Plaatbuigen : modellen en analyse : deel 2 · Plaatbuigen : modellen en analyse : deel 2 Citation...

Post on 18-Oct-2020

3 views 0 download

Transcript of Plaatbuigen : modellen en analyse : deel 2 · Plaatbuigen : modellen en analyse : deel 2 Citation...

Plaatbuigen : modellen en analyse : deel 2

Citation for published version (APA):Hoogenboom, S. M., & Perduijn, A. B. (1990). Plaatbuigen : modellen en analyse : deel 2. (TH Eindhoven. Afd.Werktuigbouwkunde, Vakgroep Produktietechnologie : WPB; Vol. WPA0709). Technische UniversiteitEindhoven.

Document status and date:Gepubliceerd: 01/01/1990

Document Version:Uitgevers PDF, ook bekend als Version of Record

Please check the document version of this publication:

• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publication

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal.

If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverne

Take down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.

Download date: 24. Mar. 2021

..

Laboratorium voor Omvormtechnologie Technische Universiteit Eindhoven

'\ ,t':;-'--\j'~-~"'::'-' .• "'-- _ .... ---

PLAATBUIGEN: Modellen en analyse (Dee12)

Auteurs: ir. S .. M. Hoogenboom ir~~{A.B. Perduijn

WPA rapport 0709 maart 1990

(:/)

[2J

tly ]

[,]

[t]

S. H.1I()1~J-166Ph-1 A. t. E. e. HeM A. 8. P.v2,tI4~·""

S. f1. H(}(}cf4-IoD()~ .4 . s. t:' I:/t all.f,Y ""

.B~.e-"'!/PI- ~ Wf4-,..~?.cz.. ~. JI!,d~# JD""-4.e...·CAh"#!. ruE. VP8 - l.¥pnt Oltro

t;,~hov~ (o4u:.. '9"'1)

P~tUJ.i~~UI!-#1 : /11()o{dk"., #!4-t fiU-r~ bn~~ f'14~~(!f)...b:t.. iuE.

W'PA 'lA.fl'rnt 063, 4.';-.qlJ..{)II'~ (.()epl. "d's)

Al'1t:1.R '1~£. V"'l.7...t~q.L"", !)"7~e. r'1A..~e.,;c.a.6.:e 114 C WPA 1..~I't1Z-t o6'11.t tc.: ...... of. kfN.e.-- (/Ike.,;, ,,8, J

A"'tAI~<. ~ik J~;-<.".. ~ "" t4!:.lZ--$1.e P tA-t.e..:. Jc.a..6.', T fA. c W PA /LyfJr,.d: () t 6 T L;t-Q(J..t"IIt..'1 (~. 1,.9,)

/'I kQ...~/')-I!- U - b ~; t.._

~klAVL""-£ pu...4t!...·t:.l!l.o:.c. ""/,Ilc t.JPA 'l~"'-I:- 0ljl ~ol.l....AT~ (~/lt. ''18j)

A 11A.-t. '14c- /+to. 't.4.f-3..4 ~ ~ ~ ~~ tVt.-k.L pll4.t~.:t!Q...b·1l. TlLE

WPA "-YjP47-f oJo9

~......«.A..Wf.+.t t I'vtM '5,0 J

fOt.~-4~~ : hto«e.bc

~ ~¥L (tJU.3)

~h ~f!./Lt1..L P~~t! .. I:l(! /'{;(1:

4/ P/9 ¥,e>'" I: 0 f08

~-oltc.IJ1J~ (ht."":" '1' oJ

I JPI~(

Bt; dIU ~et"L 1.1"'-'.. p~~t-l>~~~-G-.. t.I~ eec v~~ tCA-M.c-.lit: ~~~ JNtQ.H...L-i:

