myari deformadi sxeulis meqanikis ganviTarebis etapebi XX ...

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2.2.3.3. koSis tipis integralebis gamoyenebaamocanis efeqturi amoxsnisaTvis gansakuTrebiT sasargebloaRmoCnda qvemoT gadmocemuli meTodi, romelic uxamebskonformul asaxvas koSis tipis integralebis aparatisgamoyenebas (n. musxeliSvili, 1966, $$ 78-85). is mdgomareobsSemdegSi.(82) sasazRvro pirobebidan gamomdinare da pirobisgamosaxvidan, rom ψ(σ) warmoadgens sasazRvro mniSvnelobas ψ(ζ)funqciis wrewirze, romelic holomorfulia wris SigniT danuli xdeba roca ζ=0, miviRebT (79)-is safuZvelze, funqcionalurgantolebas1 ω(σ ) ϕ′( σ )ϕ( ζ ) + ∫ dσ= A(ξ ) , ( ζ ∈ γ ) , (90)2πiω′( σ ) ( σ −ζ)γ1 f ( σ ) dσA( ζ ) = ∫ .2πiσ −ζdamtkicebulia, rom fiqsirebuli Im[ ϕ (0) ω′(0)]γ′ mudmivisas,(90) gantoleba calsaxad gansazRvravs ϕ(ζ) funqcias. misigansazRvris Semdeg ψ(ζ) funqcia moiZebneba uSualod (82)-dankoSis integralis saSualebiT.(90) funqcionaluri gantoleba saSualebas gvaZlevssruliad elementaruli saSualebebiT avagoT amocanis zustiamonaxsnebi areebis farTo klasisaTvis. miaxloebiTi amonaxsniki SeiZleba principSi miviRoT caladbmuli ares yvelaze zogadiSemTxvevisaTvis.naTqvamis sailustraciod ganvixiloT SemTxveva, rocaamsaxveli ω(ζ) funqcia racionaluria. am SemTxvevaSigamosaxulebaω(σ )ϕ′( σ ) ,ω′( σ )romelic integralis niSnis qveS figurirebs (90)-Si, warmoadgenssasazRvro mniSvnelobas funqciisa90
ω(ζ ) ⎛ 1 ⎞ϕ ′ ⎜ ⎟ , (91)⎛ 1 ⎞′ ⎜ ⎟⎝ ζω⎠⎝ ζ ⎠romelic holomorfulia γ-is gareT, polusebis sasruli ricxvis_ ω(ζ) funqciis gansakuTrebuli wertilebis gamoklebiT.radgan (90) integralSi wertili ζ Zevs γ-s SigniT, esintegrali gamoiTvleba sasruli saxiT da warmoadgensracionalur funqcias, romelic Seicavs gaSlis ucnobikoeficientebis raRac ricxvs.aqedan gamomdinareobs, swored, n. musxeliSvilis cnobiliwinadadeba, romlis Tanaxmadac brtyeli amocanis amoxsna,areebis gansaxilveli klasisaTvis, SeiZleba miviRoTkvadraturebSi, wrfiv algebrul gantolebaTa sasruli sistemisamoxsnamde sizustiT. kerZod SemTxvevaSi ϕ(ζ) funqciis (87) saxispolinomuri asaxva (90)-Si, warmogvidgeba, koSis A(ζ)integralebsa da ζ-Ti n xarisxis polinoms, romelic Seicavsucnobis koeficientebis saxis TviT ϕ(ζ)-is pirvel n koeficients,jamis saxiT. gantolebaTa wrfivi sistema, miRebuli amukanasknelTa gansazRvrisaTvis, zustad emTxveva (88) sistemas.orive saZiebeli funqcia ϕ(ζ) da ψ(ζ), ganisazRvreba CaletilisaxiT am sistemis amonaxsniTa da mocemuli f funqciiT.Tu funqcia ω(ζ) araracionaluria, magram misi wreSi gaSlacnobilia, meTods mivyavarT wrfiv gantolebaTa usasrulosistemamde, es ki iZleva saSualebas avagoT amocanis amonaxsninebismieri mocemuli sizustiT.2.2.3.4. mravladbmul areebSi kompleqsuri warmodgenaϕ′ (σ ) drekadi velebis kompleqsuri warmodgena analizurifunqciebis sxvadasxvagvar integralur warmodgenebTan naerTSiwarmoadgens brtyeli amocanis integralur gantolebebamdedayvanisaTvis moxerxebul aparats. dReisaTvis cnobilia aseTi91
Page 1 and 2:
aleqsandre daTuaSvilimyari deformad
Page 3 and 4:
საქართველოს
Page 5 and 6:
amocanebis amoxsnis sxvadasxva meTo
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SummaryNowadays the mechanics of el
