1.1.2.1. sivrciTi amocanis integraluri gantolebebisivrciTi sasazRvro amocanebis integraluri gantolebebisSedgena, maT SeswavlasTan dakavSirebuli siZneleTa gadalaxva,arsebobis damtkiceba da maTi amoxsnebis agebis efeqturixerxebis povna _ v. kupraZis da misi TanamSromlebis mravalwlianimuSaobis Sedegia. am gamokvlevebis meTodebisa da SedegebisSinaarsis gadmocema, dawvrilebiTi bibliografiiT, moipovebaagreTve v. kupraZis, T. gegelias, o. baSaleiSvilis daT.burWulaZis monografiaSi, romelic gamoqveynda 1968 wels [11].am naSromSi ganvixilavT sivrciTi drekadobis Teoriismxolod pirveli da meore sasazRvro amocanebi izotropulierTgvarovani garemosaTvis. Cven amasTan SemovifarglebiTcalbmuli sasruli moculobisaTvis( V i) − Sida (i) amocaniT dagare (e)-Ti. RruTi aRWurvili usasrulo garemosTvis ( V e)ivaraudeba O zedapiris sigluve, romelic sazRvravs Vi-sgaredan ( V − DSignidan).edrekadobis Teoriis potencialebi. ganvixilavT Semodisu ˆ(M , Q)kelvin-somilianis tenzori, romelic gansazRvravsSemousazRvreli drekadi garemos M wertilis u ( M , Q)gadaadgilebas, gamowveuls Q wertilSi erTeulovani SeyursuliZalis moqmedebiT:ˆ⎡ ˆ ⎤u( M , Q)= U ( M , Q)⋅e,ˆ 1 E ∇∇KU ( M , Q)= ⎢ − ⎥ , (33)4πμ⎣ R 4(1 − v)⎦( Ê − erTeulovani tenzoria, R = QM = ΓM− ΓQ, R = R ), Zabvis veqtorisgamosaxuleban ˆ ˆμ⋅T= Φ(M , Q)e,Φˆ1( M , Q)=[(1− 2v)( nμR − Rnμ) −38π(1 − v)R⎤− − v En ˆ 3 12(1 )μR⋅R nμ⋅ R∇∇R ⎥. (34)⎦vTqvaT O _ Caketili zedapiria ( M ⊂ 0); maSin26
∫∫ ×Φ(M , Q)dO μ=0R ˆ0(35)da adgili aqvs gausis ganzogadebul Teoremas∫∫0Φˆ( M.Q)dO= −Eˆδ ( Q)μ,⎧ 1 Q ⊂ Vi⎪δ ( Q)= ⎨12 Q ⊂ O(36)⎪⎩ 0 Q ⊂ Vt( V i− moculoba O-s SigniT, Ve− O-s gareT).v. kupraZis mier Semotanili drekadobis Teoriis veqtorebipotencialebidan ganixileba ori: pirveli, msgavsi O zedapirze.martivi fenis A (Q)potenciali da meore msgavsi ormagi fenisB (Q) potencialiA ( Q)= ∫∫a(M ) ⋅Uˆ ( M , Q)doμ, (37)0B Q)= b(M ) ⋅Φˆ( M , Q)do . (38)∫∫aSkaraa, rom A(Q) da B(Q),(μ0Q ⊄ 0 − isas, warmoadgenen drekadobisTeoriis gantolebebis amonaxsns gadaadgilebebSi, rodesac argvaqvs moculobiTi Zalebi.pirveli potencialis zRvruli mniSvnelobebi O-zeSignidan da garedan, romlebic aRniSnuliaA ( Qi) = lim ( A(), A ( Q ) = lim ( A() − Ti0QVi⊃Q→Q0e0QVi⊃Q→Q0toli arian misi pirdapiri mniSvnelobis, gansazRvrulisarasakuTrivi krebadi integraliTA Q0 ) = ∫∫a(M )0⋅Uˆ ( M , Q0) do . (39)(μ0meore potencialis zRvruli mniSvnelobebisaTvis adgiliaqvs Tanafardobebs11B i( Q0 ) = B(Q0) − b(Q0), B e( Q0 ) = B(Q0) + b(Q0) , (40)22analogiurebs plemelis formulebisa, amasTan pirdapirimniSvneloba ganisazRvreba integraliT, romelic krebadia mxolodmTavari mniSvnelobis azriTB ( Q ) = b(M ) − Φˆ( M , Q ) do = lim b(M ) ⋅Φˆ( M , Q ) do ,0∫∫00μ∫∫ε →0o−o(Q0ε)0μ27
- 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: tenzori, romelic akmayofilebs (27)
- Page 29 and 30: ( )I i( )I e1L b(Q0) − ∫∫b(M
- 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
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- 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
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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