( Hs) ~ ole. tu"p~~.e va...-.. ~ ;o~~~

( e j t14! 8~ VG\....... oUt ~eA-(2 k~ -...: ...... 0 . /11. 6.t. ""7' VOh.!t:1...Oc .... ol ~oek. ~fe.r>t:v.Ju.. k-..t:I~e-. (£i]~ ["£]) -::<.J.e,,,,,, ,'"", d...:t: ~~ k .ev...:.;e t-..~.:f· cILA'~ t,.Jh.fI(e-.... tAa."' .... ~ e....t~ t olc:e... ~ ~ /l..e./.lt-vlt:.vu.-... ia... .LIZ- "'" t/t) e~ olL

VlOfAA.(,.)~3 e.- ,t~~fva:~ Vtil- ue ~a.; vOl- .u:-. pea.fAt ~i &~-'l ~ ~~ i. V. 1M /LtI.1c4-'7o-lc-.. ~ £/.)c..£r: ~ t ~. t,A- ./ f) h ~ J'l ~ -- i i.,.. U. M.. 'Liz klt-,o/lc ra t--a. .

~"'l ~t'''/~6"...'' :zr tJlnolt ..a...". -6~k~'-'I.J ~ .£e t H (eJ v~.t __ ",( dqLJe- vOn .u,......... dlYJt0d.. - /)teve..

~li/Jd... JM..(!1..ifA.1.Gll-a...e,.; ok.. ",....t>tJl~~ ot....'e.. ~i ilA ~&.. ~1o.-b.1! whQil If}I!.'Il.I'~~ t PIM.a..~ / 2 .. J ) {~p Ih.:c.uA. t ·eLlA. ~lc I>'k.l.i..k"i,· t ~ t il.-t fIlL 4!lP'" VLVl..c:.Vl..3Jt-.... .( PtM../II..~(/ 2.~). j):l ~Q~e. leo........ .e...e. 8 t. "" ~ IX lL~ ~ l c.J fh.Ole- e. t!. oI.A. ---- ct. on. c/')I'k.L ,;~tkJ: tL L.c.4~ vA....... t:J<"t.. e/I~ c tt:e.JoL Ple. /trL __ ~ l I.e... E. £, e.A. ee..:.ot.f col: u- .Jt/L~elf?/to{e.. H (p) /Le..€t:the • ?J..... ~ D /1fItl?) t ....... 1e 'J:o.:: w rt tJl.e........ (;l{.4 ILe/.l /A.. £ L """ t ~ 11"............ IKe

·6~~ n-..(')d.d.f~ 'ae.ae.J4--. Lfo"I wnde..-.. c...~c..~

~el4Qkk.e.- •

~

;a: 1'hr#t..P.fvv.. ...... ; &... tit-e(¥e d.' B.vl~k.en'·"t9 '*i~ ,...~ ...... ~ t CA)

rft'"vl~1 ~ ().~. Jt.~~t. J~~t tJ.lhcA~ va.­/J..£.4Jlo../;.tt.-.,. ";2.oa..&i ~ ~c.I~ >::I...i..... c..", L:l.J.

<Lt um.d f: (}1e VL u v "'1e.....-.oA.e ~ (;) tXl2 .e.t ~ k. ! l~'1~~A/.) f (~ri ~) :

- fA. t.? /l. o-v..,( &. t ~'q(C-!t.- V Ra. k (0/ ::: CI J «- ...... ~{..:..acL 2~~tIIl (X). 8tA.-'t..e- ot.:t 9~.Ivux ( 1'1/ > 'Iv l JU}(A. (.A.Oi 41. ~~ a. ~ ~el. ,/j'{a/l.

