R −r Q( O( Q0 , ) − Q0ε wertilis O-ze midamoa, 2ε diametriT).Q ⊂ V ewertilis sakmarisi moSorebiT O zedapiridan,→ Tanaxmad (33) da (37)-isa gvaqvs ( e = ν )1lim A(Q)=→Q∞16πμ(1− v)ΓQQQr Q[(3− 4v)Eˆ− e e ] a(M ) do ;es – Q-Si gadaadgilebis veqtoria, koordinatTa saTaveSimodebuli Zalis moqmedebiT, romelic moicema integraliT O-zesimkvrivisagan a(M).QQQ∫∫aμmeore potencialiQ → Q∞isas ufro nela ara xdeba nuli,vidre−2Γ ada is SeiZleba ganimartos rogorc gadaadgileba,romelic iqmneba ZalTa sistemiT, ganawilebuliT O zedapirze,nulis toli mTavari veqtoriT.integraluri gantolebebi. pirvel sasazRvro amocanaSiu(Q) gadaadgileba, romelic iRebs O zedapirze ( V imoculobaSida amocanaSi, Rru gare amocanaSi) mocemul mniSvnelobas,iZebneba drekadobis Teoriis meore potencialis formiT, ucnobisimkvriviT b(M):u Q)= B(Q)= b(M ) ⋅Φˆ( M , Q)do .(41)∫∫(μ0gare amocanis SemTxvevaSi es warmodgena miiCnevs, romu( Q ) ∞-s aqvs r 2 rigi; im ZalTa mTavari veqtori, romlebic unda− Qiyvnen ganawilebuli Rrus O zedapirze, rom mianiWon maTwertilebs u Q ) gadaadgilebis veqtori, toli unda iyos nulis.(0amitom pirveli sasazRvro amocanis amonaxsni (41) formiTSeiZleba arsebobdes mxolod u Q ) specialuri amocaniT, xolo(0zogad SemTxvevaSi amonaxsni iqneba warmodgenili (41) jamiT daubralo fenis potencialiT (`robenis elastostatikuriamocanis~ amonaxsni).Sida (i) da gare (e) amocanebis integraluri gantolebebimiiReba (41)-dan, zRvruli gadasvlis lim u(Q)= v(Q0)plemelis (4) formulebis daxmarebiT:Q→Q0gziT,28
( )I i( )I e1L b(Q0) − ∫∫b(M ) ⋅Φˆ( M , Q0) doμ= −v(Q0),(42)201L b(Q0) + ∫∫b(M ) ⋅Φˆ( M , Q0) doμ= −υ( Q0) . (43)201(30) da (36)-ze dayrdnobiT, roca δ ( Q)= , ar aris Zneli2davrwmundebiT, rom b(M)-is mocema <strong>myari</strong> tanis gadaadgilebisformiTxb ( M ) = + ω × r = υ + ω ×Γ + ω × R(44)υ0μ 0Q0warmoadgens (43)-is Sesabamisi erTgvarovani gantolebis amonaxsns( ) 1I e 0L b(Q0) = ∫∫ b(M ) ⋅Φˆ( M , Q0) do μ= 0 . (45)20amasTan erTad B( M ) = −b(M ) warmoadgens (42) gantolebisamonaxsns, roca O zedapiri gadaadgildeba rogorc <strong>myari</strong> tani,maSin mTeliVimoculoba aseve gadaadgildeba rogorc <strong>myari</strong>tani; rac gamomdinareobs (41) da (36)-dan, roca _ δ ( Q)= 1.meore sasazRvro amocanaSi O-ze moicema zedapiruli ZalebiF = ( n ⋅Tˆ) 0, xolo gadaadgilebaTa veqtori iZebneba pirvelipotencialis formiTu ( q)= ∫∫a(M ) ⋅Uˆ ( M , Q)doM. (46)0(34)-is gamoyenebiT, aq gamotovebuli (magram aratrivialuri)gardaqmnebis Semdeg, mivdivarT integralur gantolebamdeamasTannII( i)1L a(Q0) + ∫∫Φˆ ( Q0, M ) ⋅ a(M ) doM= F(Q0) = ( n0⋅Tˆ)0,(47)20( ) 1IIe L a(Q0) − ∫∫Φˆ ( Q0, M ) ⋅a(M ) doM= −F(Q0) = ( n0⋅Tˆ)0. (48)2a−Vi0− isadmi gare normalia.zemoT vaCveneT, rom (42)-(43), (47)-(48) veqtorul gantolebebSiintegralebi ganixileba maTi mTavari mniSvnelobebis azriT –gantolebaTa es sistema singularulia. Semdgomi gamokvlevebissirTule mdgomareobs maT mimarT Teoremisa da fredholmisalternativis miyenebis damtkicebaSi ( μ da v-isas, romlebic29
- Page 1 and 2: aleqsandre daTuaSvilimyari deformad
- Page 3 and 4: საქართველოს
- Page 5 and 6: amocanebis amoxsnis sxvadasxva meTo
- Page 7 and 8: SummaryNowadays the mechanics of el
- Page 9 and 10: mathematical point of view it is no
- Page 11 and 12: 2.3.1. brtyeli drekadobis Teoriis a
- Page 13 and 14: Sesavalimyari deformadi sxeulis meq
- Page 15 and 16: mravali saarqivo masalidan da damak
- Page 17 and 18: SeiZleba dakmayofildes, Tu gamovsax
- Page 19 and 20: 3da rodesac n=3, v=0,25, B0= R Y3(7
- Page 21 and 22: forma _ `srulia~, Tu sxivi Ω i -da
- Page 23 and 24: 2 2 ∇∇σ∇ T + = 0 . (21)1+vcn
- Page 25 and 26: tenzori, romelic akmayofilebs (27)
- Page 27: ∫∫ ×Φ(M , Q)dO μ=0R ˆ0(35)d
- Page 31 and 32: (i)Tanaxmad araerTgvarovan gantoleb
- Page 33 and 34: gadaadgilebisaTviswarmoadgens jamsu
- Page 35 and 36: sivrciTi amocanebi araerTgvarovani
- Page 37 and 38: mrgvali filis SemTxveva datvirTvisa
- Page 39 and 40: (1965) datvirTvis gavlena, romelic
- Page 41 and 42: gantolebebs, romlebic Seicavdnen ma
- Page 43 and 44: polusebis konusuri zedapirebiT ganx
- Page 45 and 46: zambarebis gaangariSebasTan kavSirS
- Page 47 and 48: ganxilulia rogorc pirveli da meore
- Page 49 and 50: (1953), x. muStaris (1938), a. ugod
- Page 51 and 52: 1938) [45]. is anviTarebda mcire pa
