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Дослідження напружено-деформованого стану осесиметричних пружно-пластичних циліндричних оболонок під впливом локального імпульсного навантаження: Авто

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IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

?INOEOOO I?IAEAI IAOEIIAOAeOAAIIss

?i. A.I. I?AeAI?IIAI

A?cthe Aiae??e Aaea??eiae/

OAeE 539.3

Aeine?aeaeaiiy iai?oaeaii-aeaoi?iiaaiiai noaio

inaneiao?e/ieo i?oaeii-ieanoe/ieo oeee?iae?e/ieo

iaieiiie i?ae aieeaii eieaeueiiai ?iioeueniiai

iaaaioaaeaiiy

05.02.09 – aeeiai?ea oa i?oei?noue iaoei

Aaoi?aoa?ao aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

eaiaeeaeaoa oaoi?/ieo iaoe

Oa?e?a – 1999

Aeena?oaoe??th ? ?oeiien.

?iaioa aeeiiaia o a?aeae?e? ianoaoe?iia?ieo iaoai?/ieo i?ioean?a
?inoeoooo i?iaeai iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie.

Iaoeiaee ea??aiee: eaiaeeaeao oaoi?/ieo iaoe, noa?oee iaoeiaee
ni?a?ia?oiee Eieiaeyaeiee Aiaoie?e A?eoi?iae/ ?IIao ?i. A.I. I?aeai?iiai
IAI Oe?a?ie, i?ia?aeiee iaoeiaee ni?a?ia?oiee

Io?oe?ei? iiiiaioe: aeieoi? oaoi?/ieo iaoe, i?ioani?,

Ii?a/eianueeee Ieaa Eiinoaioeiiae/

Oa?e?anueeee aea?aeaaiee iie?oaoi?/iee oi?aa?neoao,

caa?aeoth/ee eaoaae?ith oai?aoe/ii? iaoai?ee;

eaiaeeaeao oaoi?/ieo iaoe, i?ioani?

Aiaeeo A?oae?e Ieaenaiae?iae/

Oa?e?anueeee aea?aeaaiee oaoi?/iee oi?aa?neoao

a?o?oaeoo?e oa aoae?aieoeoaa,

i?ioani? eaoaae?e aoae?aaeueii? iaoai?ee

I?ia?aeia onoaiiaa: Aea?aeaaiee aa?ieini?/iee oi?aa?neoao ?i.
I.?. AEoeianueeiai “OA?”, eaoaae?a iii?o iaoa??ae?a, I?i?noa?noai ina?oe
Oe?a?ie, i. Oa?e?a

Caoeno a?aeaoaeaoueny « 8 » ea?oiy 1999 ?. i 14 aiaeei? ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.180.01 a ?inoeooo? i?iaeai
iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie ca aae?anith: 310046,
i. Oa?e?a – 46, aoe. Aei. Iiaea?nueeiai, 2/10.

C aeena?oaoe??th iiaeia iciaeiieoeny o a?ae?ioaoe? ?inoeoooo i?iaeai
iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie ca aae?anith: 310046,
i. Oa?e?a, aoe. Aei. Iiaea?nueeiai, 2/10.

Aaoi?aoa?ao ?ic?neaiee «__» ________ 199 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee

eaiaeeaeao oaoi?/ieo iaoe A.I. Caeoeaa

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. I?iaeooaaiiy iiai? oaoi?ee, noai?aiiy i?ia?aneaieo
oaoiieia?e, no/anieo iaoei ? onoaoeoaaiiy o?nii iia’ycaii c
iaiao?aei?noth iaoaiaoe/iiai iiaeaethaaiiy ? ?ic?iaethaaiiyi iiaeo
aenieiaoaeoeaieo cania?a aiae?co o?ce/ieo ? oaoiieia?/ieo i?ioean?a.
Cie?aia, aei oaeeo i?ioean?a iiaeia a?aeianoe iiaeaethaaiiy
oaoiieia?/ieo i?ioean?a oi?iioai?aiiy aeaoaeae ? ae?ia?a iaoeiiaoae?aieo
eiino?oeoe?e ?c aeei?enoaiiyi ?iioeuenieo aeaea?ae aia?a??,
i?iaiicoaaiiy aeeiai?/ii? i?oeiino? eiino?oeoe?eieo aeaiaio?a, ui
caciathoue ianoaoe?iia?ieo ?iioeuenieo iaaaioaaeaiue. Aeooaeuei?noue
oaeeo aeine?aeaeaiue coiiaeaia /eiaeei ca?eueoaiiyi /enea ia’?eo?a, ui
i?aoeththoue a aeeiai?/ieo ?aaeeiao, a oaeiae c?inoaiiyi aeiia, ui
noaaeyoueny aei ?ic?aooie?a ?o i?oeiino?.

A oaeeo caaea/ao aaaeeeaa i?noea caeia? aiae?c oaeeueiaeo i?ioean?a a
i?oaeii-ieanoe/ieo o?eao oeee?iae?e/ii? oi?ie. No/ania oai??y
aeine?aeaeaiiy ianoaoe?iia?ieo i?ioean?a aeaoi?ioaaiiy
i?oaeii-ieanoe/ieo iaieiiie ? ieanoei ?ic?iaeaia iaaeinoaoiuei iiaii,
uia aeaoe aeinoaoiuei iaa?oioiaaio ? ae/a?iio a?aeiia?aeue aeey
i?aeoeee. Aeiaaa? ?icaeoeo naiai ae??oaiiy i?yia caaea/a aeine?aeaeaiiy
i?ioeano oi?iici?ithaaiiy aeaoaeae i?ae ae??th caaeaieo ia?aiao??a ?
oiia iaaaioaaeaiiy. Caeeoa?oueny aaaeeeaei ? iaa?iaia caaea/a aeai?o
ia?aiao??a ciai?oiueiai iaaaioaaeaiiy ia i?aenoaa? aaaeaieo ?acoeueoao?a
?icae?eaiiy /e oi?iioai?aiiy.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie. Aeena?oaoe?eia
?iaioa aeeiiaia o a?aeae?e? ianoaoe?iia?ieo iaoai?/ieo i?ioean?a
?inoeoooo i?iaeai iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie
a?aeiia?aeii aei ieaio iaoeiai-aeine?aeieo ?ia?o IAI Oe?a?ie (ae/o
1.7.2. ? 173 «Nicaeaiea iaoiaeia e oaoie/aneeo n?aaenoa ?aoaiey i?iaeai
aeeiaie/aneie i?i/iinoe e aeeaaiinoeee iaoaie/aneiai ninoiyiey yeaiaioia
yia?aaoe/aneeo onoaiiaie»), a oaeiae a?aeiia?aeii aei Aeiaiai?o i?i
iaoeiai-oaoi?/ia ni?a?ia?oieoeoai c OeANI a?ae 10 ea?oiy 1997 a.
«I?oeiinoi? oa aae?noe/i? ?ic?aooiee iaoaeueieo nenoai».

Iaoa ? caaea/? aeine?aeaeaiiy. Iaoith aeena?oaoe?eii? ?iaioe ? ?ic?iaea
aoaeoeaii? iaoaiaoe/ii? iiaeae? oa ?icaeoie /enaeueii-aiae?oe/iiai
iaoiaeo aeine?aeaeaiiy i?ioeano ianoaoe?iia?iiai inaneiao?e/iiai
aeaoi?ioaaiiy i?oaeii-ieanoe/ieo oeee?iae?e/ieo iaieiiie e?ioeaaeo
?ici???a i?ae aieeaii eieaeueiiai ?iioeueniiai iaaaioaaeaiiy. Aeey
aeinyaiaiiy oe??? iaoe a aeena?oaoe?? iinoaaeai? oa aeine?aeaeai? oae?
caaea/?:

aeaaaeaiiy ? aeine?aeaeaiiy aeeiai?/ieo ??aiyiue ooi/iaii? oai???
aeaoi?ioaaiiy iaieiiie Oeiioaiea – Aeiiiaeea i?e eieaeueiiio
?iioeueniiio iaaaioaaeaii?;

?ic?iaea iaoiaeeee canoinoaaiiy iaoiaeo i?oaeieo ?ica’yce?a a aa??aio?
iaoiaeo o?eoeaieo iaaaioaaeaiue aei ?ica’ycaiiy iae?i?eieo caaea/
i?oaeiiieanoe/iiai aeaoi?ioaaiiy oeee?iae?e/ieo iaieiiie;

aeine?aeaeaiiy ? aiae?c aieeao o?ce/ieo aeanoeainoae iaoa??aeo oa
aaiiao?e/ieo ia?aiao??a iaieiiee ia ?? iai?oaeaii-aeaoi?iiaaiee noai;

aeine?aeaeaiiy ? o?aooaaiiy aieeao oaeaeeino? aeaoi?ioaaiiy ia o?ce/i?
aeanoeaino? iaoa??aeo ?, ye iane?aeie, ia iiaaae?ieo iaieiiee;

aea/aiiy iniaeeainoae i?eeeaaeaiiy iaaaioaaeaiiy, ci?ithaaiiy ? ?ooo
ciie iaaaioaaeaiiy a i?ioean? aeaoi?ioaaiiy iaieiiee.