P t AA fl:/;) d (Qt.~~(Jl.e-.. :0: ) - <Tv ~ E.2 ':::: 0

pfO-~~·ku 1.4/1: ~Q\.-.t ~ -::. C ( £: -t l'o ) '"

:be.·l .lttkk~/; ~ { c.~ 8 t. ~'(J (;!( :r rAe .I'U!. tAl ~ vOl-. fit> I>ke. g~lol..A-.. ~ ,:..... :II:' ~ vtli.- Vo"" H~~.

qt~·e..d X­

U gt.bU

£-x;: i (I)

(/ //

vo... £d g<-J,J aU 1"'4d ...... ~f!y.i.!J ePadv.,..,e ~)JdrA.6 ~o~ ./f)Q( .f!t.! .t~~ ~t:''--L-l- Mee.

.A"

1'1£.. -= f ~ u;;." /'. '1" !1l '1 '" -~ .a.

--

'l..,-eQ..6:.I. {JJ J~oli tf>£ te.~ ~{vu:o..~ 11)0 tt-::: 1 ~ ~t Jc.,p..,t vtl>~. VOtri oU Wto_ ~lta.£ 'J~~i tX-t.:t

7bt..uotl: J Jt..U.6 [to ~ ()--:;,,~ Iv'~'I'1 I

~. V'J2..- \) 1-/ I

( .:t'-h ::t I - V ) • ~o r -~ ;;?­

J -

"""fJf.vu -If-J ~b.rl.a.M Let. ;oe~/'i4~ J~t>I 1:[- J

oU. f'Le.-A t~ 'r e.- I!: <:1 d oU: L ~ h :1)

'* it" =- ~ -=

C € .6t.t d 'JJ: (7

OIM.« tU. t/!. ~ Ice ~ va- I!.e-- /l.edte /lek vd ) ka-.. I-..~ ~ ~'·~f.e ~kk.e-. J~k~lX UCt7<9tA-....; ~ pddt ";, , 'i/'~' a L

i'Ytd: tX..t. veo.et,v"en.w~ .e-. Rev,! - Vt:>k M~~

~ oU.. ~ - ~'l'd telA--, e..,/i:n,,, •. ole-.. wtn.tX-Lvz

rr?(.::: ~ if Ll067- '1 > c; v

O""x -= ":.&.... a= vOIrt '1 ~ lj v vY

of /,..I.( • .e 1m € t (it)

fJ?(": :; { w ~(I+ t) -+ ~o}n 1/011( 'I>Vv

~ =- -ole { -:( ev, (1+ .!f..) -+ 'fol~ V(}tn '1 (- 'Iv V3Z~ e 'J

~hte~ ~;€A o<.t. ~L.&Le.91e........ T ~::o:-- k~ ~ V/)n ~ t ~w,;.J.c-..G>f """'-0 "'*-~ I: {,.) hGt-t-,. Fp.,.,.. de.- :

(10)

-~ ~ ~

I'1e P -= J fT",. 8 .'1. of'1 .,. f (T". ,. 'I.' p{ '1 .,. f (IX. t. 'I- g{ 'I (!~) .. '0/2 ... YII 'tv.

0/ ~d- tLt) ~ (/3J

-'Iv

-2 c.Bj {~ l,.,(,-+.1f:) '+ roll?~. of'i + V? 6 ~ 'j

- ~DI,-Ifv

~ . .g fy 2 0l (J + I-'\)~ e I

-IfY' -4o/~

~ C. ( f {3.. en (t -+ #: ) -+ '£ 'th U tX. 4 'fi vr e. OJ I I

'-/v

-'I; -Lf {~ e"., (, + v:.) -+ £o,h.lj ~ Q('t rJI 2v3' vY ~e J .

-I I -LJ { L ~ ( ,.,. ~ J -+ 4) YI .. lf~ '" 0/ "i

~ Vi' V5' '- efl( ) ,,:

+

tftt:Ul-.U. 0 -&l v.u-la--«.. M;r ':. Hi3~ ( e"') ~.e..v~ m.el: (Jk. mA.t~·fA...dge~~ '/:'e/.Jc..A~·(/e-...tXL rYe~tJU--

~()) ", J \J ~ E"*:::: IE / c:

). f· 1/. rz-Dl~ tJlR..aA.l1le...- vdC.- e~ ka-. aU... et?- t~ ~~ olL. t.."'-tur~ -"i ,,,(lo(..(. t~()...tX.~""-o-tI-fA. v£.....,. f.e....,..... tJn d.t- 0{ t.>.?t...

