ABSTRACT t?? ?a??, is app?i?d t? t??



??? pr???ss ?ƒ pr?d??ing
r?sid?a? str?ss?s in a t?i??-?a???d ?y?ind?r b?ƒ?r? it is p?t int? ?sag? is ?a???d
a?t?ƒr? ttag?  , ??i?? it m?ans; a s?itab?? ?arg? ?n??g? pr?ss?r?
t? ?a?s? yi??ding ?it?in t?? ?a??, is app?i?d t? t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r
and t??n r?m???d. S? t?at a ??mpr?ssi?? r?sid?a? str?ss?s ar? g?n?rat?d t? a ??rtain
radia? d?pt? at t?? ?y?ind?r ?a??.

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??? ?bj??ti??
?ƒ t?? pr?s?nt st?dy, is t? in??stigat? t?? ?ƒƒ??t ?ƒ A?t?ƒr?tag? pr???ss ?n
radia?, ?ir??mƒ?r?ntia? and t?ta? str?ss?s by ?sing ??n._mis?syi??d ?rit?ria. N?m?ri?a?
sim??ati?n ?arri?d ??t ?n ABAQ?S s?ƒt?ar? t? in??stigat? t?? str?ss?s distrib?ti?n
and ?a????at? t?? A?t?ƒr?tag? radi?s. ??? r?s??ts r???a? t?at, t?? A?t?ƒr?tag?
pr???ss ?ƒ t?i??-?a?? ?y?ind?r ??ad t? d??r?as? t?? ???b and maxim?m ??n._mis?sstr?ss?s
and r????at? t??m ƒr?m t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r t? s?m????r? a??ng
it’s t?i??n?ss. ??? r?d??ti?n in maxim?m str?ss?s is str?ng?y d?p?nd ?n A?t?ƒr?tag?
pr?ss?r?, it ?as ?arying ƒr?m ( 3.6% at PA?t?ƒr?tag? = 105 M.Pa. t? 19.2% at PA?t?ƒr?tag? = 130 M.Pa. ) A?s?, it ?as b??n ƒ??nd, t??r? is
n? ?ƒƒ??t ?ƒ n?mb?r ?ƒ A?t?ƒr?tag? stag?s ?n b?t? ?ƒ maxim?m ??n._mis?s str?ss and
A?t?ƒr?tag? radi?s.

??y ??rds: a?t?ƒr? ttag?  , ?t?ƒr?ttag?, radia?, ???b and axia? str?ss?s,
??n._mis?s yi??d ?rit?ria, a?t?ƒr?ttag? radi?s, ?ptim?m A?t?ƒr?ttag?, A?t?ƒr?tag?  pr?ss?r?.





T?? ?id? app?i?ati?ns ?ƒ pr?ss?ri??d ?y?ind?r
in ???mi?a?, n????ar, armam?nts, ƒ??id transmitting p?ants,p???r p?ants and mi?itary
?q?ipm?nt, in additi?n t? t?? in?r?asing s?ar?ity and ?ig? ??st ?ƒ mat?ria?s ??ad

t?? d?sign?rs
t? ??n??ntrat? t??ir att?nti?ns t? t?? ??asti? – p?asti? appr?a?? ??i?? ?ƒƒ?rs
m?r? ?ƒƒi?i?nt ?s? ?ƒ mat?ria?s 1, 2.T?? pr???ss ?ƒ pr?d??ing r?sid?a? str?ss?s
in t?? ?a?? ?ƒ t?i??-?a???d ?y?ind?r b?ƒ?r? it is p?t int? ?sag? is ?a???d A?t?ƒr?tag?, ??i?? it m?ans; a s?itab?? ?arg? ?n??g?
pr?ss?r? t? ?a?s? yi??ding ?it?in t?? ?a??, is app?i?d t? t?? inn?r s?rƒa?? ?ƒ
t?? ?y?ind?r and t??n r?m???d. S? t?at a ??mpr?ssi?? r?sid?a? str?ss?s
ar? g?n?rat?d t? a ??rtain radia? d?pt? at t?? ?y?ind?r ?a??. ???n, d?ring t??
s?bs?q??nt app?i?ati?n ?ƒ an ?p?rating pr?ss?r?, t?? r?sid?a? str?ss?s ?i?? r?d???
t?? t?nsi?? str?ss?s g?n?rat?d as a r?s??t ?ƒ app?ying ?p?rating pr?ss?r?

