On a spatial generalization of the Kolosov-Muskhelishvili formulae

The main goal of this paper is to construct a spatial analog to the Kolosov–Muskhelishvili formulae using the framework of the hypercomplex function theory. We prove a generalization of Goursat's representation theorem for solutions of the biharmonic equation in three dimensions. On the basis o...

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Vydané v:	Mathematical methods in the applied sciences Ročník 32; číslo 2; s. 223 - 240
Hlavní autori:	Bock, S., Gürlebeck, K.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Chichester, UK John Wiley & Sons, Ltd 30.01.2009 Wiley
Predmet:	classical linear elasticity Exact sciences and technology functions of hypercomplex variables and generalized variables Goursat's representation theorem Mathematical analysis Mathematics monogenic functions Potential theory representation formulae Sciences and techniques of general use Three-dimensional calculations Linear elasticity Applied mathematics Biharmonic equation representation formulae Mathematical method monogenic functions classical linear elasticity Goursat's representation theorem functions of hypercomplex variables and generalized variables
ISSN:	0170-4214, 1099-1476
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Shrnutí:	The main goal of this paper is to construct a spatial analog to the Kolosov–Muskhelishvili formulae using the framework of the hypercomplex function theory. We prove a generalization of Goursat's representation theorem for solutions of the biharmonic equation in three dimensions. On the basis of this result, we construct explicitly hypercomplex displacement and stress formulae in terms of two monogenic functions. Copyright © 2008 John Wiley & Sons, Ltd.
Bibliografia:	ArticleID:MMA1033 istex:06E514A1B07DF179F41250F4D3EFD989F7378727 ark:/67375/WNG-JSDNF080-C ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0170-4214 1099-1476
DOI:	10.1002/mma.1033