(...)(Z~: e:

+

ElY V~~- \) +f '

~ (I - ,,2.) r 0'"

~ ~I:: t. p, V'. '! -= 'tv Uk ~~~ft;hM.,:~·t "? "'" t:(e

4J' ~ """';"""'1 e-. (11f. n. o-.x ) rn-..(Jf tA.-1: : - -U-Co-\ dl'VJt\..?J. J(!~(tI. o"l~l:- ~ ~ ~ y.> ~ In:", e..I. g~./!n;c..tX

- tU.. '[ leA plA. .. b:l~ ~kf>-k [":""IA. ~ ('£ (<<t < ~II) :: 0

~ t (,,::. 0/ "') ':f.: D J ~ lin"". (II))

6

8 1 cP~9le .t.ek~-'J ~ddt ~Jb"'-

u~fJ:::- f2C ( ~. ~/)! 1- \)<) + ~D)n \iT'" V:r s ... (IJ ':(. _ \) + 1)'/2

'? u() l.,:e....,. ~ d "e "" i (J{ "--

. '/ = :? (U:t_V'+') ~(~.

V3' v:r

(),l .t~klt~ .... 1 dal.: O'?tfJ/ o;~ ..;O~ .u.-.. '(.~~t?t Vk,rdV1A:/iLa..t

~.t.( "-'11'\ H..~ J f1A &t.4.'l IILI £.&11-3 t ~ ott. t/ '" d'"L ~ r '-0..-6; e r t:l' •

~ '-'t r.1- 2.1 l4 (23) LI t>-n ..LL..... 6..J..e..e. ta...e I'k crd .e--, .... ,; fl).. ~ tA.,.;..t. de h.e t-a.e, /uv..c tl.-t. V~ £0.

----I~------------~~~~--~

o~ __ ~ __ ~ __ ~ __ *-__ ~ __ ~ -6 -5" -l, -3 -.I -I

10 10 10 10 /D /D

--......... to

S:lJu.1

E-:: :i/().f)()() NA.,..,It C ::: 62.# NI".. ... t YI ::- ()J 2-

\) :: oJ28

Allit "'k;'" ,'fA .......

1::: ]t,()()() It lit...,.. 4.

<= '::: 12.0 If / IMI1h :l

." -= 0, () S"

~ :;. 0,.3

v=~~ /l ~ ~ tJ{M I/t:>tn kL,...;~ WfliWLfJU.-

VlL..". 1: () ~ ~ Ie en... t, '''''-14.,' t ~ l: <--",- 0;. ~~ ~-ta..a..-z.. !..uri UhNf. .

Jt fA:. ,;., ..u...... olVo k. ~ t i H..IA. ,: t e".:. t t-VL r 4. r./ (nn k. ,,""""-~ otrJl)"t LA! ~..e-"~

b.e ..Le IA V () fA. c;f .... : 'J~ te.. I'I-t A.. ~ ()""" I!. ~ ~ t./t. vt>fol.~ ~ l.p_../. (/I) V(>ln l' u()1olt ~i/.)~-t...-..:

~:= .A...l", ( I..,. 't. - ~) \/()~ 'f ';p. I.f v vr e

tt CC/L..........u. t.J tHtX/:

';z.Q tJl.&d

U-xf ::- ?k . 't .., V1

0

~ - ..2- (\J'<._\j+/)'I~ -f7"-x.e v:1'

C!X..e.:: I~ () 2 ~ u?r ~

~ t!II.A:l t/) ~ tt:>~~.-6~.

fYI. tv. (::lS-) k-- 11-"" ..e.e-.. V~~~· v~ ... Va- ~ -6~J'-ot ~.-c-I: f,.)~ -t~4.~o(.