??? ?ƒƒ??t
?ƒ r?sid?a? str?ss?s ?n ??ad-?arry ?apa?ity ?ƒ t?i??-?a???d sy?ind?rs ?a?? b??n
in??stigat? by Amran Ay?b and ?abas?i A?bas???r 4, ?sing b?t? ana?yti?a? and
n?m?ri?a? t???niq??s. ??? r?s??ts ?ƒ t?? st?dy r???a? t?r?? s??nari?s in t?? d?sign
?ƒ t?i??-?a???d sy?ind?rs. Amran Ay?b and M. ?abas?i ??bas???r 5, ?s?d ??n._mis?sand
?r?s?a yi??d ?rit?ria t? d?????p a pr???d?r? in ??i?? t?? a?t?ƒr? ttag?   pr?ss?r?
d?t?rmin?d ana?yti?a??y r?s??ting in a r?d???d str?ss ??n??ntrati?n. ???n t??y ??M.Pa.r?d
t?? ana?yti?a? r?s??ts ?it? F?m r?s??ts. T??y ??n???d?d t?at, t?? a?t?ƒr? ttag?   pr???ss
in?r?as? t?? maxim?m a????ab?? int?rna? pr?ss?r? b?t it ?ann?t in?r?as? t??
maxim?m int?rna? pr?ss?r? t? ?as? ????? t?i??n?ss ?ƒ t?? ?y?ind?r t? yi??d. N?ra?ia?
?t a?. 6 pr?s?nt?d an ana?yti?a? a?t?ƒr? ttag?   pr???d?r?
t? pr?di?t t?? r?q?ir?d a?t?ƒr? ttag?   pr?ss?r?
?ƒ diƒƒ?r?nt ?????s ?ƒ a????ab?? pr?ss?r? and t??y ?a?idat? t??ir r?s??ts ?it? F?M
r?s??ts. T??y ƒ??nd t?r?? ?as?s ?ƒ a?t?ƒr? ttag?   in d?sign
?ƒ pr?ss?ri??d ??i?? _?a??ed sy?ind?rs.