Iniiaia caaea/a iieyaa? a oai?aoe/iiio aeine?aeaeaii? ianoaoe?iia?ieo
oaeeueiaeo i?ioean?a a i?oaeii-ieanoe/ieo oeee?iae?e/ieo iaieiieao i?e
eieaeueiiio ?iioeueniiio iaaaioaaeaii?, ooai?aii?, iaa?oiooaaii? ?
ai?iaaoe?? eiiieaeno i?ia?ai, ui aeicaieyoue ?aae?coaaoe ia IAII
/enaeueii-aiae?oe/iee niin?a ?ica’ycaiiy ianoaoe?iia?ieo caaea/ oai???
Oeiioaiea – Aeiiiaeea. O ?iaio? iaea?aeaa iiaeaeueoee ?icaeoie
/enaeueii-aiae?oe/iee niin?a iiaeaethaaiiy ? aea/aiiy iaoai?/ieo
aeaoi?iaoe?eieo i?ioean?a a oiiaao ianoaoe?iia?iiai iaaaioaaeaiiy.
Iae?i?eia caaea/a i?oaeii-ieanoe/iiai aeaoi?ioaaiiy iaieiiee
ae??oo?oueny iie?ieiaei iaoiaeii i?oaeieo ?ica’yce?a a iinoaiiaoe?
iaoiaeo o?eoeaieo iaaaioaaeaiue. Aeei?enoaiiy aiae?oe/ieo ia?aoai?aiue
Eaieana, ?icae?eaiiy ia?ai?iieo oiui aeicaiey? nooo?ai ni?inoeoe
ia/eneaiiy ? i?enei?eoe i?ioean iaea?aeaiiy ??oaiiy. O?ce/iee caeii
aeaoi?ioaaiiy SYMBOL 115 \f “Symbol” \s 14 s – SYMBOL 101 \f “Symbol”
\s 14 e (ae?aa?aia iai?oaeaiiy – aeaoi?iaoe??) ai?ieneio?oueny
a?e?i?eiith aai a caaaeueiiio aeiaaeeo iie?e?i?eiith caeaaei?noth.

Iaoeiaa iiaecia ? oai?aoe/ia oe?ii?noue ?iaioe iieyaa? a oiio, ui:

ia iniia? ??aiyiue ooi/iaii? aeeiai?/ii? oai??? iaieiiie Oeiioaiea –
Aeiiiaeea iiaoaeiaai? iaoaiaoe/i? iiaeae?, ui iienothoue ianoaoe?iia?i?
oaeeueia? i?ioeane a i?oaeii-ieanoe/ieo o?eao oeee?iae?e/ii? oi?ie i?e
?iioeueniiio iaaaioaaeaii? c o?aooaaiiyi aieeao oaeaeeino?
aeaoi?ioaaiiy, cnoaieo aeaoi?iaoe?e oa ?ia?oe?eieo aeanoeainoae nenoaie;

?ic?iaeaiee /enaeueii-aiae?oe/iee niin?a aeine?aeaeaiiy ianoaoe?iia?ieo
oaeeueiaeo i?ioean?a a oeee?iae?e/ieo eiino?oeoe?eieo aeaiaioao;

ia i?aenoaa? ?ic?iaeaieo iiaeaeae ae??oaia caaea/a aeaoi?ioaaiiy
i?oaeii-ieanoe/ii? oeee?iae?e/ii? iaieiiee i?ae aieeaii eieaeueiiai
?iioeueniiai iaaaioaaeaiiy. I?iaaaeaii aeine?aeaeaiiy ianoaoe?iia?ieo
oaeeueiaeo i?ioean?a a oeee?iae?e/ieo iaieiieao i?e ??ciiiai?oieo oiiaao
cae??ieaiiy ? a ??cieo ?aaeeiao iaaaioaaeaiiy, a oiio /ene? i?ae aieeaii
?ooiiiai iaaaioaaeaiiy;

aeine?aeaeaii aieea o?ce/ieo ? aaiiao?e/ieo ia?aiao??a, oaeaeeino?
aeaoi?ioaaiiy, i?oei?nieo aeanoeainoae iaoa??aeo ia
iai?oaeaii-aeaoi?iiaaiee noai iaieiiee;

?ic?iaeaiee eiiieaen i?ia?ai, ui aeicaieyoue ?aae?coaaoe ia IAII
/enaeueii-aiae?oe/iee niin?a ?ica’ycaiiy ianoaoe?iia?ieo caaea/
i?oaeii-ieanoe/iiai aeaoi?ioaaiiy oeee?iae?e/ieo iaieiiie.

A??ia?aei?noue ?acoeueoao?a ? aeniiae?a i?aeoaa?aeaeo?oueny ei?aeoi?noth
iinoaiiaie caaea/, iaa?oioiaai?noth oai?aoe/ieo i?eiouaiue, oi/i?noth
cania?a, ui aeei?enoiaoaaeeny i?e iaea?aeaii? ?ica’yceo, ioe?ieith
ca?aeiino? ?acoeueoao?a ia iniia? /enaeueieo aenia?eiaio?a, c?noaaeaiiyi
iaea?aeaieo ?acoeueoao?a ?c aiae?oe/ieie ? /enaeueieie ?ica’yceaie,
iaaaaeaieie a e?oa?aoo?ieo aeaea?aeao, a oaeiae ?c aenia?eiaioaeueieie
aeaieie.

I?aeoe/ia oe?ii?noue ?iaioe iieyaa? a oiio, ui iaoiaeeee ? ?acoeueoaoe
aeine?aeaeaiiy iai?oaeaii-aeaoi?iiaaiiai noaio (IAeN) oeee?iae?e/ieo
iaieiiie i?e eieaeueiiio ?iioeueniiio iaaaioaaeaii?, iaea?aeai? a
aeena?oaoe??, iiaeooue ciaeoe canoinoaaiiy i?e i?iaeooaaii? ? aiae?c?
ia?aiao??a eiino?oeoe?e, ye? i?noyoue iaieiieia? eiino?oeoe?ei? aeaiaioe
i?ae aieeaii ei?ioei/anieo aeeiai?/ieo iaaaioaaeaiue.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe
aeena?oaoe?eii? ?iaioe aeiiia?aeaeeny ? iaaiai?thaaeeny ia i?aeia?iaei?e
eiioa?aioe?? «Nia?aiaiiua i?eai?u, iaoa?eaeu e oaoiieiaee aeey
oaoie/aneie aeeaaiinoeee e ia?ac?ooathuaai eiio?iey i?iiuoeaiiiai
iai?oaeiaaiey. Yeaiaioiay aaca e eiiieaeoothuea aeey i?eai?ia IE.
Iiaeaioiaea niaoeeaeenoia a noa?a ia?ac?ooathuaai eiio?iey e oaoie/aneie
aeeaaiinoeee» (OAeOO?A, 1998 ?.), ia XXVII oa XXIX eiioa?aioe?yo
aeeeaaea/?a, ani??aio?a ? ni?a?ia?oiee?a OAeAIO (1996 ? 1998??.).

Ioae?eaoe??. Ii oai? aeena?oaoe?? iioae?eiaaii 9 ae?oeiaaieo ?ia?o: 5
noaoae, 3 aeiiia?ae? ia iaoeiaeo eiioa?aioe?yo, 1 i?ai?eio.

