myari deformadi sxeulis meqanikis ganviTarebis etapebi XX ...

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amonaxsnTa formebi, miTiTebuli i. arJanixisa da f.Curikovis mier (1953)12μ u = (1 − 2v)B − ∇× ( R×B), (10)2ar gansxvavdeba arJanixisa da slobodianskis (5)-isagan.ufro zogadi forma aqvs miTiTebuli v. deevs (1959)[(4v− 3) β + 4(1 − v)(ε −δ)] B + ( ∇B⋅ +2μu = β ) R=2[ 2(4v− 3) −δ] R ⋅∇B+ εR∇∇ ⋅ Bε , (11)amasTan β, ε, δ _ mudmivebia, romlebic SeiZleba nebismieradavarCioT. am mudmivebis jerovani arCevisas vubrundebiT (4), (5),(9) amonaxsnebs. (11)-Si Sedis agreTve amonaxsni2(4v− 3) 122μ u = 4(1 − v)B + R∇ ⋅ B + R∇∇⋅ B,(12)7 −8v7 −8vromelic gamosaxulia B harmoniuli veqtoriT da misi ∇BdivergenciiT.o. liavis [9] cnobili amonaxsni aqsialuri simetriis (zRerZis garSemo) SemTxvevisaTvis gamomdinareobs (2)-dan TumiviRebT = χ( r,z), G = 0 , G = 0 . ufro zogadi warmodgenaG zxycilindrul koordinatebSi (harmoniuli da biharmoniulifunqciebiT) mocemulia s. gutmanis mier (1948) [10].mravalbmuli D0midamosaTvis, romelic SemosazRvruliagaredan O 0 zedapiriT da Signidan O i zedapirebiT ( i = 1, L,k),mTlianad mdebareobs D-Si da erTmaneTTan da O 0 -Tan saerTowertilebi ar gaaCnia, gadaadgilebis veqtori v ≠ 0,25-isaswarmovadginoT saxiT (m. slobodianski, 1959)uku = u( 0)+ ∑u( i),B = B0 + ∑ B( i),i=1= 4 (1 − v)B(0)− ∇R⋅(0),, u( i)= 4(1− v)Bi− ∇R(i)⋅ B(i),0Bki=1sadacxoloB (i)− veqtoria, harmoniul midamoSi, gareTa O i -is mimarT,B − harmoniuli D − Si, amasTan saTave Ω i R i veqtorisa(0)0ganlagebulia RruSi, romelic SemosazRvrulia O i . am amonaxsnis20
forma _ `srulia~, Tu sxivi Ω i -dan kveTs O i -s erT wertilSi; isiqneba `saerTo~, roca R i -liapunovis Caketili zedapiria.aseve unda aRiniSnos, rom wrfivi diferencialurigantolebebis sistemis `zogadi amoxsnebis~ agebis amocanan∑j=0L = 0 ( i = 1,2, L,n)iju j(masSiLij_wrfivi diferencialuri operatorebia mudmivikoeficientebiTx , x2,, x1LmcvladebiT) daiyvaneba (a. lurie, 1937;ufro mogvianebiT (1953 w.) rumineli mecnieri g. moizeli)`potencialebis~ ϕs( s = 1, L,n)moZebnamde, romlebiTac u jamonaxsnigamoisaxeba Tanafardobis meSveobiT, saxiTu=n∑jM sjs=1ϕs( j = 1,2, L,n)sadacMsj− saZiebeli wrfivi diferencialuri operatorebia, xoloTiToeuli _ ϕspotencialTagan, akmayofilebs erTi da imavediferencialur gantolebasKϕ = 0 . ( s = 1,2, L,n)sadvilad SeiniSneba, rom operatori K = LijwarmoadgensoperatorebisLijkvadratuli matricis ganmsazRvrels, xoloMsj_ am ganmsazRvrelis j-uri svetis algebrul damatebas.gadaadgilebebSi drekadobis Teoriis gantolebebisadmimoxmarebisas, izotropuli tanebisaTvis, aRweril gamoTvlasmivyavarT galiorkin-busineskis (2) amoxsnamde. aSkaraa, rom esxerxi, gamodgeba anizotropuli garemosaTvis, drekadobisTeoriis dinamikuri gantolebebisaTvis da a.S.1.1.2. ZabvaTa funqciis tenzoriviciT, rom rotors Φˆ tenzoris transponirebuli rotorisaewodeba araTavsebadobis ( I ik) tenzori Φˆ -ze:21
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: 3da rodesac n=3, v=0,25, B0= R Y3(7
Page 23 and 24: 2 2 ∇∇σ∇ T + = 0 . (21)1+vcn
Page 25 and 26: tenzori, romelic akmayofilebs (27)
Page 27 and 28: ∫∫ ×Φ(M , Q)dO μ=0R ˆ0(35)d
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
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 and 90:
maSin (82)-is safuZvelze, winare mw
Page 91 and 92:
ω(ζ ) ⎛ 1 ⎞ϕ ′ ⎜ ⎟ , (
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
Page 141 and 142:
adgan xSiri iyo SeduRebuli liTonis
Page 143 and 144:
proporciulad ar izrdeba. maRali wne
Page 145 and 146:
Psadac σo= ; P mimdinare datvirTvi
Page 147 and 148:
daskvnis saxiT xazgasmulia, rom mus
Page 149 and 150:
18. Виноградов А.И. -
Page 151 and 152:
54. Лурье А.И. - Труды
Page 153 and 154:
87. Тимошенко С.П. - И
Page 155 and 156:
119. Динник А.Н. - Усто
Page 157 and 158:
158. Упругость и плас
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