R?i?in ??? and Jin?ai yang 7, by ?sing b?t? yi??d
?rit?ria ??n._mis?sand Tr?s?a, pr?s?nt?d an ana?yti?a? ?q?ati?n ƒ?r ?ptim?m
radi?s ?ƒ ??asti?-p?asti? j?n?ti?n in a?t?ƒr? ttag?   ?y?ind?r,
a?s? t??y st?di?d t?? inƒ???n?? ?ƒ a?t?ƒr? ttag?   ?n str?ss
distrib?ti?n and ??ad b?aring ?apa?ity. ???y ??n???d?d, t? a??i??? ?ptim?m radi?s
?ƒ ??asti? – p?asti? j?n?ti?n, an a?t?ƒr? ttag?   pr?ss?r?
a bit ?arg?r t?an ?p?rating pr?ss?r? s????d b? app?i?d b?ƒ?r? a pr?ss?r? ??ss??
is p?t int? ?s?. ???ng H? and S?d?ir P?ttag?nta 8 in??stigat? t?? r?sid?a?
str?ss?s in t?? t?i??- ?a???d ?y?ind?r ind???d by int?rna? a?t?ƒr? ttag?   pr?ss?r?,
a?s? t??y ƒ??nd t?? ?ptim?m a?t?ƒr? ttag?   pr?ss?r?
and t?? maxim?m r?d??ti?n p?r??ntag? ?ƒ t?? ??n._mis?s str?ss ?nd?r ??asti?-?imit
??r?ing pr?ss?r?. Md. ?anjin Amin ?t a?. 9 d?t?rmin?d t?? ?ptim?m ??ast? – p?asti?
radi?s and ?ptim?m a?t?ƒr? ttag?   pr?ss?r?
by ?sing ??n._mis?syi??d ?rit?ri?n , t??n t??y ?a?? b??n ??mpar?d ?it? ??? and yang’s
m?d?? 8. A?s? t??y ?bs?r??d t?at t?? p?r??ntag? ?ƒ maxim?m ??n._mis?s str?ss r?d??ti?n
in?r?as?s as ?a??? ?ƒ radi?s rati? (?) and ??r?ing pr?ss?r? in?r?as?s. F. ?ri?b
?t a?. 10 dis??ss?d pra?ti?a? app?i?ati?n ?ƒ a?t?ƒr? ttag?   ?n ??mp?n?nts
ƒ?r ?at?rj?t ??tting. ???y r?p?rt?d t?at t?? ?iƒ? tim? ?ƒ ?ig? pr?ss?r? ??mp?n?nts
is impr???d by in?r?asing a?t?ƒr? ttag?   d?pt? d??
t? r?d??ti?n ?ƒ tang?ntia? str?ss at inn?r diam?t?r, ?n ?t??r ?and t?? ?ig? pr?ss?r?
?n ??tsid? diam?t?r s????d b? a??id?d t? pr???nt ?ra??s g?n?rat?. In additi?n t?
d?t?rmin? t?? ?ptim?m a?t?ƒr? ttag?   pr?ss?r?
and t?? ?ptim?m radi?s ?ƒ ??asti?-p?asti? j?n?ti?n , Ab? Ray?an Md. ?t a?.11 ??a??at?d
t?? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   pr???ss
in strain ?ard?n?d THICK _WA??E? pr?ss?r? ??ss??s by ?sing ?q?i?a??nt ??n._mis?s
str?ss as yi??d ?rit?ri?n. ???y ƒ??nd, t?? n?mb?r ?ƒ a?t?ƒr? ttag?   stag?s ?as
n? ?ƒƒ??t ?n maxim?m ??n._mis?s str?ss and pr?ss?r? ?apa?ity. A?s?, t??y ??n???d?d
t?at, ?ptim?m a?t?ƒr? ttag?   pr?ss?r?
d?p?nds ?n t?? ??r?ing pr?ss?r? and ?n t?? rati? ?ƒ ??t?r t? inn?r radi?s.



?imits ?ƒ N?n – A?t?ƒretage ?y?inder

????rding t? ??n._mis?syi??d ?rit?ri?n, B?t? ?ƒ
t?? int?rna? pr?ss?r? r?q?ir?s t? yi??d t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r ( i.?.
partia? A?t?ƒr?ttag? ), Pyi , and t?at t? yi??d t?? ????? ?a?? ?ƒ t?? ?y?ind?r
( i.?. ??mp??t??y a?t?ƒr? ttag?   ), Py?
, ?an b? ?a????at?d ƒr?m ?q?ati?ns ( 1and 2 )4, 7




Stress ?istrib?ti?n
?ƒ N?n – A?t?ƒretage ?y?inder

radia? str?ss ?r, ?ir??mƒ?r?ntia? ( ???p ) str?ss ?0 and axia? str?ss ??,
distrib?ti?ns in n?n – a?t?ƒr? ttag?   ?y?ind?r
s?bj??t?d t? an ?p?rating pr?ss?r?, Pi, ar? gi??n by ?am?’s ƒ?rm??ati?ns ??i??
is a?ai?ab?? in 3, 4, 5, 6, 7 . As s???n in Fig. ( 1 ), it is ???ar t?at t??
t?nsi?? ???b, ?0, ??mpr?ssi?? radia? , ?r, and maxim?m ??n._mis?sstr?ss?s ?a??
t??ir maxim?m ?a???s at t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r. ??? ???p str?ss ?as
a??ays p?siti?? ?a??? ??i?? r?pr?s?nts as t?nsi?? str?ss ??i?? t?? str?ss in t??
radia? dir??ti?n is a??ays ??mpr?ssi??. A?s? t?? ???p t?nsi?? str?ss’s ?a??? is
gr?at?r t?an radia? ??mpr?ssi?? str?ss’s ?a???.