Iniaenoee aianie aaoi?a: an? ?acoeueoaoe aeena?oaoe?eii? ?iaioe
iaea?aeai? iniaenoi aaoi?ii. A ?iaioao [1-9] aaoi?ia? iaeaaeeoue
?ic?iaea iaoaiaoe/ieo iiaeaeae ? /enaeueii-aiae?oe/iiai iaoiaeo
aeine?aeaeaiiy inaneiao?e/iiai aeaoi?ioaaiiy i?oaeii-ieanoe/ieo
oeee?iae?e/ieo iaieiiie, /enaeueia ?aae?caoe?y iaoiaeo, ocaaaeueiaiiy
iaea?aeaieo ?acoeueoao?a ? oi?ioethaaiiy aeniiae?a.

No?oeoo?a ? ianya ?iaioe. Aeena?oaoe?eia ?iaioa neeaaea?oueny ?c anooio,
/ioe?ueio ?icae?e?a ? aeniiaeo, nieneo aeei?enoaieo e?oa?aoo?ieo
aeaea?ae ?c 86 iaeiaioaaiue, 39 ?enoie?a, 3 oaaeeoeue. Iiaiee ianya
aeena?oaoe?? i?noeoue 140 noi??iie, na?aae ieo 130 noi??iie ae?oeiaaiiai
oaenoo.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiao?oueny aeooaeuei?noue oaie aeena?oaoe??, ?? i?aeoe/ia
? iaoeiaa oe?ii?noue, oi?ioeth?oueny iaoa ?iaioe.

O ia?oiio ?icae?e? iaaaaeaiee iaeyae aeine?aeaeaiue c ieoaiue
iai?oaeaii-aeaoi?iiaaiiai noaio oeee?iae?e/ieo iaieiiie i?e eieaeueiiio
inaneiao?e/iiio ?iioeueniiio iaaaioaaeaii?, aenieioaeaee?niiai
aeaoi?ioaaiiy o?e oeee?iae?e/ii? oi?ie, aeanoeainoae iaoa??ae?a a
i?oaeiiieanoe/i?e iaeano?. Aaeeeee aianie a ioi?ieaiiy eeane/ii?
iaoai?ee iaieiiie cae?enieee ?iaioe N.A. Aiaa?oeoiyia, A.A. Aieioiia,
A.C. Aeaniaa, A.N. Aieueii?a, A.A. Aaeuei?eiia, A.?. Eo?’?. Iioe?aiiy
iiaeeeainoae eeane/ii? oai??? iia’ycaia c aianaiiyi ei?aeoea, ui
nie?athoueny ia “cnoaio” iiaeaeue, oa aoee aianai? ?aea?i ? N.I.
Oeiioaieii a oai??th iiia?a/ieo eieeaaiue noa?aei?a. Oeei i?iaeaiai
i?enay/ai? aeine?aeaeaiiy E.ss. Aeiiee, O.E. Iiaoea, I.C. sseooaaa. Ca
iaaaeeeei aeiyoeii an? oe? oai??? a?oioothoueny ia iiaeae? Oeiioaiea ?
a?ae??ciythoueny iaeia a?ae ?ioi? eeoa oa?aeoa?ii aeaaaeaiiy ??aiyiue.
Ieoaiiy aeine?aeaeaiiy ianoaoe?iia?ieo aeeiai?/ieo i?ioean?a a ieanoeiao
? iaieiieao, ca’ycaieo ?c ?iioeueniei iaaaioaaeaiiyi, ?icaeyaeaeeny a
?iaioao A.A. Aaaoiiiaa, Spillers’a oa ?i. Ie??i oiai, o?aaa a?aecia/eoe
caaea/o i?i aeeiai?eo iaieiiie, ui ciaoiaeyoueny i?ae ae??th oaea?ieo ?
?ooiieo iaaaioaaeaiue. Iiae?ai? caaea/? ?icaeyaeathoueny a ?iaioao
A.E. Aaaii?iaa, A.N. Aieueii?a, TH.N. Ai?iaeiaa, A.?. Naa?theiaa,
A.A. Eieiaeyaeiiai, A.I. Oieiiiiaa, ?.A. ssithoiia, N.N. Eioiaithea.
Aaeeeee aianie a oai??th ? i?aeoeeo ??oaiiy iae?i?eieo caaaeaiue aoei
c?iaeaii A.A. Iiaiaeeeiaei, A.N. Aieueii?ii, I.O. Iaieiae/ai.
??ciiiai?oiei aniaeoai oai??? i?oaeiiieanoe/iiai aeaoi?ioaaiiy iieiaeo
iaieiiie ? ieanoei, ae??oaiith aaiiao?e/ii ? o?ce/ii iae?i?eieo caaea/
i?enay/ai? ?iaioe A.ss. Eaioi?a, A.A. Ao?eaeiaa, A.A. Oaiae/eeiaa,
TH.A. Ei?ioeeo.

Aeaoi?iaoe?eia oai??y ieanoe/iino? a ??cieo iiaeeo?eaoe?yo oe?iei
canoinoaaeanue aaaaoueia aaoi?aie i?e aeine?aeaeaii? i?oaeiiieanoe/ieo
aeaoi?iaoe?e aeaiaio?a eiino?oeoe?e. Iniiae ?? aoee caeeaaeai?
O. Ea?iaiii, ?icaeioo? a ?iaioao Ae. Oaeei?a, O.A. ?aoiaooeeiia,
A.A. Ieuethoeia. Aaoi?e nie?aeeny ia i?eiouaiiy i?i ?nioaaiiy ?aeeii?
aeeiai?/ii? ae?aa?aie aeaoi?ioaaiiy, ui aeicaieeei ?i onoaiiaeoe i?yio
ooieoe?iiaeueio caeaaei?noue i?ae iai?oaeaiiyie ? aeaoi?iaoe?yie i?e
aeoeaiiio iaaaioaaeaii? c aeinoaoiuei aaeeeith oaeaee?noth. A
aeeiai?/ieo caaea/ao aeaoi?iaoe?eia oai??y ieanoe/iino? oni?oii
aeei?enoiaoaaeany a ?iaioao A.A. Ieuethoeia, I.I. Aaeiia,
O.A. ?aoiaooeeiia, A.I. Oieiiiiaa, A.N. Aieueii?a, Naeiiiaena oa ?i.
Aeaaeai?eii A.I. Oieiiiiaei aeieeaaeii aeeeaaeaiee ? iaa?oioiaaiee
niin?a ae??oaiiy caaea/ i?oaeiiieanoe/iiai aeaoi?ioaaiiy aeaiaio?a
eiino?oeoe?e ca aeiiiiiaith ?iceeaaeo ooeaieo ooieoe?e a ?yaee, c
aeae?eaiiyi i?oaeii? ? ieanoe/ii? neeaaeiaeo aioo??oi?o coneeue.
Iiaeaeueoee ?icaeoie oe? iaoiaee iaea?aeaee a ?iaioao o/aieo ?inoeoooo
i?iaeai iaoeiiaoaeoaaiiy ?i. A.I. I?aeai?iiai IAI Oe?a?ie
A.A. Eieiaeyaeiiai, A.?. Naa?theiaa, A.A. Neey?, A.A. Aicthea,
A.A. Eeeiaiea, ?.?. Neiaeee, E.A. ?iiaiaiea, N.N. Eioiaithea,
?.A. ssithoiia, TH.N. Ai?iaeiaa, I.I. Iaooaeiaa. A?aeiieo ?acoeueoao?a
aeinyaiooi i?aaenoaaieeaie ieaeiueiai?iaenueei? oeiee iaoaiaoee?a
A.A. Oaiae/eeiaei, TH.A. Ei?ioeeo, A.A. Aaaeaiiaei, ye? canoiniaoaaee
aa??aoe?eii-??cieoeaa? iaoiaee, a oaeiae iaoiae ne?i/aiieo aeaiaio?a
aeey ae??oaiiy aeaii??ieo caaea/ aeeiai?ee i?oaeii-ieanoe/ieo iaieiiie.
Ia i?aenoaa? i?iaaaeaiiai iaeyaeo iiaeia c?iaeoe aeniiaie i?i
iaaeinoaoiuei iiaio ?ic?iaeo iaoiae?a iaoaiaoe/iiai iiaeaethaaiiy
ianoaoe?iia?ieo oaeeueiaeo i?ioean?a aeaoi?iaoe?e a iaieiieiaeo
eiino?oeoe?eieo aeaiaioao. Aeieea? iaiao?aei?noue noai?aiiy aoaeoeaieo
/enaeueieo aeai?eoi?a aeine?aeaeaiiy ia?ao?aeieo i?ioean?a aeey
neeaaeieo aeiaaee?a iaaaioaaeaiiy. Ae??oaiith aeayeeo ieoaiue a oeueiio
iai?yi? i?enay/aiee iaoa??ae aeaii? aeena?oaoe??.

