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GREEN'S TENSOR OF MIXED BOUNDARY VALUE PROBLEM OF THE THEORY OF ELASTICITY AND ITS APPLICATIONS

GREEN'S TENSOR OF MIXED BOUNDARY VALUE PROBLEM OF THE THEORY OF ELASTICITY AND ITS APPLICATIONS 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 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Demonstratio Mathematica de Gruyter

GREEN'S TENSOR OF MIXED BOUNDARY VALUE PROBLEM OF THE THEORY OF ELASTICITY AND ITS APPLICATIONS

Demonstratio Mathematica , Volume 2 (3): 14 – Jul 1, 1970

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Publisher
de Gruyter
Copyright
© by Romuald Stańczak
ISSN
0420-1213
eISSN
2391-4661
DOI
10.1515/dema-1970-0302
Publisher site
See Article on Publisher Site

Abstract

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

Journal

Demonstratio Mathematicade Gruyter

Published: Jul 1, 1970

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