myari deformadi sxeulis meqanikis ganviTarebis etapebi XX ...

SeiZleba dakmayofildes, Tu gamovsaxavT gadaadgilebaTa uveqtors biharmoniuli G veqtoriT TanafardobiT22μ u = ∇∇ ⋅G− 2(1 − v)∇ G . (2)es amonaxsni im miTiTebiT, rom misgan miiRebian adrecnobili SemoTavazebuli iyo u. busineskis mier jer kidev 1889wels. p. papkoviCma (1937, 1939) miuTiTa, rom (2) warmoadgensgadaadgilebebSi drekadobis Teoriis zogad amonaxsns2(1 − 2v ) ∇ u + ∇∇ ⋅u= 0 . (3)es gamomdinareobs iqidan, rom (3) gantolebis struqtura,marjvena nawilSi masaTa Zalebis arsebobisas imeorebs (2)amonaxsnis struqturas. amitom, (2)-Si u veqtorad drekadobisTeoriis sasazRvro amocanis amoxsnis miRebisas (romelicakmayofilebs O tanis zedapirze sam pirobas), Cven SegviZliamovelodeT, rom G veqtoric SeiZleba daeqvemdebaros kidev sampirobas 0-ze, rac, rogorc Cans zedmetia.gadaadgilebaTa veqtoris povnisas harmoniuli veqtorisada χ skalaris gradientis jamis formiT2u − 4 (1 − v)B + ∇χ , ∇ B = 0 .(3)-Si Casmis Semdeg, mivdivarT gantolebamde∇ 2 χ = −2∇ ⋅ B .misi amonaxsni warmodgeba kerZo amonaxsnisaRniSnulia veqtor-radiusi). ase, romχ = −R ⋅ B jamiT (R-iTχ = −( R ⋅ B + B0), u = (1 − v)B − ∇ ⋅ ( R ⋅ B + B ) . (4)40drekadobis Teoriis gantolebis amonaxsnis aseTiwarmodgena mocemuli iqna p. papkoviCis mier (1932) da ramdenamdegvian g. neiberis [4] mier. p. papkoviCis gadmocemiT, igi ufro adrecnobili iyo g. grodskisaTvis. (4) gadaadgilebis veqtoriwarmodgenili harmoniuli veqtoris B da harmoniuli skalarisB0jamiT an oTxi harmoniuli funqciis B0, B s( s = 1,2,3)jamiT,sadacB s− B -s proeqciebia dekartes koordinatTa sistemisRerZebze. (4) amonaxsnis Caweris forma ekuTvnis i. arJanixsa [5]da m. slobodianskis (1954) da aqvs saxe17