O ae?oaiio ?icae?e? ?icaeyiooa caaea/a ianoaoe?iia?iiai i?oaeiiai
aeaoi?ioaaiiy oeee?iae?e/ii? iaieiiee e?ioeaai? aeiaaeeie.
Ianoaoe?iia?ia ?aaeoe?y iaieiiee coiiaeaia i?ioeanii ?iciianthaeaeaiiy
oaeeue iai?oaeaiue a i?e. Iiaaae?ieo iaieiiee aeine?aeaeaii ia iniia?
??aiyiue oai???, ui a?aoiao? aeaoi?iaoe?th cnoao ? ?ia?oe?th iiai?ioo
oa?o:

;

;

. (1)

Oey nenoaia o?ueio aeeoa?aioe?aeueieo ??aiyiue a /anoeiieo iio?aeieo
a?ia?aie?/iiai oeio uiaei iaa?aeiieo ooieoe?e ia?ai?uaiue u(x, t), w(x,
t), SYMBOL 106 \f “Symbol” \s 14 j (x, t) ? iniiaiith nenoaiith
caaea/?. Aiia ia? o?e oa?aeoa?i? aei?noeino?: caeiaeueio,
?icoyaiaiiy-noeniaiiy, iiia?a/iiai cnoao, oa o?e ?ia?oe?eieo /eaie :
iicaeiaaeith, iiia?a/io oa iaa?oaeueio ?ia?oe??.

Inaneiao?e/ia iaaaioaaeaiiy iiaea aooe i?eeeaaeaii aeia?eueii ocaeiaae
oa??ii? iaieiiee. Iniaeeaa oaaaa i?eae?eyeany iaaaioaaeaiiyi, ciia
i?eeeaaeaiiy yeeo iineea eieaeueiee oa?aeoa? – nioaith a?ae o0 aei o1.
Oei/aniaa neeaaeiaa iaaaioaaeaiiy a caaea/ao oeueiai eeano iiaea
noaiiaeoe eiia?iaoe?th iino?eii? ? caoooath/i? eiiiiiaio. I?e ae??oaii?
i?aeoe/ieo caaea/ aeei?enoiaoaaany aeniiiaioe?aeueiee caeii oaoaaiiy
iaaaioaaeaiiy c /anii, a?aeiia?aeiee oaeeueiaiio iaaaioaaeaiith :

. (2)

?ica’ycie nenoaie ia?aaeaa/a?oueny ooeaoe o aeaeyae? noie ?yaeo, ui
aeeth/a? aeiaooie aeaio eiiiiiaio – iaa?aeiieo ooieoe?e un (t), ye?
caeaaeaoue a?ae /ano ? i?aeeyaathoue aecia/aiith, oa aacenieo
eii?aeeiaoieo ooieoe?e ux (n, o), ui caaeiaieueiythoue a?aie/i? oiiae.
Iaaeaiee niin?a ae??oaiiy caaea/ oaeaee?niiai i?oaeiiieanoe/iiai
iaaaioaaeaiiy aeieeaaeii ?icaeyiooee a ?iaioao aeaaeai?ea
A.I. O?e?iiiaa. I?e ae??oaii? caaea/, ye i?aaeei, i?eeiaeeny ioeueia?
ii/aoeia? oiiae ? a?aie/i? oiiae, ui a?aeiia?aeathoue oa?i??iiio
cae??ieaiith, aeey yeeo o aeaeyae? aacenieo i?eeiyo? o?eaiiiiao?e/i?
ooieoe??

,

,

. (3)

I?e oeueiio iaaaioaaeaiiy ?iceeaaeathoueny o a?aeiia?aei?
o?eaiiiiao?e/i? ?yaee ca an??th aeiaaeeiith iaieiiee. I?ney i?aenoaiiaee
oeueiai ?ica’yceo a nenoaio (1) ? ia?aoiaeo a i?ino?? cia?aaeaiue
(ia?aoai?aiiy Eaieana) aeey /aniai? neeaaeiai?, iiaeia iaea?aeaoe aeey
ooieoe?e ia?ai?uaiue ?ica’ycie o aeaeyae? a?aeiioaiiy iie?iii?a.
Iai?eeeaae, aeey u

, (4)

aea SYMBOL 119 \f “Symbol” \s 14 w 2i – eaaae?ao a?aeiia?aeii? aeanii?
/anoioe,

SYMBOL 97 \f “Symbol” \s 14 a i – eiao?oe??io caoooaiiy i-? neeaaeiai?
iaaaioaaeaiiy (i = 1..3).

Ae?ace aeey eiao?oe??io?a (a /anoeiaiio aeiaaeeo iaaaioaaeaiiy, ui
oaoaa? ii aeniiiaioe?aeueiiio caeiio ) iiaeia caienaoe oae:

,

,

. (5)

I?ney a?aeiiaeaiiy c i?inoi?o Eaieana ?ica’ycie iiaea aooe caienaii o
aeaeyae? noie ?yaeo, a yeiio eiao?oe??ioe Ni, Di, ei ciaoiaeyoueny ii
oi?ioeai (5). No?oeoo?a ?ica’yceo a?aeiia?aea? noi? aeanieo eieeaaiue
(aa?iii?e) c aiie?ooaeith, i?iii?oe?eiith ciai?oiueiio iaaaioaaeaiith, ?
aeiooaii? neeaaeiai?, a?aeiia?aeii? ciai?oiueiio iaaaioaaeaiith
(aeniiiaioa, ui oaoaa?):

(6)

?c aeei?enoaiiyi iaea?aeaieo cia/aiue ia?ai?uaiue ii oi?ioeao Eio? ?
o?ce/ieo ni?aa?aeiioaiiyo eaaei ciaeoe ?iciiae?e aeaoi?iaoe?e ?
iai?oaeaiue ocaeiaae oa??ii? iaieiiee ? ii oiauei? iaieiiee a aeaiee
iiiaio /ano.

Aeia?euei? a?aie/i? oiiae i?iiiio?oueny ?aae?coaaoe ca ?aooiie
o?eoeaiiai iioe?aiiy aeiaaeeie iaieiiee L ? aaaaeaiiy ia aeaye?e
a?aenoai? a?ae e?a?a aeiaeaoeiaeo o?eoeaieo iaaaioaaeaiue. Aeai?
o?eoeai? iaaaioaaeaiiy iiaeii? aoaeooue eiiiainoaaoe ia?ai?uaiiy aai
coneeey, ui aeieeathoue i?e ae??oaii? caaea/? aeey oa?i??iiai nie?aiiy
iaieiiee, caiaey/e ?o aei iaiaaeaiue eiie?aoieo a?aie/ieo oiia.

sse i?eeeaae ?icaeyiooa caaea/a ianoaoe?iia?iiai i?oaeiiai aeaoi?ioaaiiy
oeee?iae?e/ii? iaieiiee i?e ??ciiiai?oieo oiiaao cae??ieaiiy, i?ae
aieeaii ?iioeueniiai ? ?ooiiiai iaaaioaaeaiue.

O o?aoueiio ?icae?e? aeine?aeaeo?oueny iai?oaeaii-aeaoi?iiaaiee noai
i?oaeii-ieanoe/ii? iaieiiee i?e eieaeueiiio ?iioeueniiio iaaaioaaeaii?.
Iaoaiaoe/ia iiaeaeue iaoa??aeo a?aoiao? aieea oaeaeeino? aeaoi?iaoe??.
?ic?aooiee aaaeooueny ?c canoinoaaiiyi iai?aaiae?oe/iiai iie?ieiaiai
iaoiaeo i?oaeieo ?ica’yce?a o aa??aio? iaoiaeo o?eoeaieo iaaaioaaeaiue.
Aioo??oi? coneeey (caeiaeueiee iiiaio, coneeey a na?aaeeii?e iiaa?oi?
iaieiiee, ia?a??coth/? neee) iaaaaeai? o aeaeyae? ??cieoeue:

O1oi? = O1 – O1s ; (7)

aea O1oi? – i?oaei? coneeey,

O1s – o?eoeai? aioo??oi? coneeey a?ae ??cieoe? iai?oaeaiue, ui
ci?iththoueny ii i?oaeiiio caeiio, ? iai?oaeaiue, ui aecia/athoueny
caeiiii ci?oeithaaiiy a ciiao ?icaeoeo ieanoe/ieo aeaoi?iaoe?e.