("t)

h1.e;t t£ r) (,J In gt:l be- k. c/ otn. o-x ,~

tr')( -::. ~ { ~ .eh (I + 'i-elf/;/.) -t- It)}h

h-tek (Jl.;J ~ et.:~£. ..... /:n.:e..-tDtrJ ~ec~~ ulhol/: ol.(/J.~

VOIn Hs? '~,,",-Q{~ VI

-«v _ .l.-Ji ~ !M (,..,. ~..,..,.'t: ) -t- 10}t"I 'ttl( til '1 ~ .2. V3' vy 2. e""

I -I

+ ~ J J ~l"(I+ 'I:

R «. "'" 4rk t. w i. Ie tc ~ ..... S vA-.""

JtL~

1-1: -I::>p -

(3 oJ

h1u ~Lu.Rf'J"-- Q(.L 1?Jf;lI.nolfAAA..ol t;",..~ yz~ (,8) lIJ'JdtYlt-

J ~I /; Ifi.A,t .

9

f(ett:t.ti-£ tt~) I.uJ~ .LeI: .i.~~_otX..e..e ~<..eA. 7u:>~ d~1. t.d ~'~l:Jtv.J! L~ ..u..,.., 41.1:1t--lA.R ""-A~C/) t/~ ,PttaQ.t-4~d -p/Wc~CA-.. ( L3] tin. [6J> t.t.t! . .LLr-. /,,:r.. 1~9, t .. ,,:{~e,)oVt« 1/'10- '/.I.E pfa.M~~Q~i~(!t,. rlA.v. r;<e eJ~i?~tIl v"'- o(.,.:f:- ~ ole ~M..~(l. i",.,. eL.-l /LA!, pn I: v ()tn.i< OA.-. .e.-.o(..e 1+\.001 d.t e-- Ie. ~ ~ t:X.4

~K. 1.10 ~.e.- c:>£c.. ey:>"'" &It Ai ..... ,.I.-- W n ()i,- & fl.""'" AlA k I: ;

~ 12~I(A.t,:c. lib) ("uc.~c.~k ~c.L·""t.e.r-U/LtJl ..e.......

~/lQ.?d. tJ.f.t/L'JIl.'j.e..u-.. ~-- rl 3.1 J u v~fi.e........ 7> .&~ vA-- ~ ~tJ...l ~.cu-to...ot~""" qe- J J~ th.o ~

- \J~~vi-!J V'R- ~ #'f..~U4..Le v--RA.-k tA

I'f..U ,:... /L6Icl~-i gJA-A.-cLl: . - €A i.4 Q u..... f>k ~ "'d ~ 3€ 64A-Q. 4.. A f t~.c.-...

ole. t,' fA.. C. t ,:.;:.l.(. e....... tJl€ Jtt,.. 0 Wt e-. tA.k tl f' f);)-r.: A:~ v tt-hAQ,l,tf..A.A.i:.t fl K.u.L '-/4A J tX,:i:- /,.JV/.. k I:: 0 .. ca.. g( (Xn.

/.A,.,. CI!e L-k-truyta..L~~~~ "",dice. c~t"",,- t tlffl.t.H.

crt fl H "I! ...... ,xll. ~e 11. A ~ ..... 1 ~ w en. ~ /.).tL e.L.' e;'l... n aJ'J/l. ~t:t te aU kA.~uh!A~ k£u.~ un.d./;.