- Page 53 and 54: kveTis mqone Reros grexis amocanis
- Page 55 and 56: cilindruli RruTi (1953) [62]. Serma
- Page 57 and 58: (1956) [69]. ori wriuli segmentis s
- Page 59 and 60: lilvebis grexis amocanis amoxsnisas
- Page 61 and 62: gamokvlevaTa dazusteba da ganviTare
- Page 63 and 64: janeliZis xerxis ganzogadeba almanz
- Page 65 and 66: problemebi principSi daiyvaneba gan
- Page 67 and 68: v.mosakovski, 1953); toroiduli koor
- Page 69 and 70: sxvadasxva garemos kontaqtis Sesaxe
- Page 71 and 72: simetruli guli aqvs. amoxsnis aseTi
- Page 73 and 74: yvelaze efeqturi aRmoCnda wyvil int
- Page 75 and 76: unvis elifsoidis kumSvisa da grexis
- Page 77 and 78: wertilebis gareSe. amasTan, ukanask
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sadac ϕ * (z) da ψ * (z) holomorf
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formis xist profilTan urTierTSexeba
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III. firfitis kide dayrdnobilia _ k
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L-ze) uwyvetia Sesabamis Sekrul+S +
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aSkaraa, rom f(z) uban-uban holomor
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maSin (82)-is safuZvelze, winare mw
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ω(ζ ) ⎛ 1 ⎞ϕ ′ ⎜ ⎟ , (
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sami tolobis kombinirebiT, maTSi z-
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(94) warmodgena gamosadegia agreTve
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ogorc amaSi advilad davrwmundebiT g
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X ( z)b(t)dtF( z)= ∫ + X ( z)P(z)
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lim( z − z)Φ′ ( z)= 0 .roca z
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xerxebiT, magaliTad furie da melini
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2.3. myari deformadi sxeulis meqani
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da konfiguraciis naxvretebis dros Z
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am meTodis gamoyeneba brtyeli amoca
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gamoyeneba brtyeli deformaciis Sesa
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sazRvrisa da imyofeba misgan manZil
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ori parametriT, romlebic zemoT dasa
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[ tϕ′( t)+ ψ ( )]xk1ϕk( t)−k
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amocana). sxvadasxva masalebisagan
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gadaadgilebebis tolobas. es pirobeb
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wibos mqone elifsuri firfita) ixsne
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v. abramovis (1937), n. glagolevis
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kompleqsuri cvladis analizur funqci
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nawilobriv Camagrebuli kides mqone
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(125)-is amonaxsni warmovadginoT fu
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Kni( λ , n ) ⋅ σi⋅ f l ,Ki bz
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1. qaris zemoqmedebis gavlena, nage
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λ1,10ξ = 3 + ln .265es formula mi
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(v.panasiuki da d. bereJnicki, 1964
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adgan xSiri iyo SeduRebuli liTonis
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proporciulad ar izrdeba. maRali wne
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Psadac σo= ; P mimdinare datvirTvi
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daskvnis saxiT xazgasmulia, rom mus
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18. Виноградов А.И. -
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54. Лурье А.И. - Труды
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87. Тимошенко С.П. - И
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119. Динник А.Н. - Усто
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158. Упругость и плас