Aeey ?ioeo coneeue ae?ace aiaeia?/i?.

Aeey aeyao ? ianooiiiai aiae?co aianeo oeeo aeiaeaoeiaeo /eai?a
i?aenoaaey?ii ae?ac (7) a nenoaio (1). *eaie, ui a?aoiaothoue aieea
iae?i?eiino? (O1s , O2s , M1s , Q1s), c a?aeiia?aeieie eiao?oe??ioaie
ia?aiinyoueny a i?aao noi?iio ??aiyiiy ? i?e canoinoaaii? iaoiaeo
i?oaeieo ?ica’yce?a ?icaeyaeathoueny ye aeayea aeiaeaoeiaa
iaaaioaaeaiiy, ae?ac aeey yeiai a?aeiiee c iiia?aaeiueiai e?ieo
?ioaa?oaaiiy. A ?acoeueoao? iaea?aeo?ii nenoaio o?ueio ??aiyiue a
ia?ai?uaiiyo, e?a? /anoeie yeeo e?i?ei?, a i?aa? i?noyoue ?aaeuei? ?
o?eoeai? iaaaioaaeaiiy, ui caeaaeaoue iae?i?eii a?ae ooieoe?e
ci?oeiaiiy. Nenoaia (1) i?eeia? aeaeyae:

;

;

. (8)

Aaee/eie o?eoeaieo aeiaeaoeiaeo iaaaioaaeaiue, ui a?aoiaothoue aieea
iae?i?eiino? caeiio ci?oeiaiiy, aecia/athoueny ia iniia? ??cieoe?
i?oaeieo coneeue ? iiiaio?a (?ica’ycie e?i?eii? caaea/?) ? a?aeiia?aeieo
?aaeueieo coneeue ? iiiaio?a ca?aeii c (7), oa ciaoiaeyoueny /enaeueiei
?ioaa?oaaiiyi ii oiauei? iaieiiee ca aeiiiiiaith eaaae?aoo?ieo oi?ioe
Iuethoiia – Eioana. Cia/aiiy iai?oaeaiue a aeai?e oi/oe? iaieiiee c
eiie?aoiith eii?aeeiaoith z ii oiauei? ciaoiaeyoueny a?aeiia?aeii aei
oai??? iaeeo i?oaeii-ieanoe/ieo aeaoi?iaoe?e. I?e aeeiiaii? ?ic?aooie?a
aeei?enoiaoaaeany, ye i?aaeei, a?e?i?eia aai iie?e?i?eia (o?eeaieiaa)
ai?ieneiaoe?y ae?aa?aie ?icoyaiaiiy-noeneoaaiiy iaoa??aeo :

, (9)

aea ?iaeaenii k iicia/aia a?aeiia?aeia ae?eueieoey eaiaii?.

Oaeiae a?aoiaoaaany aieea oaeaeeino? aeaoi?ioaaiiy ia aaee/eio a?aieoe?
oaeo/ino? o noaiaiaaiio aeaeyae?:

, (10)

– aeeiai?/ia ? noaoe/ia a?aieoe? oaeo/ino? a?aeiia?aeii,

SYMBOL 101 \f “Symbol” \s 14 e i – ?ioaineai?noue oaeaeeino?
aeaoi?iaoe??,

D ? n – ia?aiao?e, ui oa?aeoa?ecothoue aieea oaeaee?niiai aeaoi?ioaaiiy
ia i?oei?ni? aeanoeaino? iaoa??aeo.

Aeey o?aooaaiiy caeeoeiaeo iai?oaeaiue ? aeaoi?iaoe?e, ui aeieeathoue a
iaieiioe? aiane?aeie ae?? i?oaeiiai ?icaaioaaeaiiy, caieoaii
a?aeiia?aei? o?ce/i? ni?aa?aeiioaiiy:

,

,

. (11)

I?ney aeei?enoaiiy aeaieo ae?ac?a aeey ciaoiaeaeaiiy aaee/eie aioo??oi?o
coneeue ? iiiaio?a (neeaaeaiiy oi?ioe) c’yaey?oueny aeiaeaoeiaee
aeiaeaiie, ui a?aoiao? naia aieea caeeoeiaeo iai?oaeaiue ? aeaoi?iaoe?e.
Oe? coneeey oaeiae ?icaeyaeathoueny ye aeiaeaoeia? o?eoeai?
iaaaioaaeaiiy.

Ia eiaeiiio /aniaiio e?ieo ?ic?aooieo o iaoiae? i?oaeieo ?ica’yce?a
ciaoiaeeii ?ica’ycie a?aeiia?aeii aei oi?ioe (3 – 6). Aeae? ii oi?ioeao
Eio? ? o?ce/ieo ni?aa?aeiioaiiyo eaaei ciaoiaeeii ?iciiae?e aeaoi?iaoe?e
? iai?oaeaiue ocaeiaae oa??ii? iaieiiee ? ii oiauei? iaieiiee a aeaiee
iiiaio /ano. sseui ?ioaineai?noue iai?oaeaiue oaea, ui a ia?aoei?
ianooia? noai ieanoe/iino?, oi ia/eneththoueny o?eoeai? aeiaeaoeia?
iiiaioe ? coneeey (7). I?e ?icaaioaaeaii?, eiee i?e??no aeaoi?iaoe?e a
aeaiiio ia?aoei? noa? a?ae’?iiei, ia/eneththoueny aeiaeaoeia? aeiaeaiee
o a?aeiia?aeiino? c (11). Oe? aeiaeaiee iaaeae? a?aoiaothoueny o
aeaeyae? o?eoeaieo iaaaioaaeaiue ia ianooiiiio e?ioe? ?ioaa?oaaiiy
a?aeiia?aeii aei (8).

O /aoaa?oiio ?icae?e? iaaaaeai? ?ica’ycee caaea/ i?oaeiiieanoe/iiai
aeaoi?ioaaiiy iaieiiee i?e ??ciiiai?oieo oiiaao iaaaioaaeaiiy ?
cae??ieaiiy, i?iaiaeeoueny c?noaaeaiiy oanoiaeo ?ica’yce?a ?c a?aeiieie
a e?oa?aoo?? aeaieie. Oae, a na??? /enaeueieo aenia?eiaio?a
?icaeyaeaeeny ??ci? iaoaiaoe/i? iiaeae? o?ce/ieo aeanoeainoae iaoa??ae?a
: ui aeei?enoiaothoue aieii?eio aai iie?e?i?eio ai?ieneiaoe?th caeiio
aeaoi?ioaaiiy ( SYMBOL 115 \f “Symbol” \s 14 s – SYMBOL 101 \f
“Symbol” \s 14 e ); ui a?aoiaothoue aieea oaeaeeino? aeaoi?iaoe?? a
oi?i? (10) ? ui ia a?aoiaothoue oaeo. Oeiia? ?acoeueoaoe ?ic?aooie?a
iaaaaeai? ia ?en. 1.

?en. 1 – ?icaeoie ?ioaineaiino? iai?oaeaiue c ieeiii /ano aeey ??cieo
iaoaiaoe/ieo iiaeaeae o?ce/ieo aeanoeainoae iaoa??aeo.

Ia ?en. 1 ioieoe?ii iicia/ai? ?acoeueoaoe ?ic?aooie?a aeey iaoaiaoe/ieo
iiaeaeae, ui aeei?enoiaoaaee a?e?i?eio ai?ieneiaoe?th caeiio
aeaoi?ioaaiiy, nooe?eueiith e?i??th – ?acoeueoaoe ?ic?aooie?a aeey
iaoaiaoe/ieo iiaeaeae, ui aeei?enoiaoaaee iie?i?eio ai?ieneiaoe?th.
A?eueo oiano? e?i?? a?aeiia?aeathoue iiaeaeyi c o?aooaaiiyi aieeao
oaeaeeino? aeaoi?iaoe??, a?eueo oiie? – iiaeaeyi aac o?aooaaiiy oeueiai
aieeao. A?ao?ee iathoue nai? oa?aeoa?i? aeanoeaino? aeey ??cieo
iaoaiaoe/ieo iiaeaeae o?ce/ieo aeanoeainoae iaoa??aeo ? aeayeo ??cieoeth
a aaniethoieo cia/aiiyo. Aeine?aeaeaiiy ??ciiiai?oieo aa??aio?a
o?aooaaiiy o?ce/ieo ia?aiao??a iaoa??aeo aeicaiey? iaaeaoe ia?aaaao
iaoaiaoe/i?e iiaeae? ae?aa?aie aeaoi?ioaaiiy i?oaeiiieanoe/iiai
iaoa??aeo ?c iie?e?i?eiith (o?eeaieiaith) caeaaei?noth ( SYMBOL 115 \f
“Symbol” \s 14 s – SYMBOL 101 \f “Symbol” \s 14 e ) ? c o?aooaaiiyi
oaeaeeino? aeaoi?ioaaiiy iaoa??aeo a noaiaiaa?e oi?i?, ioa?aeoa?ecoaaaoe
aeaio iiaeaeue ye iioeiaeueio.