()d i!.u./ 0.1i, If>t ~e.t/£~ r;la.t v~c..Je~tl ~ Q./j'Jhtn...~ va-. QU. "'--4..-I~;·Ic.e. ~i..-.L {v~. tI3)) ol.e. nn".,. A Q..l KAlldf N:f: 0 lUtnoU: ('2.c..e h 3.!2 1

fIll( -:: N I(C h -:So):; '/(C ..-\D) J 0-" t1l'l ).; oLc.:l V,) i ..... 4rlA.i III fk~ oLe ~14-t.L V'A...... ~ ~vve.c. -4 ~--, • l>ii:. ,ft:ULfAJt~ k~ KfA.. w~ tI~~ QLI>tn. v/rtn

oU 14..i"'-".ryk(! k(~l-.,c.. ~ ~ 1tA-~b:~ te lite. ".....c.-... (1/4. ('1)) fIltI.tVt-venn (.j~~ p d,,< f: f:IltU IY:::- 0 .,

CJt..~I>.ef.ik.«£ ~MI.~~3 ~/i It>c ,w".lg "'-Q..l tJlf; i. ... u~J a-.Q..ry l1/Jc.L kfit- Un 1JIl.......... c:f,c.~h'f

~.t. J'l .IU./,.1 d~ ,u L:"", r'1 s./ r-~CL /.,J.uA..g~~~ .u..tA.l~ (/~). ?2t>~ ,:1-1.. 4>C.t. Ie. &u/I ~ ,f:( ~ V,:) te ~ J ~ l.e..1: ,,~d c:L l ~.e.-. a<...e -8~ 12.€ .Ro-H4V:> Ie t' ~"'" , U8n~I..I()f>e-..ol ~ cXc. ~tA-.ftA.le-... ,,~ ~ Vt:-1."~-

e'1k~.e-1c f,J LJ~i ..t::.e. ...... t.JD..(LIl~(~ lko~7 t 'Ad. vVVldt-:.. tA'_, ~ ~ /IIle-..tA.A.4. v~Q..I<)

10

lit Mb

0.3

0.2

0.1

0.0 0.00 0.50 1.00 1.50

h. 3.1 11: - 'Ie lt v.vz.b",,-tX. Vpen.

SI:.tA..A.i: n = OJ 2..lf J C: :;-80 N /ht_ '-,) fo:::- ~ oo~

E: ~/O kN/~~ttJ \):::~.'(8.

/-}ftA~il'titA.lNt.: 1'1: ~OS) (!: IltoN/It...".,,:tJ fc":::~OOS

E::= to kHI"",,,.,,a.., 'V:::-q3.

- - - - - V.IVL~. ( I h )

--- v~.(/,)

0.06 ,------,------,---..,.------,----.........,..---..,

0.05

0.04

• N 0.03

0,02

0.01 l-:;;;;;;;;;;;;;~~~=====:==~:=J 0.00 0.00 0.50 1.00 1.50

lJe ntn.""" ~1otA.d ft.,. v. M'1;..... ........... ~ v~ otc...

ntit t,AAA.A '7' kL eo! A/L, .. :t 1Ik.-L

( ht~ .. Jn~ ~~ f, 3.1)

~ t~£.~Q../.lt e-t tJePkt!:.. l~VI.. 'je'&-fl..e-....... H",'*'- 'Ie'" luto"' ....... ~_ op-eev~!:. J 1A-1~ 'iec />"IAc.l",,~tX.. t.Jtn.~ otot ruR .. f ... "t- ((,,) tJ~'d~'J-1Pik t.eC~ ~dvz. VI) e 01. t>,-l (!;{ A- (I b J •

.8:. f3it' oUt. ... /ec(.·~",,-~ V~ Ve/l..~. (lt1) V:! eA -u.V\. 0(. t/3 k i)"'IA f ":VI. fA.;': t. e".: t L:/A ot.L E: ~ of.t:;.. tVl-~ ..e.e L ~ o;c

* Mb

~L.)~ (PtR/l. 2.:< ) r,' :<.1). bit. ~ Ii tot: 1. e t/a-t 3- ~ v Pin kPc"f.:IA.£. W a.aA. ~ VA- ie 4l hW_ lie" l/(A..8t:?o-..Pl ,:", t>U o~"/t:""'i­

v~ e; t.'k ~7"'" a;~e.f~~ 1Ut-"'- ~ kOrk ~l·lA.lA.. v&tR()~() ~~/t (>;u;er3 3.'3) J' tfYL"'-!VC/'I.A.lAd £.-""-

~/; ~L~l.fIl bvVLt ~ ~dfo .u..~ te..q~~€./:Y~~

/VU)/Nt. ~ fA Q t> P .

