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DEMONSTRATIO MATHEMATICAVol. IINO 31970RomualdStariczakGREEN'S TENSOR OF MIXED BOUNDARY VALUE PROBLEMOF THE THEORY OF ELASTICITY AND ITS APPLICATIONS1. INTRODUCTIONl e t us consider the system of p a r t i a lequations of e l l i p t i c type of the formA(^)uU)=0differential(1)wherei e e=1,2aconstant square matrix of theik j=1 2 beingsecond rank and u(x) = ^u^(x), Ug(x)J denoting an unknownv e c t o r f u n c t i o n of the v a r i a b l e x ( x 1 t x 2 ) .withAj jjAWe assume t h a t the constants•symmetry condition*deikAejkia^.ieJkAsatisfythe following(2\Prom the above assumption i t follows t h a t (1) i s a stronglye l l i p t i c system i n V i s h i k ' s sense. I f A ^ are constants ofthe generalized Hook' a law. we obtain a system of s t a t i c s of an- 145-R. Stane zak2anisotropic body in which condition (2)tisfied[l]. Fundamental solutionis automatically sa-of the system (1) is givenin the monograph [3] and has the following form(3)In 6.r(x,y) = Imwhere6kandPk =?matrix+"jee=1 t 2kj=1 2aCx2-y2)aksy^e^^ic matrix depending on
Demonstratio Mathematica – de Gruyter
Published: Jul 1, 1970
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