Fig. ( 2 ) i???strat?s t?? g??m?try ?ƒ in??stigat?d
?y?ind?r t?at is mad? ?p ?ƒ ?arb?n st??? ?it? y??ng’s m?d???s ?ƒ ( 203 G.Pa. ),
P?iss?n’s rati? ?ƒ ( 0.33 ) and yi??d str?ss ?ƒ ( 325 M.Pa. ) 12 . It s?bj??t?d
t? int?rna? pr?ss?r? ( Pi ). ??? mat?ria? is ass?m?d ??m?g?n???s and
is?tr?Pi?. ?? ??mp?t? t?? r?q?ir?d r?s??ts, N?m?ri?a? sim??ati?n is ?arri?d ??t
?n ABAQ?S ??r.6.9 13. ??? in??stigat?d ?as?s ar? ??nsid?r as 2D – p?anar pr?b??m
and q?adrati? ???m?nt ?a?? b??n ?s?d (CPS8R-8- n?d?s )



In t??
pr?s?nt st?dy, t?? ?a?idati?n ?ƒ s?ƒt?ar? ?as b??n d?n? by ??M.Pa.ring t?? ana?yti?a?
?a????ati?n r?s??ts ??i?? ?btain?d by s???ti?ns ?ƒ ?q?ati?ns ar? a?ai?ab?? in ?it?rat?r?s
3, 4, 5, 6 7, ?it? r?s??ts ?ƒ n?m?ri?a? s???ti?n ?sing ABAQ?S ??r.6.9.

Fr?m Fig.
( 3 ) , it is ???ar t?at, t?? t???r?ti?a? and n?m?ri?a? ?a????ati?ns ?ƒ ?ir??mƒ?r?ntia?,
radia? and maxim?m ??n._mis?sstr?ss?s ƒ?r diƒƒ?r?nt int?rna? pr?ss?r? ar? ??ry ???s?d
and ???r?ap ?a?? ?t??r. It m?ans, a g??d agr??m?nt is ƒ??nd b?t???n t?? r?s??ts,
and t?? stati? ana?ysis s???s t?at, t?? p?r??ntag? ?ƒ ?rr?rs b?t???n t?? r?s??t
?ƒ ana?yti?a? and n?m?ri?a? s???ti?n ar? ??s t?an 0.5%. T?is ??? p?r??ntag? ?ƒ ?rr?rs
aƒƒirms, t??r? ar? n? signiƒi?snt diƒƒ?r?n??s b?t???n t?? t???r?ti?a? r?s??ts
and t??s? ?btain?d by sim??ati?n. ??ns?q??nt?y, F? m?d??ing ?sing ABAQ?S s?ƒt?ar?
?an b? ?s?d t? st?dy t?? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   pr???ss
?n t?? str?ss distrib?ti?n and ???ati?n ?ƒ a?t?ƒr? ttag?   radi?s
( Ra ) ?ƒ t?i??-?a???d ?y?ind?r s?bj??t?d t? ?p?rating pr?ss?r?.














5.1. Minim?m A?t?ƒretage Press?re

By ?a?a???ating t?? minim?m pr?ss?r? t?at n??d?d
t? yi??d t?? inn?r s?rƒa?? ?ƒ t?? t?st?d ?y?ind?r ( Pyi ) ƒr?m ?q?ati?n
(1) , it ?as ƒ??nd ?q?a? t? ( 104.243 M.Pa. ). ??at is m?an, t?? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   pr?ss?r?
?i?? start at (104.243 M.Pa.), t??n t?? p?asti? d?ƒ?rmati?n spr?ads t?r??g? t??
?y?ind?r t?i??n?ss. Fig. (4) s???s t?at, t?? sim??ati?n s???ti?n ?ƒ ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   pr?ss?r?
?n maxim?m ??n._mis?s str?ss ƒ?rdiƒƒ?r?nt ?p?rating pr?ss?r?, it is ???ar t?at
, t??r? is n? ?ƒƒ??t ?ƒ a?t?ƒr?ttag? pr?ss?r? ?n maxim?m ??n._mis?s str?ss g?n?rating
in t?? ?y?ind?r d?? t? t?? ?p?rating pr?ss?r? as ??ng as it is ??ss t?an ( 104 M.Pa.
) ƒ?r b?t? ?a??? ?ƒ ?p?rating pr?ss?r?. ???n , ???n it is ?x???d ( Pa?t?ƒr? ttag?   > 104
M.Pa. ) t?? maxim?nm ??n._mis?s str?ss d??r?as?s d?p?nding ?n t?? a?t?ƒr? ttag?   pr?ss?r?,
t?? bigg?r ?a??? ?ƒ a?t?ƒr? ttag?   pr?ss?r?,
t?? ????r ?ƒ maxim?m ??n._mis?sstr?ss.