A ?io?e na??? aenia?eiaio?a aoa aeeiiaiee aiae?c aieeao oe?eie ciie
iaaaioaaeaiiy ia iai?oaeaii-aeaoi?iiaaiee noai i?oaeiiieanoe/ii?
iaieiiee. Iaaaioaaeaiiy – ?iciiae?eaia oeniaiiy, ui iienaii oi?ioeith
(2). Oene i?eeeaaeaiee nioaith iina?aaeei? iaieiiee. Oe?eia ciie
i?eeeaaeaiiy iaaaioaaeaiiy ? ?? ii/aoeiaa aiie?ooaea aa??thaaeeny oaeei
/eiii, uia noia?iee ?iioeuen iaaaioaaeaiiy caeeoaany iino?eiei.

?en. 2. – Caeaaei?noue aaee/ei iaeneiaeueieo iai?oaeaiue ?icoyaiaiiy ?
iai?oaeaiue cnoao a?ae a?aeiioaiiy oe?eie ciie iaaaioaaeaiiy aei
aeiaaeeie iaieiiee

Ia ?en. 2 iaaaaeaiee a?ao?e iaeneiaeueii aeinyaiooeo iai?oaeaiue
?icoyaiaiiy ? cnoao caeaaeii a?ae ni?aa?aeiioaiiy oe?eie ciie
iaaaioaaeaiiy l0 aei aeiaaeeie iaieiiee L. Iai?oaeaiiy ?icoyaiaiiy
SYMBOL 115 \f “Symbol” \s 14 s SYMBOL 113 \f “Symbol” \s 14 q iieacai?
nooe?eueiith e?i??th, ia?a??coth/? (oaiaaioe?aeuei?) SYMBOL 116 \f
“Symbol” \s 14 t oo – ioieoe?ii.

I?e iaaaeee?e oe?ei? ciie i?eeeaaeaiiy iaaaioaaeaiiy oaiaaioe?aeuei?
iai?oaeaiiy ia?aaaaeathoue iaae iai?oaeaiiyie ?icoyaaiiy, a cia/eoue,
iaea?eueo a??ia?aeiei aoaea i?ioean ?icae?eaiiy ii noai? c??co. I?e
ca?eueoaii? oe?eie ciie iaaaioaaeaiiy aaee/eia oaiaaioe?aeueieo
iai?oaeaiue o a?aeiioaii? aei ?icoyaoth/eo ciaioo?oueny, ? a?eueo
a??ia?aeiei noaia ?icae?eaiiy ii noai? ?ic?eao.

Oaeiae o oeueiio ?icae?e? ?icaeyioo? aeaye? ?io? i?aeoe/i? caaea/?,
cie?aia ia/eneaia e?eoe/ia oaeaee?noue ?iciianthaeaeaiiy iaaaioaaeaiiy,
ui aeeeeea? iaaacia/ia c oi/ee ci?o i?oeiino? ?aciiainia c?inoaiiy
aiie?ooaee eieeaaiue. ?icaeyiooa oaeiae caaea/a ia/eneaiiy ia?aiao??a
iai?oaeaii-aeaoi?iiaaiiai noaio oa ia?aaaioaaeaiue o nenoaiao
?icnoeeoaaiiy aeie?a eini?/ieo aia?ao?a.

INIIAI? AENIIAE? OA ?ACOEUeOAOE

A caeeth/i?e /anoei? noi?ioeueiaai? iniiai? oai?aoe/i? ? i?aeoe/i?
aeniiaee, iaea?aeai? aiane?aeie iaaaaeaieo a aeena?oaoe?? aeine?aeaeaiue
:

?ic?iaeaiee /enaeueiee iaoiae ?ica’ycaiiy aeeiai?/ii? caaea/? aeey
iaeii??aeii? oeee?iae?e/ii? iaieiiee a oiiaao ieinei? aeaoi?iaoe?? i?e
inaneiao?e/iiio iaaaioaaeaii?. Aeei?enoiaoaaeany nenoaia ??aiyiue oeio
Oeiioaiea – Aeiiiaeea ooi/iaii? oai??? iaieiiie. Ia iniia? iiaoaeiaaiiai
?ica’yceo aeine?aeaeaii aeeiai?/io iiaaae?ieo inaneiao?e/ii?
oeee?iae?e/ii? iaieiiee i?e aieea? ia ia? eieae?ciaaiiai oa ?ooiiiai
?iioeueniiai iaaaioaaeaiiy. Aiae?c /enaeueieo ?acoeueoao?a aea?
iiaeeea?noue ioe?ieoe caaaeueio ea?oeio iai?oaeaii-aeaoi?iiaaiiai noaio
iaieiiee, aeae?eeoe iaea?eueo iaaacia/i? c oi/ee ci?o i?oeiino? ciie
iaieiiee, ioa?aeoa?ecoaaoe noaio ?oeioaaiiy iicaiaaeii aeaoi?iiaaieo
ia?aoei?a.

?ic?iaeaia iaoiaeeea aeine?aeaeaiiy ianoaoe?iia?ieo eieeaaiue
i?oaeiiieanoe/ii? oeee?iae?e/ii? iaieiiee ia iniia? iaoiaeo i?oaeieo
?ica’yce?a a aa??aio? iaoiaeo o?eoeaieo iaaaioaaeaiue. Iaoiaeeea
aeei?enoiao? caeii aeaoi?ioaaiiy iaoa??aeo ?c aieii?eiei aai
iie?e?i?eiei ci?oeiaiiyi ? a?aooaaiiyi oaeaeeino? aeaoi?iaoe?e iaoa??aeo
a ia?aoei? o aeaeyae? noaiaiaai? caeaaeiino?. ?icaeyioo? ye
i?oaeiiieanoe/ia c?inoaiiy aeaoi?iaoe?e, oae ? noaae?y i?oaeiiai
?icaaioaaeaiiy c aecia/aiiyi caeeoeiaeo aeaoi?iaoe?e ? iai?oaeaiue.
I?iiiiiaaia iaoiaeeea aea? caaeia?euei? ?acoeueoaoe ia o?eueee o ?ac?,
eiee a i?ioean? ?icaaioaaeaiiy iaoa??ae ia aeoiaeeoue ciia ca a?aieoe?
i?oaeiino?, aea ? a neeaaeieo aeiaaeeao iiaoi?iiai iaaaioaaeaiiy, ca
oiiae, ui nenoaia ciai?oi?o nee ia ci?ith?oueny ye?nii, a eeoa
i?iii?oe?eii ii/aoeia?e nenoai? iaaaioaaeaiue.

?ic?iaeaiee aeai?eoi /enaeueii-aiae?oe/iiai ?ica’yceo caaea/? ia IAII.
Aeine?aeaeaii iaea?aeaiee ia?ao?aeiee ?ica’ycie aeey ii/aoeiaiai
ia??iaeo eieaeueiiai ?iioeueniiai aeaoi?ioaaiiy oeee?iae?e/ii? iaieiiee
? aieea aa??aoe?e ia?aiao??a iaieiiee ia aaee/eie i?iaei?a ?
iai?oaeaiue. Anoaiiaeaii ia?aaaaeaiiy iai?oaeaiue ?icoyaaiiy a iaieiioe?
?, ye iane?aeie, ?oeioaaiiy iaieiiee ca noaiith a?ae?eao. I?ioa i?e
aeayeeo noaiao iaaaioaaeaiiy ? aieea? e?aeiaiai aoaeoo (caio?oaaiiy)
aeyaeaii ia?aaaaeaiiy ia?a??coth/eo nee iaae aeaeiieie, iniaeeai a
ii/aoeia? iiiaioe /ano. Oaeei /eiii, a oeeo aeiaaeeao ?oeioaaiiy aoaea
a?aeaoaaoeny ca noaiith c??co. ?ic?aooiee iieacaee, ui aeaiee aoaeo ia?
i?noea i?e neeueii eieae?ciaaiiio iaaaioaaeaii? aeniei? ?ioaineaiino?
iiaeeco cae??ieaieo iii?.