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mathematical point of view it is no
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2.3.1. brtyeli drekadobis Teoriis a
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Sesavalimyari deformadi sxeulis meq
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mravali saarqivo masalidan da damak
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SeiZleba dakmayofildes, Tu gamovsax
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3da rodesac n=3, v=0,25, B0= R Y3(7
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forma _ `srulia~, Tu sxivi Ω i -da
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2 2 ∇∇σ∇ T + = 0 . (21)1+vcn
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tenzori, romelic akmayofilebs (27)
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∫∫ ×Φ(M , Q)dO μ=0R ˆ0(35)d
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( )I i( )I e1L b(Q0) − ∫∫b(M
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(i)Tanaxmad araerTgvarovan gantoleb
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gadaadgilebisaTviswarmoadgens jamsu
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sivrciTi amocanebi araerTgvarovani
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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
Page 79 and 80: sadac ϕ * (z) da ψ * (z) holomorf
Page 81 and 82: formis xist profilTan urTierTSexeba
Page 83 and 84: III. firfitis kide dayrdnobilia _ k
Page 85 and 86: L-ze) uwyvetia Sesabamis Sekrul+S +
Page 87 and 88: aSkaraa, rom f(z) uban-uban holomor
Page 89: maSin (82)-is safuZvelze, winare mw
Page 93 and 94: sami tolobis kombinirebiT, maTSi z-
Page 95 and 96: (94) warmodgena gamosadegia agreTve
Page 97 and 98: ogorc amaSi advilad davrwmundebiT g
Page 99 and 100: X ( z)b(t)dtF( z)= ∫ + X ( z)P(z)
Page 101 and 102: lim( z − z)Φ′ ( z)= 0 .roca z
Page 103 and 104: xerxebiT, magaliTad furie da melini
Page 105 and 106: 2.3. myari deformadi sxeulis meqani
Page 107 and 108: da konfiguraciis naxvretebis dros Z
Page 109 and 110: am meTodis gamoyeneba brtyeli amoca
Page 111 and 112: gamoyeneba brtyeli deformaciis Sesa
Page 113 and 114: sazRvrisa da imyofeba misgan manZil
Page 115 and 116: ori parametriT, romlebic zemoT dasa
Page 117 and 118: [ tϕ′( t)+ ψ ( )]xk1ϕk( t)−k
Page 119 and 120: amocana). sxvadasxva masalebisagan
Page 121 and 122: gadaadgilebebis tolobas. es pirobeb
Page 123 and 124: wibos mqone elifsuri firfita) ixsne
Page 125 and 126: v. abramovis (1937), n. glagolevis
Page 127 and 128: kompleqsuri cvladis analizur funqci
Page 129 and 130: nawilobriv Camagrebuli kides mqone
Page 131 and 132: (125)-is amonaxsni warmovadginoT fu
Page 133 and 134: Kni( λ , n ) ⋅ σi⋅ f l ,Ki bz
Page 135 and 136: 1. qaris zemoqmedebis gavlena, nage
Page 137 and 138: λ1,10ξ = 3 + ln .265es formula mi
Page 139 and 140: (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
Page 157 and 158:
158. Упругость и плас
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myari deformadi sxeulis meqanikis ganviTarebis etapebi XX ...

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