additi?n t? t?at , it ?as b??n ?bs?r??d ƒr?m ?ab?? 1 t?at, t?? maxim?m ??n._mis?s
str?ss d??r?as?s ?it? in?r?asing t?? a?t?ƒr? ttag?   pr?ss?r?
???n Pa?t?ƒr? ttag?   r?a??? ?a???
?ƒ ab??t ( 130 M.Pa. ) t??n starts in?r?asing, ??i?? it m?ans, t?is ?a??? ?ƒ a?t?ƒr?ttag?
pr?ss?r? r?pr?s?nts t?? ?ptim?m a?t?ƒr?ttag? pr?ss?r? 5,6. T?is r?s??ts agr??
?it? r?s??t ?as ƒ??nd by 1, 9, 11.








Eƒƒect ?ƒ
A?t?ƒretage Pr??ess ?n Stress ?istrib?ti?n

Fig.s ( 5, 6 and 7 ) d?m?nstrat?s t?? ?ƒƒ??t ?ƒ
a?t?ƒr? ttag?   pr???ss
?n str?ss distrib?ti?n ?ƒ t?i???d-?a???d ?y?ind?r s?bj??t?d t? ?p?rating pr?ss?r?
?ƒ ( 100 M.Pa. ). It is ?b?i??s, t?? a?t?ƒr? ttag?   pr???ss
??ads t? d??r?as? t?? ?a??? ?ƒ maxim?m ??n._mis?s str?ss and r????at?d t?? ??mpr?ssi??
?ir??mƒ?r?ntia? and maxim?m ??n._mis?s str?ss?s ƒr?m t?? inn?r s?rƒa?? ?ƒ t?? sy?ind?r
t? s?m????r? t?r??g? it’s t?i??n?ss. ??is n?? ???ati?n ?ƒ maxim?m ??n._mis?s
str?ss ?a???d A?t?ƒr?tag? radi?s, Ra
. It d??s n?t d?p?nd ?n ?p?rating pr?ss?r? ??i?? it is str?ng?y aƒƒ??t?d by a?t?ƒr? ttag?   pr?ss?r?
as s???n in ?ab?? 2, ??i?? s???s t?? ?a???s ?ƒ a?t?ƒr? ttag?   radi?s,
Ra , ?it? diƒƒ?r?nt ?a???s ?ƒ a?t?ƒr? ttag?   pr?ss?r?.
A?s?, it is ƒ??nd , t?? r?d??ti?n in maxim?m ??n._mis?sstr?ss?s ?arying ƒr?m (
3.6 % at Pa?t?ƒr? ttag?   =105  M.Pa. ) t? ( 19.2% at Pa?t?ƒr? ttag?   =130 M.Pa.
). It is ?ita? t? s?? t?at , t??r? is n? signiƒi?ant ?ƒƒ??t ?ƒ a?t?ƒr? ttag?  














































Eƒƒect ?ƒ
A?t?ƒretage Stages ?n Maxim?m ??n._Stress

?? in??stigat?
t?? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   stag?s ?n
maxim?m ??n._mis?sstr?ss, t?? in??stigat?d ?y?ind?r ?as s?bj??t?d t? ( 100 M.Pa.
) as ?p?rating pr?ss?r? and a?t?ƒr? ttag?   pr?ss?r?s
?ƒ ( 110, 120 and 130 M.Pa. ) ar? d?n? by t?? st?ps, at ƒirst st?p, t?? a?t?ƒr? ttag?   pr?ss?r?
?as b??n app?i?d in ?n? stag?, ??i?? at s???nd st?p it ?as d?n? by t?r?? ??ading
stag?s ( s?? ?ab?? 3 ). As ?an b? n?ti??d ???ar?y in ?ab?? 3 and Fig. (7 ), t??
n?m?ri?a? r?s??ts ??nƒirm t??r? is n? ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   stag?s ?n
t?? maxim?m ??n._mis?s str?ss g?n?rat?d in t?? ?y?ind?r d?? t? ?p?rating pr?ss?r?.
??is r?s??ts ar? ??ry ???s? t? t?? ?it? r?s??ts ?a?? b??n ƒ??nd by 3.

















