Ae??oaia caaea/a i?oaeiiieanoe/iiai aeaoi?ioaaiiy inaneiao?e/ieo
oeee?iae?e/ieo iaieiiie i?e aieea? ia ieo oaea?ii-?iioeuenieo eieaeueieo
iaaaioaaeaiue. I?e ?ic?aooieao aeei?enoiaoaaeany aiae?oe/ia oi?ia caeiio
aeaoi?ioaaiiy ( SYMBOL 115 \f “Symbol” \s 14 s i – SYMBOL 101 \f
“Symbol” \s 14 e i) a i?oaei?e (e?i?ei?e) ? ieanoe/i?e (iae?i?ei?e)
iaeanoyo i?e caaeaiiio caeii? aeaoi?iaoe?eiiai ? e?iaiaoe/iiai
ci?oeiaiue. A?aoiaoaaany oaeiae aieea oaeaeeino? aeaoi?iaoe?? ia
aaee/eio a?aieoe? oaeo/ino? iaoa??aeo o aeaeyae? noaiaiaai? caeaaeiino?.
C?noaaeaiiy oanoiaeo ?acoeueoao?a ?c a?aeiieie aeaieie ?ioeo aaoi??a
iieacaei aenieo oi/i?noue ? aeinoia??i?noue ?iaioe i?ia?aie.
Aeine?aeaeaiiy ??ciiiai?oieo aa??aio?a o?aooaaiiy o?ce/ieo ia?aiao??a
iaoa??aeo aeicaiey? ia?aoe iiaeaeue ae?aa?aie aeaoi?ioaaiiy
i?oaeiiieanoe/iiai iaoa??aeo c iie?e?i?eiith (o?eeaieiaith) caeaaei?noth
( SYMBOL 115 \f “Symbol” \s 14 s i – SYMBOL 101 \f “Symbol” \s 14 e i)
ye iioeiaeueio.

Aeine?aeaeaii iai?oaeaii-aeaoi?iiaaiee noai i?oaeii-ieanoe/ii?
oeee?iae?e/ii? iaieiiee i?e aieea? ia ia? aioo??oiueiai oeneo c ciiith
iaaaioaaeaiiy, ui iioe?th?oueny c /anii. Aecia/ai? e?iaiaoe/i? ?
aeaoi?iaoe?ei? oa?aeoa?enoeee iaieiiee, ?iciiae?e iai?oaeaiue c /anii a
i?inoi?? ocaeiaae oa??ii? iaieiiee. Aeaia ioe?iea aeeiai?/ii? i?oeiino?
eiino?oeoe?? ii cia/aiith aeeiai?/ii? a?aieoe? oaeo/ino?, ui aeicaieeoue
aeyaeoe ?aca?ae a i?aeaeuaii? iaaaioaaeaiue, ye? aeiioneathoueny.

Oaeei /eiii, i?iaaaeaiee /enaeueiee aiae?c aeeiai?/ii? iiaaae?iee
oeee?iae?e/ii? iaieiiee i?e eieaeueiiio inaneiao?e/iiio ?iioeueniiio
iaaaioaaeaii? iieacaa, ui aeey ae??oaiiy aeaiiai eeano caaea/
iioeiaeueiith o?aaa aaaaeaoe iaoiaeeeo, yea a?oioo?oueny ia ??aiyiiyo
ooi/iaii? oai??? iaieiiie Oeiioaiea – Aeiiiaeea, ui a?aoiao? aieea
ia?a??coth/eo nee oa ?ia?oe?? iiai?ioo ii?iaeueiiai aeaiaioa iaieiiee.
Iaoiaeeea, ui i?iiiio?oueny, aeei?enoiao? aiae?oe/io oi?io caeiio
aeaoi?ioaaiiy ( SYMBOL 115 \f “Symbol” \s 14 s i – SYMBOL 101 \f
“Symbol” \s 14 e i) a i?oaei?e (e?i?ei?e) ? ieanoe/i?e (iae?i?ei?e)
iaeanoyo i?e caaeaiiio caeii? aeaoi?iaoe?eiiai ? e?iaiaoe/iiai
ci?oeiaiue. A?aoiao?oueny oaeiae aieea oaeaeeino? aeaoi?iaoe?? ia
aaee/eio a?aieoe? oaeo/ino? iaoa??aeo o aeaeyae? noaiaiaai? caeaaeiino?.
Aeei?enoaiiy ?icaeyiooi? iaoaiaoe/ii? iiaeae? i?e noai?aii? ? ?ic?aooieo
iiaeo oaoiieia?e ?iioeuenii? ia?iaee iaoa??ae?a aea? iiaeeea?noue
?ic?iaeyoe aoaeoeai? iaoiaeeee, i???ioiaai? ia aia?ai- oa
?ano?nicaa??aaiiy, aenieo oi/i?noue ? i?oei?noue ae?ia?a, ui iathoue
aaaeeeaa cia/aiiy a aaaaoueio aaeocyo ia?iaeiiai ainiiaea?noaa.

Iioae?eiaai? ?iaioe ca oaiith aeena?oaoe?? :

Eieiaeyaeiue A.A., Aecthe A.A. Enneaaeiaaiea inaneiiao?e/iuo
aeeiaie/aneeo aeaoi?iaoeeiiiuo i?ioeannia a oi?oaiieanoe/aneeo
iaiei/a/iuo eiino?oeoeeiiiuo yeaiaioao // Aanoi. Oa?uee. iieeoaoi.
oi-oa. – 1998. – Aui. 12. – N. 101 – 108.

Aecthe A.A., Eieiaeyaeiue A.A. Ioeaiea aeeyiey eieaeecaoeee iaa?ocee i?e
aeaoi?ie?iaaiee oeeeeiae?e/aneie iaiei/ee // Aanoi. Oa?uee. iieeoaoi.
oi-oa. – 1998. – Aui. 11. – N. 19 – 24.

Aecthe A.A. ?an/ao ia i?i/iinoue ?acaiiiuo ono?ienoa n o/aoii aeeiaieee
oaea?ieea // Aanoi. Oa?uee. iieeoaoi. oi-oa. – 1998. – Aui. 8. – N. 88 –
93.

Aecthe A.A. E?eoe/aneea nei?inoe aeaeaeaiey oaea?ieea a nenoaiao
?acaiiiuo ono?ienoa // Aanoi. Oa?uee. iieeoaoi. oi-oa. – 1998. – Aui.
11. – N. 14 – 19.

Aecthe A.A. Oi?oaia aeaoi?ie?iaaiea oeeeeiae?e/aneeo iaiei/ae i?e
eieaeueiii eiioeueniii iaa?oaeaiee. – O.: 1995. – 23 n. (I?ai?. / IAI
Oe?aeiu, EIIao ei. A.I. Iiaeai?iiai; 372).

Aecthe A.A. Enneaaeiaaiea aeeiaie/aneeo aeaoi?iaoeeiiiuo i?ioeannia a
inaneiiao?e/iuo oi?oaiieanoe/aneeo iaiei/a/iuo eiino?oeoeeiiiuo
yeaiaioao. // O/aiua caienee Oa?ueeianeiai aoiaieoa?iiai einoeoooa
«Ia?iaeiay oe?aeineay aeaaeaiey». – O.: «IEI», 1997. – o.III. – N. 345 –
354.

Aecthe A.A, Aecthe A.A., *a?iia?uaei I.A. Ioeaiea ianouae niiniaiinoe
eiino?oeoeaiuo yeaiaioia i?e eieaeueiii oaea?ii-eiioeueniii iaa?oaeaiee.
// Oac. aeiee. XXVIII iao/.-oaoi. eiio. i?aiiaeaaaoaeae, anie?aioia e
nio?oaeieeia Oa?uee. aeaaeaiee ai?iae. oic-aa – O.: OAAAO. – 1996 a. –
N. 59.