0.05 l 0.04 l 0.03

0.02

0.01 ./

0.000 Vev

L LIfk.~I:i<f,h ... 1

vtll3' (19) ,., ...... /

/

0.001

i __

0.002

Nbtlr - '/ eo« vt/'t.8",-rA.. I.:.,.,.. ~

on...~e..c.n.: ..... ~ ~ ev· ( St6U/l-l: n :: OJ:2'1

C'::: S80 N/J-t.,,,,,,,f( ) '., :: OJ 0001 ).

/)il f!rllt.el: ka.-.. v/L~' ~lA.vi>~ G:,~(l..k~ te..~t w~ ,£.~ tJloh ~t~H-:w.;;t.e.c..'t U ~.e.-. vA......

r l.p.v. 0/ .. {VUl.t.(2t,J e.", (.:lS'")).

'-I -

~ J!.oe 1£ ..... 4A.~ ..o~. <i c~t;..e,,;z cy' ~~ Vt"f.-.

let ~~ t>f>~ t-:.fA.3 z. (ehO€~rX~ J ~t::LJ. ~u:;td.t (,J11'1-1IIlc.-... q£a..t vVt1 ( 3 d -tUtA. "4J vo~«~)

m. 11. 1/ #!t't !UlVC4 R. u. t'1J!e H.u. "'-c..Ik-'e k. II!- Jf/2wen.. k..;V!.. J­~/I= tJa..Il/l..~~· t:t/. hi. ~/c,/.u.ft "uulc~ vr...: ....... ,.L-... ':1-1. rXt. 19':"'1£ ,...,..,~ 1Itc-... lie: oIL (e.oV./IG/t.e-t~ V61,.."",­

l,,)f17.. oI.i b" e ~ tI./,a.-:> e- I e..;~ l $" J ) .

~.., aU.. f>'I-.~ £. t/1.'~ ~ ~ 'I~: >:Gi.j.... ~ (.'... ot.:.. ~ /I. a.!,P ~ t­,,?,ek~ ~~'"-o«,,~ ~i ,..e vl>e4', t/otn. ote tJ~ot..e. V~ ro #

Vlltn ot.Ar. .t,.;~,;~ Eo ~ 0 (e: -.. co) ~ v~~ (3')

N,f/tf - I ~ - -(~--)-{--)~h-+-'-e-~~n-

h+~ • VS' •

~ t4 tX ""-.. t Lt. 6'\. d ~ 1":10 d. a t.. ~oI. ~ • -he-{; IIVL~ ~~ ~"'ev.e.t.:.'"-d tn-. t'l' t?iL "tt..~-1 ()~ tN. ""-o..i:~~~e.oe"'~ ~. t. v. olt ~~L I u. "'- ~ k ~ '&"'e,. tK 64 lc.:.t.A.e.- ~ IJ7.1.. ~J.cvt- enr~ k ~ t n-el::: o<..e. ~ ~tX.d.d r.X.e..

.Jz.ek "ii £.d. tL-wl/~~ ~~~pAA>c.e/J.

R~e/t.ehrA kit.- ec-4e.l6e. wtn..Ole- ~1Z~C.e....~e;>( If1la..I::: v~ of.&. ~ ilA- 6f!,;.C 'l..Q../'FIl.t v~JrX..e ~~~'-olJll.ebe.- (~. (,oj ) (Ifj) ~ (3/)) ~~ (l/J 4 ~ -t Q/.) 6i:- t:l.d V e-tole>~", •

Iv