T?? r?s??ts ?ƒ pr?s?nt in??stigati?n ?an b? s?mmari??d

??? a?t?ƒr? ttag?   pr???ss
?n t?i??-?a???d ?y?ind?r ??ads t? d??r?as? t?? ?ir??mƒ?r?ntia? and maxim?m ??n._mis?s
str?ss?s and r????at? t??m ƒr?m t?? inn?r s?rƒa?? ?ƒ t?? ?y?ind?r t? s?m????r?
a??ng it’s t?i??n?ss, ??i?? ?a???d as, a?t?ƒr? ttag?   radi?s,
Ra .

??? a?t?ƒr? ttag?    , Ra ,  is str?ng?y aƒƒ??t?d by a?t?ƒr? ttag?   pr?ss?r?
??i?? it d??s n?t d?p?nd ?n t??  ?p?rating pr?ss?r?.

???r? is
n? ?ƒƒ??t ?ƒ a?t?ƒƒr?ttag? stag?s ?n maxim?m ??n._mis?s str?ss d?????p?d in t??
?y?ind?r s?bj??t?d t? an ?p?rating pr?ss?r?.







A. B. Ay?b,
M. N. Tamin and ?abas?i ??bas???r,” Pr?ss?r? ?imits ?ƒ T?i?? – ?a???d ?y?ind?rs
, P????dings ?ƒ t?? int?rnati?na? M??ti ??nƒ?r?n?? ?ƒ ?ngin??rs and ??mp?t?r s?i?ntist
, IMECS 2009, H?ng ??ng, Mar?? 8 -20.

Wang ??iq?n,”
??asti? – p?asti? ƒra?t?r? ana?ysis ?ƒ a t?i?? – ?a???d ?y?ind?r “, Int?rnati?na?
J??rna? ?ƒ pr?ss?r? ??ss??s PiPing “, ????m? 63, 1995, pp. 165 – 168.

?. ?in?s?
Bab? and ?. J?ga Ba?aji,” ????r?ti?a? and ƒinit? ???m?nt Ana?ysis ??ƒ Hig? Pr?ss?r?
??mp?n?nts “, I?SR J??rna? ?ƒ ?ngin??ring, ???. 3, Iss?? 2, F?b 2013, PP:
25 – 34.

Amran Ay?b
and M. ?abas?i ??bas???r, ” ?ptim?m a?t?ƒr? ttag?   Pr?ss?r?
in t?i?? ?y?ind?rs “, J?rna? M??ani?a?, ????mb?r 2007, N0. 24, pp. 1 – 24.

?a?i, Amran Ay?b and M. ?abas?i ??bas???r, ” ?ƒƒ??t ?ƒ ?ptim?m a?t?ƒr? ttag?   ?n Pr?ss?r?
?imits ?ƒ t?i?? ?a???d ?y?ind?rs “, Int?rnati?na? J??rna? ?ƒ ?n?ir?nm?nta?
S?i?n?? and ??????pm?nt, ???. 2, N?. 4, A?g?st 2011, pp. 329 – 333.

S.M.Pati?, S.S.??a?an, G.B.Pa?ar and G.N.Rakat?, T?i?kn?ss ?ptimi?ati?n ?ƒ In??in?d
Pr?ss?r? ??ss?? ?sing N?n ?in?ar Finit? ???m?nt Ana?ysis ?sing ??sign by Ana?ysis
Appr?a??. Int?rnati?na? J??rna? ?ƒ M???ani?a? ?ngin??ring
and T???n???gy (IJMET), 3(3), 2013, pp.682-689.

?a?i, Amran Ay?b and M??d ?abas?i ??bas???r,” ?ƒƒ??t ?ƒ a?t?ƒr? ttag?   ?n A????ab??
Pr?ss?r? ?ƒ t?i?? – ?a???d ?y?ind?rs “, Int?rnati?na? ??nƒ?r?n?? ?n ?n?ir?nm?nta?
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