Aecthe A.A, Aecthe A.A., *a?iia?uaei I.A. Ioeaiea aeeyiey eieaeecaoeee
iaa?ocee ia ianouoth niiniaiinoue eiino?oeoeaiuo yeaiaioia iaiei/a/iiai
oeia i?e oaea?iuo iaa?oceao. // Oac. aeiee. XXIO iao/.-oaoi. eiio.
i?aiiaeaaaoaeae, anie?aioia e nio?oaeieeia Oa?uee. aeaaeaiee ai?iae.
oic-aa – O.: OAAAO. – 1998 a. – N. 70.

Aecthe A.A., Eieiaeyaeiue A.A., *a?iia?uaei I.A., ss?auaiei A.A.
Ioeaiea aa?iyoiinoe ?ac?ooaiey oiieinoaiiuo eiino?oeoeee a oneiaeyo
nei?inoiiai aeaoi?ie?iaaiey // O?oaeu iaaeaeoia?. eiio. «Nia?aiaiiua
i?eai?u, iaoa?eaeu e oaoiieiaee aeey oaoie/aneie aeeaaiinoeee e
ia?ac?ooathuaai eiio?iey i?iiuoeaiiiai iai?oaeiaaiey. Yeaiaioiay aaca e
eiiieaeoothuea aeey i?eai?ia IE. Iiaeaioiaea niaoeeaeenoia a noa?a
ia?ac?ooathuaai eiio?iey e oaoie/aneie aeeaaiinoeee». – O.: OAOO?A. –
1998 a. – N. 144.

A?cthe A. A. Aeine?aeaeaiiy iai?oaeaii-aeaoi?iiaaiiai noaio
inaneiao??/ieo i?oaeiiieanoe/ieo oeee?iae?e/ieo iaieiiie i?ae aieeaii
eieaeueiiai ?iioeueniiai iaaaioaaeaiiy. – ?oeiien.

Aeena?oaoe?y ia caeiaoooy o/aiiio nooiaiy eaiaeeaeaoa oaoi?/ieo iaoe ca
niaoe?aeuei?noth 05.02.09 – Aeeiai?ea ? i?oei?noue iaoei. – ?inoeooo
i?iaeai iaoeiiaoaeoaaiiy ?i. A. I. Iiaeai?iiai IAI Oe?a?ie, Oa?e?a,
1998.

A aeena?oaoe?? ?icaeiooi /enaeueii-aiae?oe/iee iaoiae iiaeaethaaiiy ?
aeine?aeaeaiiy iaoai?/ieo aeaoi?iaoe?eieo i?ioean?a a oiiaao
ianoaoe?iia?iiai iaaaioaaeaiiy. Iae?i?eia caaea/a i?oaeii-ieanoe/iiai
aeaoi?ioaaiiy iaieiiee ae??oo?oueny ca aeiiiiiaith iie?ieiaiai iaoiaeo
i?oaeieo ??oaiue a aa??aio? iaoiaeo o?eoeaieo iaaaioaaeaiue.
Aeei?enoaiiy aiae?oe/ieo ia?aoai?aiue Eaieana, ?iciiae?eo ci?iieo ?
?iceeaaeo oeeo ooieoe?e ia?ai?uaiue a ?yae ii aaceniei ooieoe?yi
aeicaiey? cia/ii ni?inoeoe ia/eneaiiy ? i?enei?eoe i?ioean io?eiaiiy
?ica’yceo. O?ce/iee caeii aeaoi?ioaaiiy SYMBOL 115 \f “Symbol” \s 14 s
– SYMBOL 101 \f “Symbol” \s 14 e (ae?aa?aia iai?oae – aeaoi?iaoe??)
ai?ieneio?oueny iie?e?i?eiith aai a?e?i?eiith caeaaei?noth.
A?aoiao?oueny aeaoi?iaoe?eia, oaeaee?nia ? e?iaiaoe/ia ci?oeiaiiy
iaoa??aeo.

Eeth/ia? neiaa: oeee?iae?e/ia iaieiiea, oaeaee?nia i?oaeiiieanoe/ia
aeaoi?ioaaiiy, aeaoi?iaoe?eia ci?oeiaiiy, e?iaiaoe/ia ci?oeiaiiy,
o?eoeai? iaaaioaaeaiiy, /enaeueii-aiae?oe/iee iaoiae.

Aecthe A.A. Enneaaeiaaiea iai?yaeaiii-aeaoi?ie?iaaiiiai ninoiyiey
inaneiiao?e/iuo oi?oai-ieanoe/aneeo oeeeeiae?e/aneeo iaiei/ae iiae
aicaeaenoaeai eieaeueiiai eiioeueniiai iaa?oaeaiey. – ?oeiienue.

Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa oaoie/aneeo iaoe
ii niaoeeaeueiinoe 05.02.09 – Aeeiaieea e i?i/iinoue iaoei. – Einoeooo
i?iaeai iaoeiino?iaiey ei. A.I. Iiaeai?iiai IAI Oe?aeiu, Oa?ueeia, 1998.

A aeenna?oaoeee ?acaeaaaony /eneaiii-aiaeeoe/aneee iaoiae iiaeaee?iaaiey
e eco/aiey iaoaie/aneeo aeaoi?iaoeeiiiuo i?ioeannia a oneiaeyo
ianoaoeeiia?iiai iaa?oaeaiey. Iaeeiaeiay caaea/a oi?oaiieanoe/aneiai
aeaoi?ie?iaaiey iaiei/ee ?aoaaony iioaaiaui iaoiaeii oi?oaeo ?aoaiee a
iinoaiiaea iaoiaea oeeoeaiuo iaa?ocie. Eniieueciaaiea aiaeeoe/aneeo
i?aia?aciaaiee Eaieana, ?acaeaeaiey ia?aiaiiuo e ?aceiaeaiey eneiiuo
ooieoeee ia?aiauaiee a ?yae ii aaceniui ooieoeeyi iicaieyao cia/eoaeueii
oi?inoeoue au/eneaiey e onei?eoue i?ioeann iieo/aiey ?aoaiey. Oece/aneee
caeii aeaoi?ie?iaaiey SYMBOL 115 \f “Symbol” \s 14 s – SYMBOL 101 \f
“Symbol” \s 14 e (aeeaa?aiia iai?yaeaiey – aeaoi?iaoeee)
aii?ieneie?oaony iieeeeiaeiie eee a /anoiii neo/aa aeeeiaeiie
caaeneiinoueth. O/eouaaaony aeaoi?iaoeeiiiia, nei?inoiia e
eeiaiaoe/aneia oi?i/iaiea iaoa?eaea.

Eeth/aaua neiaa: oeeeeiae?e/aneay iaiei/ea, nei?inoiia
oi?oaiieanoe/aneia aeaoi?ie?iaaiea, aeaoi?iaoeeiiiia oi?i/iaiea,
eeiaiaoe/aneia oi?i/iaiea, oeeoeaiua iaa?ocee, /eneaiii-aiaeeoe/aneee
iaoiae.

Bizjuk A.V. The investigation of stress-strained state of an
axisymmetric elastoplastic cylindrical shell under local impulse
loading. – Manuscript.

Thesis for the candidate degree by speciality 05.02.09 – dynamic and
strength of machines. The Institute for Problems in Machinery named by
A.M. Pidgorny of National Academy of Science of Ukraine, Kharkov 1999.

The numerical-analytical method of modelling and investigation of
mechanical strain processes has been elaborated. A nonlinear problem of
elastoplastic shell deformation is solved by the step-by-step method of
elastic decisions in the version of the method of fictitious loadings.
The using of analytical Laplace transformations, dividing of variables
and decomposition in rows on basis functions allows to simplify
calculations and to speed up the process of solving problem. A physical
law of deformation SYMBOL 115 \f “Symbol” \s 14 s – SYMBOL 101 \f
“Symbol” \s 14 e (stress-strain diagram) is approximated by polylinear
or, in particular case, bilinear dependence. A strain, high-rate and
kinematic strengthening of material is taking into account.

Key Words: cylindrical shell, elastoplastic deformation, strain
strengthening, kinematics strengthening, fictitious loads,
numerical-analytical method.

A?aeiia?aeaeueiee ca aeione noa?o. iaoe. ni?a?., eaiae. o?c.-iao. iaoe
No?aeuei?eiaa I.I.

I?aei. aei ae?oeo Oi?iao 60o90, 1/16

Iai?? ae?oea?nueeee ? 1.

Oiiai. ae?oe. a?e. 1,0. Iae.-aeae. a?e. 0,96.

Oe?aae 100 i?ei. Cai. ?

?AA OA? “IOA”, 310000, i. Oa?e?a, aoe. Ea?iiioianueea, 27

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