1 0 0 . 0 0 0 6 9 . 1 7 4 5 3 . 4 9 0

1 2 0 . 0 0 0 1 0 4 . 4 5 8

6 3 . 2 6 2 5 4 . 9 3 9 5 1 . 5 9 6

1 1 0 . 0 0 0 5 6 . 0 0 8 4 4 . 1 7 0

1 0 0 . 0 0 O 8 5 . 8 2 3 4 8 . 7 5 3 4 0 . 1 8 8 3 6 . 7 4 5

1 2 O . 0 0 0 3 2 . 8 9 1 2 6 . 4 4 8

1 0 0 . 0 0 0 2 5 . 1 8 9 1 8 . 7 0 2

1 2 0 . 0 0 0 8 4 . 8 5 3

O.OOn 0 . 0 0 0 0 . 0 0 0

1 1 0 . 0 0 0 0 . 0 0 0 0 . 0 0 0

1 0 0 . 0 0 0 7 0 . 7 1 1

0 . 0 0 0 O.OOO 0 . 0 0 0

CARDS TYPE 11 AND 21 ARE NOW PREPARED

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